mit radiation lab series v14 microwave duplexers
TRANSCRIPT
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MAS ,7A CH (TS I?TTS INST IT [’TE OF TECH.VOLOGY
RADIATION LABORATORY SERIES
Board of Editors
LOUIS ~. RIDE OUR, Editor-in-(’hiej
GEORGE B. COLLINS, Deputy Edi(or-in-Chzef
1 3Rrr roN CHANCE , S. A, GOUDSMIT, R. G. HERB, HUBERT 11. JAMES , JULIAN K. KNIPP
J AMES L. LAWSON, LEON B. LINFORD, GAROL G. 31OXTGOMERY, C. NEWTON, ALBERT
M. STONE ,LOU ISA. TURNER, GEORGE E. VALLEY, J R., HERBERT H. WHEATOX
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RADAR SYSTEM ENG1xEERING—Riden ouT
RADAR AIDS TO Navigat ion—ffal l
RADAR BEAcoNs—Robe,!s
LORAN—P2f?J Cf?,.$f cKenzie, aTLdWoodward
PULSE GENERATORs+kMoe
ond Lebncqz
lWICROB”AVE MAcxmROxs--Co//ins
KLYSTRONS AND MICROWAVE Tm o],E>-Ha?r? dlon, h -nipp, and Kuper
PRINCIPLES OF LIICROWAVE CIR(vtT$-,lfontgonzery, Dicke, and Pu rcell
MICROWAVE TRANSMISSION Cnwrm -l{agu n
WAVEGUIDE HANDBOoK—~fa rc lwi(z
TECHNIQUE OF MICROWAVE MEAsri+E31ExTs-J fOm/ gOme.y
MICROWAVE ANTENNA THEORY AND ~ESIGN—.$’~/ l’S~
PROFALIATION OF SHORT RADIO W.4vEs-Kc,,
3fICROWAVE DumBxms-S’rnuRm and M0nlg0me7y
CRYSTAL Rect ifier s—~owe~ a nd tf’h ?l?n er
MICROWAVE. h ’kERs -.Doun a
COMPONENTS HANDBOOK—B/ ackb Mrll
VACUUM TUBE / LMFLIFIERs -~a [/ ey a n d J $’a[lvtu n
WAVEFORMS—6’hQnC% Hugh es, .11ac.T ichol, S ayT e, ana Willis VIA
ELECTIZONIC TILIE MEASUREMENTS-~hUnCC?, Hulsi zer l ,l facNichoL
an d William s
ELECTRONIC I NSTRUMENTS~W3nW00d , Holdam , and MacR ae
CATHODE RAY TUBE DISPLAYS—SOUeT, S [arr, an d I’alley
MICROWAVE REcENERs—Van
Voorhis
THRESHOLD &GNALs-Law30n and L:h lenbeck
THEORY OF SERVOMECHANISMS—James, Nichols, and Ph ilL ips
RADAR SCANNE IW AND RA1 )oxE s–-~a dy, Ka reld z, a n d Turn@
CoMpuTIk’G MECHANISMS AND LINmiGEs—i%oboda
IND!rx--Henneg
i
.,,
:.
MICROWAVE DUPLEXERS
llliled by
LOUIS D. SMULLIN
‘+-
*~~~ ~:!
RESEARCH LABORATORY OF ELECTRONICS
M,4 SSACHUSETTS IN STI L-TE OF TECHNOL()(:Y
/
CAROL G. MONTGOMERY
ASSOCIATE PROFESSOR OF PHYSICS
/
I-ALE UNI\ -ERSITY
/
01WIC13 OF SCIENTIF IC RESEARCH A.ND DEV13LOP \ l lHST
NATIONAL DIH?ENSIZ RESEARCH COllll [’ITEE
171FHT l~DITTON
MICROWAVE DUPLEXERS
cOPYItIGHT, 1948 , BY THE
MCGRATY-FIILL BOOK GmP.NY, INC.
s lxr};s OF .*\ l
,411 rights T eserud . Th is book, or
parts th ereof, m ay 710[be reprod{{c((l
i t( (l?L?Jorm without perm isslnn of
lhe publ ishers,
THE. MAPLE PRESS COMPANY, YORK, P.A.
m
Foreword
T
HE t r emendous research and development effor t tha t went in to the
development of radar and rela t ed techniques dur ing Workf War II
resu lted not on ly in hundreds of radar set s for milita ry (and some for
possible peacet ime) use but a lso in a grea t body of informat ion and new
techniques in the elect ron ics and high-frequency fields. Because this
basic mater ia l may be of gr ea t va lue t o s ience and engineer ing, it seemed
most impor tant to publish it as soon as secur ity permit ted.
The Radiat ion Labora tory of MIT, which opera ted under the super -
~ vision of the Nat iona l Defense Resea rch Commit t ee, under took the grea t
; t ask of prepar ing these volumes. The work descr ibed herein , however , is
Q the collect ive resu lt of work done a t many labora tor ies, Army, Navy,
un iversity, and indust r ia l, both in this count ry and in England, Canada,
and other Domin ion s.
.
The Radia t ion Labora tory, once it s proposa ls were approved and
-> fina nces pr ovided by t he Office of Scien tific Resea rch and Developm en t,
chose Louis N. Ridenour as Editor -in-Chief to lead and direct t he en t ir e
project . An editor ia l sta ff was then select ed of those best qualified for
,,.
th is t ype of task. Finally the authors for the var ious volumes or chapt ers
.
~ or sect ions were chosen from among those exper t s who wer e in t imately
‘: familiar with the var ious fields, and who were able and willing t o wr ite
the summaries of them. This en t ir e staff agreed to remain at work a t
MIT for six months or more a ft er t he work of the Radia t ion Labora tory
was complete. These volumes stand as a monument to this group.
These volumes serve as a memoriaf to the unnamed hundreds and
thousands f ot her scient ist s, engineers, and oth ers who actually car r ied
on the research , development , and engineer ing wor k t he resu lt s of which
are herein descr ibed. There were so many involved in this work and th y
worked so closely t oget her even t hou gh oft en in widely sepa ra ted labor a-
tor ies that it is impossible t o name or even t o kn ow t hose who cont ribu t ed
t o a pa r ticu la r idea or developmen t .
Only cer ta in on es wh o wr ot e r epor ts
or a rt icles h ave even been men tion ed.
But to all those who cont r ibu t ed
in any way to this grea t coopera t ive development en terpr ise, both in this
count ry and in England, t hese volumes ar e dedica ted.
L. A. DUBRIDGE.
‘.
MICRO WAVE D UPLEXER$
EDITORIAL STAFF
CAROL G. MONTGOMERY
LOUIS D. SMULLIN
CONTRIBUTING AUTHORS
W. C. CALDWELL
H . K. F ’ARR
H . A. LEITER
C, G. 1W0NTG0MER%
L. D. SMIJ LLIN
C. W. ZABEL
Preface
T
HIS volum e of th e Radia t ion Labora tory Ser ies is con cern ed with th e
th eoret ica l an d pra ct ica l a s pect s of th des ign of du p lexin g cir cu it s
for u s e in m icrowave rada r equ ipmen ts , an d of th e ga s -filled switch in g
tu bes (TR an d ~TR tu bes ) u sed in th es e du p lexer s . For a clea rer p ic-
tu re of th e equ ipm en t with wh ich a du p lexer m u s t work th e reader is
refer red to th e followin g volu m es of th is s er ies : Vol. 16 “ Microwave
Mixers , ” F’01 . 9 “ Microwa e ~ra n sm is s ion cir cu its , ” vo1 . 23 “ Micro-
wave Receiver s , ”
an d Yol. 6 (‘ Microwave Magn etron s . ”
Th e work upon which this book is based was done under the urgency
of war commitmen ts, and the main goal was always e product ion of a
par t icu lar tube or duplexer cir cu it before a cer ta in t a rget da te. As a
r su lt , many cor ner s wer e cu t and many in tu it ive steps wer e taken with-
ou t clear ly under stood reasons, and there ar e today many gaps in our
knowledge of the phenomena involved.
This applies with par t icu lar
emphasis t o th e pr oblem of th e h igh-fr equ en cy gas disch arge.
It is our
belief tha t th e mater ia l pr esen ted h er e fa ir ly r epr esen ts th e pr esen t st ate
of the ar t .
Besides the authors of the individual sect ions of t h i s book, we wish
to ment ion the following Radia t ion Labora tory per sonnel who act ively
par t icipa ted in the design , study, and test ing o the var ious tubes and
duplexer s discussed here. These people are: I. H. Dearn ley, . W. J ones,
T. K&, F. L. McMillan , J r ., H. Margenau , C. Y. Meng, C. S. Pearsa ll,
J . Reed, F . Rosebury, and Arorma Wolf.
Much work was done ou tside the Radia t ion Labora tory on these
problems. The outstanding con t r ibutor s wer e M. D. Fiske a t the
Gen er al E lect ric Resear ch Labor ator ies, H, J . McCar th y of t he Sylvania
E lect r ic Pr odu cts Co., A. L. Samuel of t he Bell T leph on e Labor atones,
and S. Krasik and D. Alper t of th e West ingh ouse Resear ch Labor at or ies.
The editor s wish to acknowledge the work of C. W. J ones in the col-
lect ion of da ta and photographs and in the organiza t ion of Chapter 9.
The prepara t ion of the manuscr ipt was grea t ly facilita ted by the effor t s
of Gwenyth J ohnson, J anet M. J ackson, and Anne
son and his gr oup pr odu ced all of t he illustra t ions.
CAMSRIDGE, XIASS.,
J une 25, 1946.
Whalen . V. J oseph-
THE AUTHORS.
Contents
FOREWORD BYL. .4. DIIBR IDGE .
P REFACE . . . . . . . . . . .
CHAP .1. INTRODUCTION . . . . .1
12.RadarC opponent s . . . . . . .2
1.3. Microwave Duplexcm. 4
1.4, Duplexing Tubes . . . . . .5
1.5. Microwave Circu ite
. . . 6
CHAP. 2. LINTEAR THEORY OF HIGH-Q TR TUBES 8
2.1,
2.2,
23.
24.
2.5.
26.
27.
2.8.
29.
2.10
211
Linear Behavior of the TR Tube
Lumped-con st an t Reson an t Tr an sform er s
Cavit y Resona tor s.
Corn parieon of Loop- and Ir is-coupled C vit ies.
h let hods of Tuning.
E qu iva len t Cir cu it Ca lcu la tion s
E lect roma gn et ic Calcu la tions of Cavit ies
Cell-type TR Tubes
Tu nin g Tem pera tu re Compen sa tion
Cavit y Couplin gs
Dir ect -cou rJ in a At ten ua tion .
,.. . . . 8
9
13
25
27
29
34
. 35
46
49
55
“
2.12. In tegra l-cavity TR Tubee 59
CHAIJ .3, BANT)PASSTRTUBMS 67
31. In t roduct ion . . . . . . . .,67
THEORETIC~L CONWDERATIONW. 70
3,2. Resonan tenement s.... 70
33. Mult iple Resonant Elements in ;J ”aveguides. 76
3.4. VJ ave Equilibr ium Calcu la t ions 80
35.
}fa t r ix Method, ...,..,. .,, , . ., .,,,..85
36, N”umerica lR exult s... ,. ..88
EXFERIM~XTAL RESU TS, . . . . . . . . . . . . . . ..91
37. Mult iple-element ,Circu it s. 91
3+3. Bandp ss-TR-tube Design 95
CONTENTS
3.9. Remnant-gap Data ..... . . . . . . . . . . . . . ...96
3.10. Reecmant -windowD ata. .I02
3.11. Presen t Band Coverag . .106
3.12. Suggest io s for Fur ther Improvement s . 112
CHAP. 4. CHARACTERISTICS OF ATR SWITCHES AT LOW-POWER
LEVELS . . . . . . . . . . . . . . . . . . . . . . . . ...115
4.1. Equivalen t Circu it s. .115
4.2. Genera l Considera t ions of Design and Teet ing. . 123
4.3. Low-Q ATR Switches . . . . . . . . . . . . . . . . . ...127
4.4. ATRSwitches in Use... . . . . . . . . . . . .. 131
CHAP. 5 . MICROWAVE GAS DISCHARGES. . . . . . . 139
5.1. In t roduct ion . . . . . . . . . . . . . . .. 139
5.2. High-frequency Gas Discharges 145
5.3. Leakage Power and Crysta l Burnou t . . 151
5.4. The Spike . . . . . . . . . . . . . . . . . . . . . . ...153
5.5. Linear Theory of the Spike. 156
5.6. Nonlinear Theory of the Spike. 162
57. Ef ect of n , u pon Spike Leakage Energy . 166
5.8. Effect of Gas Fillin upon Spike Energy 167
5.9. Arc Leakage Power . . . . . . . . . . . . . . . . . . . . . 171
5,10. Dependence of Arc Leakage Power upon Transmit t ing Power 175
5.11. Effect of Gas Filling upon P~ 179
512. TheRecoveryP er iod . . . . . .181
5.13. Theory of the Recovery Period 182
5.14. Elect ron-capture Proper t ies of Var ioue Gases 187
5.15. Recovery-t ime Data . 190
5.16. Effect of Keep-a live Discharge on Recovery Time 197
5.17. The Keep-alive . . . . . . 199
5,18. Keep-alive Charact er ist ics. 208
519. Keep-alive Discharge and Tube Life 210
520. Keep-alive Circu it s and Power Supplies. 211
5,21. Prepulsed Keep-alive Circu it s . . 212
5.22. Radioact ive Priming . . . . . . . . . . . . . . 216
5.23. Tube Life and Gas Cleanup. . . , 217
5.24. Chemica l Reservoir s . . . . . . . . .219
5.25, iner t Coat ings .,...,. . . . . . . . . . . . 221
5.26. Bandpass and P re-TR Tubes . . 223
CIIAF. 6. THE TR AND ATR TUBES AT HIGH POWER . . 226
6.1. In t roduct ion ...,..... , . . . .. ’........226
62. High -power Character ist ics of High-Q TR Tubes. 227
6.3. High-level Character ist ics of Bandpass and Pre-TR Tubes and
Low-Q ATRTubcs . . . . . . . . . . . . . . . . . ...230
64. Spike Leakage Energy... .232
65. Spike Leakage Energy. Gap Design . 235
6.6, Direct -coupled Spike Leakage Energy. 237
CONTENTS
6.7. Arc I.eakage Power ....
238
6.8. Effect of Grur-filling upon High-power Character ist ics 239
6.9. Effect of Liie Power upon Leakage Character ist ics. 243
6.10. Keep-alive Elect rodes. 245
6.11. High-power Character ist ic . . 247
6.12. Present and Future Sta tus of Imw-Q and Bandpass Tubes and
ATR Tubes . . . . . . . . . . . .,, . . . . . . ...252
6.13. Constn rct ion Techniques—Metal-to-glass Seals 255
6.14. Solder ing of Windows nto Cavit ies. 258
6.15. Tuning Techniques . . . . . . . . . . . . . . . . . . ...259
6.16. Mount ing Devices . . . . . 260
CHAF. 7. THE PRINCIPLES OF BRANCHED DUPLEXING CIRCUITS 262
71.
72.
73.
7.4.
75.
76.
77.
78.
79.
710,
7.11.
7.12.
713.
714.
The J unct ion Circuit . . . . . . . .,262
Coaxia l J unct ions . . . . . . . . . . . . . . . . . . ...265
Waveguide J unct ions. 269
Duplexing Loss without an ATR Tube “. “. 274
Duplexing Loss wi h an ATR Switch. 279
Tuning of the ATR Switch. .284
Distance between TR and ATR Switches. 288
Branching Loss for Fixed-tuned ATR Circuit s. 292
Duplexing Loss under Condit ions of Receiver Mismatch 300
Duplexers with Mult iple ATR Circu its. 308
Double Tuning for Wideband ATR Circuit s. 317
ATR Circuit s with More than Two Switches 318
Branching Loss with the Available ATR Tubee 322
Branching Loss for a General T-junct ion 323
CHAP. 8. PRACTICAL BRANCHED DUPLEXERS AND BALANCED
DUPLEXES . . . . . . . . . , .,........,..329
BRANCHEn DUPLEXEES .,.... . . . 329
8,1. The Elect r ica l Design of a Duplexer 329
8.2. Mechanical Design Problems 333
8.3. Duplexers in Coaxia l Line. 336
8.4. A Double-tuned Duplexer . 339
85. Waveguide Duplexers.
341
8.6. Two-channel Duplexers. 3 7
8.7. An At tenuator Switch
349
BMANCEDDUPLEXERS . . . . . . 350
8,8. Proper t ies ofa Magic T. 35o
8,9. Linear Ba lanced Duplexer .
352
8,1 . Nonlinear Balanced Duplexer 355
8.1 . Ring-circuit Duplexer . 357
812. Pract ica l ilfagic T’s
361
8.1 . Cir cu la r-pola riza tion Duplexer .
369
8.1 . Turnst ile Duplexes. 72
CONTENTS
CHAP. 9. MEASUREMENT TE HNIQUES. . . . 376
9,1. Basic Low-1evel Test Equipment . 376
9.2. Inser t ion-loss Measurement . 382
9.3. Pass Band of High-C? TR Switches. . 385
9.4. Pass Band of Broadband TR Tubes . 393
9.5. Impedance Measurements of ATR Tubes. . 397
9.6. Low-1evel Product ion Test ing . 400
9.7. Leakage-power Measurements . 405
98. Measurements of Spike Energy . 409
9.9. Direct -coupling Measurements . . . . 412
9.10. At tenuat ion at Harmonic Frequencies 412
9.11. Measurement of Arc~s es . . . 413
9 2. Minimum Firing Power. . . . . . 414
9,13. An R-f P ressure Gauge. . . . . . .415
914. Measurement s on Recovery Time of TR Tubes . . 417
9.15. Measurements of the Recovery Time of ATR Tubes . 423
916. LifeT est . . . . . . . . . . . . . . . . . . . . . . ...423
9.17. Proper t ies of the Keep-a live. 426
918. Duplexer Inser t ion Loss. 427
9.19. Effect of Transmit ter Impedance. 428
9.20. High-power Opera t ion of Duplexers 429
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . ...431
CHAPTER 1
INTRODUCTION
BY C. G. MONTGOMERY
1.1 . Microw a ve Ra da r.-Th e im portan ce of the m ilitary applications
of rad io d irection and range, or radar, in the las t w ar is common k now l-
ed ge. For the d etection of enem y s hips and aircraft, for precis e bom bing
at night or through overcas t, and for the con trol of night figh ters of ra id -
ing squadrons , radar has been unexcelled . At the beginning of the w ar
there w ere only a few long-w ave radar equipments ; a t the end of the
hos tilities m any thous and s of radar s ets w ere in operation . Alm os t a ll
of th is equipment w as developed during the w ar and m os t of it opera t d
in the m icrow ave region . Although no defin ite boundaries are es tab-
lis hed , the m icrow a ve region that has been d eveloped extend s from fre-
quencies of about 1000 Me/ s ee or w avelengths of 30 cm to frequencies
near 3 0,000 Me/ s ee or w a velen gth s near 1 cm .
The m icrow a ve region is
characteriz ed by the fact that he com ponen ts us ed for the genera tion
and for the trans mis s ion of w a ves of thes e high frequencies have d im en-
s ions that are comparable w ith the w avelength , and the form of the
m icrowa v e c rcu its is grea tly in flu en ced by th is fa ct.
An importan t part of a m icrow ave radar is the duplexer. In ord er
to apprecia te fu lly the problem s involved in the d evelopm ent and d es ign
of d uplexers and d uplexing com ponen ts , it is neces sary to have in m ind
the param eters that d es cribe the perform ance of a radar s y s tem and the
orde s of magnitud e of the various quantities involved . A radar s et
opera tes by the d etection of the energy reflected from a d is tant target.
A s hort pu ls e of energy is s ent out by the radar trans mitter, and the pu ls e
s trik es a reflecting object that s catters it. The s cattered w ave, s till in
the form of a s hort pu ls e, a lthough very much reduced in amplitude, is
pick ed up by the adar receiver.
The range of the target object is
obta ined from the length of tim e betw een the transm is s ion of the h igh-
pow e r pu ls e and the reception of the w e ak reflected puls e. The d irection
of the target is obta ined by measuring the d irection in w hich the radar
antenna is poin ted w h en a s ignal of m axim um in tens ity is being received .
The rela tion betw een the pow er
P,
in the transm itted pu ls e and the
power PR in the received echo s ignal is k now n as the radar equation ,
w h ich is ,
(1)
1
2
INTRODUCTION
[SEC.1.2
The pow er
PT
is not rad ia ted uniform ly in all d irections by the radar
antenna, but is concentra ted in a narrow beam by an amount that is
m eas ured by the antenna gain G of the transm itting antenna.
Th e
prod uct of the firs t tw o factors of Eq. (1) is thus the pow er cros s ing a u it
area at a d is t a n te R from the antenna .
The target is characterized by
the s catte in g cros s s ection u , and the receiving antenna by the abs orbing
cros s s ection or effective a rea A.
The m agnitude of the received pow er
as given by Eq. (1) is not explicitly d ependent upon the w avelength k
of the rad ia tion . It d epend s on A implicitly through the quantities G
and u. For targets that have d im ens ions large compared w ith X, u is
independent of A.
The maximum range at w hich a target can be detected is obta ined
from Eq. (1) if the va lue for P. corres pond in g to th e m in imum detecta ble
s ignal is ins erted . In ord er to avoid con fus ion of the s ignal w ith the
th ermal n ois e tha t is in evita bly pres en t in a ny electrica l circu it, th e s ign al
pow er mus t be greater than s om e m inimum value. The nois e pow er in
an electrica l circu it is proportional to the band w id th Af of th e circu it.
For an id eal circu it that has no oth er s ou rces of nois e except tem perature
fluctuations , the nois e pow er is lcTAf. The bandw id th of the radar
receiver mus t be large enough s o that the s hort pu ls es are s u fficien tly
s harp for accurate range determ ination . If t e length of the pu ls e is
1 ps ec, a common value, Af is us ually about 2Mc/ s ee, and k !l”A~ is
8 X 10-’6 w att. An actual receiver, of cours e , has oth r s ources of
nois e; it is not id eal. The magnitude of the smalles t s ignal that can be
recognized is d ependent on a great m any variables , and a d is cus s ion of
thes e w ould lead too far a field . A repres en ta tive va lue for the s malles t
s ignal pow er w ould be 100/ cAf, or 8 X 10–13w att.
Values of the other
quantities in Eq. (1) w hich are ty pica l are PT = 106 w atts , G = 1000,
A = 10 ft’. If o is 103 ft’, the va lue for a m ed ium bomber, then the
maxim um value of R is found to be 3 X 10s ft or 50 nautica l m iles . It
is evid en t tha t the m os t effective radar equipm ent has the highes t pos s i-
ble transm itter pow er, the mos t s ens itive receiver, and the larges t
a nten na s for tra nsm is s ion a nd reception .
1 .2 . Rad ar Compon en ts .—At m icrow a ve frequ encies , the h igh -pow e r
trans mitter is a m agnetron . A m agnetron tube has a cy lind rica l ca thode
capable of the em is s ion of large currents . Around the ca thode there is a
ring of clos ely coupled res onant cavities tha t form the “ tank ” circuit
of the os cilla tor. There is an axia l magnetic field of s evera l thous and
gaus s s upplied by a perm anent m agnet.
A h igh -volta ge pu ls e is a pplied
betw een the ca thode and the res onant cavities , and a bunched rota ting
s pace charge is s et p w hich tak es energy from the d -c field and delivers
ra dio-frequ en cy en ergy o th e ca vities .
Us efu l pow e r is extra cted from
the ring of cavities by a coupling loop or s eries w avegu id e circu it and is
SEC.1.2]
RADAR COMPONEN TS
3
made available in the m icrow ave transm is s ion line. The value of one
megawa tt ch os en for PT in the previous s ection is a va lue near the upper
lim it of the pra ctica l range for m agnetron os cilla tors near a w a velength
of 10 cm . At s horter w avelengths , the tta inable pow er d ecreas es and ,
in fa ct, is rough ly proprotion al to th e w a velen gth .
The m icrow a ve trans mis s ion line is us ually a rigid coaxia l line, for
w avelengths above 10 cm and for low pow ers a t 10 cm .
Th e d iameter
of the coaxia l line mus t be small enough to preven t the propagation of
higher transm is s ion m od es a long it.
Con sequ en tly , d ifficu lties of con -
s truction and voltage br ak dow n at high pow e r levels m ak e it neces sary
to us e w a veguid e, us ually of rectangular cros s s ection , for h igh pow ers
and s hort w avelengths . Coaxia l line may be us ed in the 10-cm region
for pow ers up to about 100 kw ; above th is l vel, w aveguide 1+ by 3
in . OD, is employ ed . For smaller w avelengths , w aveguide is us ed
exclusively.
The s ens itive receiver th t is neces s ary for good rad ar perform ance is
a s uperhet erody ne receiver w ith a s ilicon cry s ta l converter.
Th e
received echo s ignal is m ixed w ith a m icrow a ve loca l-os cilla tor s ignal
w ithout any am plifica tion , and an in term ed ia te frequency s ignal in the
neighborhood of 30 Me/ s ee is prod uced . The s ignal is am plified , recti-
fied y a d iod e, further am plified by a w id eband vid eo-frequency am pli-
fier, and applied to one or more cathod e-ray tubes tha t are w atched
by the rad ar opera tor. The proper s w eep voltages are a ls o applied to the
ca thod e-ray tubes in order tha t the range and d irection of the ta get
may be read off the tubes . The s ens itive converter cry s ta l is eas ily
dam aged by overload . The large d ifference in pow er level betw een the
transm itted and reflected pu ls es (180 db in the example given) mak es
the im portan t problem of rotecting the cry s ta l a d ifficu lt one.
Microw ave antennas have form s that are characteris tic of the s hort
w avelength . The d im ens ions of the antenna are large compared w ith
the w avelength and it is pos s ible to obta in igh gain and narrow beam -
w id th w ith an antenna that is not too large. Microw a~re antennas are
des igned on optica l princip les .
La rge con vergin g m irrors or, more ra rely ,
lens es , are us ed to focus the s ignal and d ivert it d om the small trans -
m is s ion line to the receiver.
The effective area A of the antenna is
rela ted to the beam w id th @ and to the w a velength; approxim ately ,
‘=+”
(2)
For A equal to 10 ftz and k equal to + ft or about 10 cm , @ is about 6
d egrees . The quantity @ is the res olving pow er of the radar s y s tem in
angle. The accuracy of a determ ination of d irection may be about
4
[SEC.1.3
@/ IO. Thegain of thereceiving antenna is approxim ately
(3)
or about 1000 for the exam ple cited .
Th e receivin g and tra nsm ittin g
antennas have equal va lues of gain and cons equen tly equal areas .
A radar antenna, to be able to s earch a volum e of s pace for a target,
m us t s c n or be poin ted to cover the angle s ubtended by that volum e.
If t e transm itting and receiving antennas are s epara te, both of them
m us t be s canned together. It is evid ent that there are m any advantages
to be gained by the us e of a s ingle antenna for both reception and trans -
m is s ion . A sw itch mus t be provid ed to connect the ante na to the
trans mitter or to the receiver, and th is s w itch is called the d uplexer.
1 .3 . Microw a ve Duplexers .—The requ irem ents of a radar d uplexing
sw itch a re ea s ily s ta ted :
1 . During the period of transm is s ion the sw itch mus t connect the
antenna to the trans mitter and d is connect it from the receiver.
2 . The receiver mus t be thoroughly is olated from the transm itter
d uring the em is s ion of the h igh-pow er pu ls e to avoid d am age of the
3 .
4 .
s en s itiv e conve rte r e lemen ts .
After trans mis s ion , the s w itch m us t rapid ly d is connect the trans -
m itter and connect the receiver to the antenna.
If targets clos e
to the radar are to be s een , the action of the sw itch mus t be
e xtremely fa s t.
The s w itch s hould abs orb little pow e r, either d uring transm is s ion
or during reception .
A radar duplexer is thus the m icrow ave equivalen t of a fas t, double-
pole d ouble-throw s w itch , w ith low los s .
S ince the tim es involved are
m eas ured in m icros econd s , no m echanica l s w itch is pos s ble, and elec-
tron ic d evices mus t be us ed . The electron ic tubes that have been
developed for this purpos e tak e form s s im ilar to s park gaps w here high-
cu rren t m icrow a ve d is ch arges furn is h low -im ped an ce pa th s . A d uplexer
us ually con tains tw o s w itching tubes onnected in a m icrow a ve circu it
w ith three term inal trans mis s ion lines , one each for the trans mitter, the
re eiver, and the antenna. One tube is ca lled the trans mit-receive tube
or TR tube; the other is ca lled the anti transm it-receive tube or ATR
tube. The nam es are neither particularly appropria te nor des criptive,
bu t they have received comm on acceptance and w ill be us ed throughout
th is book . The TR tube has the primary function of d is connecting the
re eiver, the ATR tube of d is connecting the transm itter.
The com monly accepted m eaning of duplex operation is opera tion
tha t perm its the s im ultaneous pas s age of s ignals in both d irections long
sEC.14]
DUPLEXING TUBES
5
a tra sm is s ion line. In the narrow s ens e, it is im proper to apply the
term to the sw itching opera tion in a radar equipm ent, s ince the trans -
m itted and received pu ls es a re not s im ulta neou s.
S t rictly s imultaneous
opera tion mus t in volve a 3 -d b los s in ea ch d irection (th is is d em ons trated
in Chap. 8), and s uch a los s is too large to be tolerated for rad ar purpos es .
Alth ou gh it is pos s ib le to bu ild m icrow a ve d uplexers for con tin uou s -w a ve
opera tion , little a ttention has been given to th e practica l d evelopm en t of
such dev ice s .
104. Duplexing Tubes .—The des ign and development of a radar
duplexer involves tw o m ajor problem s w h ich are related to each other.
The tubes for the d uplexer m us t be d es igned , engineered , and prod uced ,
and the m icrow a ve circuits in w h ich th e tu bes are us ed mus t be d eveloped .
A tube for a duplexer mus t opera te properly under tw o very d ifferen t
cond itions : w h en a gas d is charge is pas s ing through the tube and the tube
is a nonlinear device, and w hen the tube is xpos ed to low pow er levels
and behaves linearly . The des ign of a TR tube to have the des ired low -
level properties is s im ilar to the des ign of m any other m icrow ave com -
ponents . A k now ledge of the behavior of cavities and method s of
coupling to them is neces s ary .
Mea su rem en ts , s uch as th os e d es cribed
in Chap. 9 , m us t be m ad e of the reflected and trans mitted pow er through
the sw itch . The d im ens ions and olerances of the sw itch mus t be
d eterm ined to a great exten t by experim ent, a lthough theoretical ca lcu-
la tion are importan t s ince they m ak e it pos s ible to hold the num ber of
experiments that m us t be done to a m inimum .
The opera tion of linear
m icrow ave device s is w e ll unders tood .
Chapters 2 , 3 , and 4 of th is book
are d evoted to the linear behavior of d uplexin tubes .
On the other hand , the opera tion of a sw itch i g tube at high pow er
levels is not s o eas y to und ers tand .
Alth ough th e phenomena occu rrin g
in d is charges of electricity through gas es have been k now n for a long
tim e and have been the s ubject of coun tles s inves tigations , m any prob-
lem s rem ain to be s olved . In fact, a principal res ult of the m any inves ti-
ga tions is that the extrem e complexity of even the s imples t form s of
d is ch arge h as been emph as iz ed .
The fact that the d is charges encoun-
tered in radar duplex rs are excited by h igh-frequency voltages in a
frequency range w here very little fundam ental inves tiga tion has been
done renders it d ifficu lt to pred ict the behavi r by extrapola tion from
.—
pas t experience . -–TliF_iie s lgn proce~ie ‘has .t_her&:e beep_a~rnos t corn -
—- -.—.-
.—
Wes ca l._ The-u igency of the m ilitary need s w as grea t, and
than an unders tand ing of the phenomena involved . Chapters 5 and 6
are d evoted to the h igh-level behavior of d uplexing tubes .
An im portan t cons ideration in the des ign of a m icrow ave tube is the
e as ew ith w h ich it ca n b e manu fa ctu red ,
Microw a ve tubes m us t be m ad e
6
INTRODUCTION [sEC,15
of m eta l in order that no energy m ay be los t by rad iation. The envelope
of a m icrow ave tube is often a portion of the w a lls of a res onant cavity ,
and is therefore an importan t circu it elem ent.
The cons truction is
undamentally d ifferent from that of low -frequency tubes w here the
circuit elem ents are ins id e an envelope that has only the function of
retaining the vacuum . The d evelopm ent of new m icrow ave tubes mus t
th erefore be pa ralleled by th e d evelopm en t of n ew techn iqu es of con stru c-
tion . ~\ Tea rl a ll d uplexer tu bes in volve con structiona l features that w e re
d eveloped during the w ar. Thus the firs t TR tubes employ ed copper-
gla s s d is k s e als ; in tegra l~ca vity tu be s w e re pos s ib le on ly a fter th e d e ve lop -
m ent of Kovar-glas s s ea ls in the form of w i dow s for res onant cavities ;
and bandpas s TR tubes and broadband ATR tubes w ere concurren tly
d eveloped w ith th e la rge res on an t Fern ico-glas s w in dow . Clos e coopera -
ion w as neces s ary at all tim es b tw een the tube m anufacturers and the
d es ign ers of compon en ts for ra da r equ ipmen t.
An add itional com plica tion to be overcom e in the s ucces s fu l d es ign
of a duplexing tube aris es from the fact th t a gas mus t fill the tube. A
high-frequ en cy d is ch arge in a gas mak es it extrem ely active ch em ica lly .
For good perform ance the gas filling m us t rem ain unchanged in com pos i-
tion and pres s ure d uring s evera l hu nd red h ou rs of opera tion .
1 .5 . Microw a ve Circu its .—Th e sw itching tu bes m us t be incorpora ted
in a m icrow ave circu it to produce a complete duplexer.
The circu it
its elf is linear, and the nonlinear duplexing tubes can be regarded for
m any purpos es as s im ple k nife s w itches th t are opened or clos ed by the
gas d is charge. One of the im ortan t d evelopm ents during the w ar has
been the e tens ion of the concepts of the conven tional netw ork theory ,
applicable at low frequencies ,
to m icrow ave frequencies and to the
propagation of m icrow a ve pow e r in w a veguid es . Th is generaliz ation has
been m ade rigorous ly and it w ill be adopted w ithout explanation in the
s ucceed ing chapters . A m ore com plete explana tion of the bas ic princi-
ples involved is given in other volum es of the s eries .
The practica l as pect of the generalization is that the fam iliar con -
cepts of im ped an ce, of im ped an ce-m atch in g, and of in sertion los s , and th e
trans mis sion-line equations m ay be us ed w ith confid ence. Thus trans -
m is s ion through a cavity w ith tw o coupling lines may be regarded .as
equiva len t to trans mis s ion through a length of trans mis s ion line a lm os t
s hort-circu ited at each end by a high s hunt s us ceptance.
The pow er
trans fer from a genera tor connected to one coupling line to a loa con -
nected to the other coupling line ma be computed from w ell-k now n
rela tions . An ob tacle in a w aveguid e w hich is th in in the dk ection
along the axis of the g id e is equiva len t to a shunt s us ceptance, and the
and 10.
SEC.13]
MICRO WAVE CIRCUITS
7
s ca ttered w a ve from the obs tacle can be accurately d es cribed by circuit
equations.
Duplexing circuits can be d ivid ed in to tw o cla ss es , branched circuits
and balanced circuits . The branched circu its are s im ple in principle and
are w id ely us ed . A T-s haped junction in w aveguid e or coaxia l line w ith
three arm s , ca lled a T-junction , is provid ed w ith sw itches in the tw o
arm s that are connected to the transm itter and to the receiver. The
th ird arm is connected to the antenna.
Du rin g tra nsm is s ion on e sw itch
is open and the other los ed ; during reception the revers e is true. The
ch ief des ign roblem in a branched duplexer is that of m inim iz ing the
los s es over a broad band of frequencies . In Chap. 7 the m ethod s of
d es ign are d is cus sed . S om e practica l b anched d uple ers are d es cribed
in Chap. 8 .
Balanced duplexing circu its are m ore com plica ted and involve the
combination of tw o mag c T’s and tw o TR tubes , A magic T is the
m icrow a ve analogue of a balanced bridge circuit a t ow frequencies . It
m ay have any of a num ber of d ifferent form s in w a veguid e or coaxia line.
Although ba lan ced circu its h ave been d eveloped on ly recen tly , th ey s how
great prom is e for the fu ture. Ba lanced circu its are d es cribed in Chap. 8 .
Although the d uplexers that are d es cribed here w ere des igned w ith a
highly s pecia liz ed application in m ind , there is m uch to be learned from
a s tud y of the d evelopm ent. A good duplexer can res ult only from a
carefu l combina tion of the mos t advanced techniques in three field s :
linear m icrow ave circu its of the mos t h ighly d eveloped ty pe mus t be
com bined w ith a k now led ge of the properties of electrica l d is charges in
ga ses a t m icrow a ve frequ en cies and w ith the bes t techniques of con stru c-
tion of m icrow a ve vacuum tubes .
CHAPTER 2
LINEAR THEORY OF HIGH-Q TR TUBES
BY LOUIS D. SMULLIN
2.1 . Linear Behavior of the TR Tube.—The TR tube is a sw itch
w h ich is us ed to s hort-circu it th e receiver d uring th e tra nsm ittin g period ,
and it a ls o a llow s e hoes to pas s to the receiver w hen the transm itter is
off. An id ea l TR tube w ould pres en t a perfect s hor circu it during the
transm itting period an w ou ld caus e no los s of the received s ignal.
Thes e functions could be performed by a s im ple k n ife sw itch bu t the
s peed and frequency of opera tion w hich are
need ed are far bey ond the pos s ibilities of any
m echanica l s w itch . Ty pica l opera ting require-
m en ts are repres en ted by a repetition ra te of 2000
cy cles per s econ d, w ith th e tra ns ition from eith er
open to s hort circu it or s hort to open circu it tak -
ing place in les s than 10-7 s ec. S uch h igh-s peed
perform ance can be atta ined by us ing a s park gap
for the s w itch . In s om e ins ta lla tions thes e s park
FIG. 2,1.—Duplexing
gaps have tak en the form of very s imple a ir
cir cu it wit h spa rk ga p a nd
s park gaps ; in others , the gaps have been placed
idea l t ransformer .
in low -pres s ure a tm os ph eres to red uce th e brea k -
dow n and the s us ta in ing voltages of the d is charge.
From the poin t of view of transm itter efficiency , it is d es irable to
mak e t e d is charg appear as a very low impedance in s eries w ith the
line. S im ila rly , to get bes t receiver protection , the voltage s tepdow n
ratio from the gap to the receiver line s hould be as large as pos s ible .
Figure 2 .1 ird ca tes how s uch a circu it w ou ld appear if id ea l trans form ers
w ere us ed . During the fired cond ition the arc or dk charge im pedance
2. will trans form to the term inals in the antenna line as ZJN!. The
leak age pow er to the receiver load w ill be (VJNJ2/Z1 where V= is the
voltage d rop a cros s the d is cha rge.
During the receiving cond ition the
receiver im pedance w ill appear to b e ZJ(N2 / NJ 2 at the antenna-Iine
terminals.
Except a t compa ra tively l w frequ en cies , it is d ifficu lt if n ot im pos s ible
to cons truct an ‘(id ea l” trans form er or even one w hk h is approxim ately
“id ea l.” How ever, it is fa irly s imple to mak e res onan t trans formers .
Thes e m ay tak e the form of either lum ped -cons tan t or d is tribu ted -con -
s ta nt n etw ork s .
Th e lumped -con s ta nt circu its a re ma de of con ven tion al
8
SEC,22]
LUMPED-CON STAN T TRAN SFORMERS
9
ind uctors and capacitors s uitable for the d es ired frequency range, The
d is tribu ted -cons t n t circu its us ually ak e the form of a cavity or trans -
m is s ion-line res ona tor. Such res ona tors m ay have unloaded Q’s of
s everal thous and , w hereas ord inary LC-ci cu its have m axim um Q’s of
th e ord er of s evera l h un dred .
Although in the m icrow ave region the us e of lum ped -cons tan t ele-
m erits an d circu its in th e us ua l s en s e is im pra ctica l, it w ill be in forma tive
firs t tod is cus s the TRtubes as ifs uch cons truction w ere pos s ible. Then
in s ucceed in g s ection s, ca vity res on ators and their equiva lent circu its ,
h igh-Q TRtubes and their characteris tics , and bandpas s TR tub s w ill
b e d is cu s s ed .
FIG. 2.2.—Ser ies LC-cir -
FIG. 2 .3 .—Frequency dependence of circu it
cuit.
p ar amet er s of F ig. 22.
2.2 . Lum ped -cons tan t Res onant Trans form ers .-The circuit of Fig.
2 .2 has a number of in teres ting properties . A s how n, it cons is ts of a
s eries LC-circuit w ith in ternal los ses repres en ted by the res is tance r,
s hunted by as us cepta ce b,. Theinput s us ceptanceis
r
(
x
)
—+j h-x2+T2J
Y= X,+r?
(1)
w here X = (w 5 – I/ m C).
If res onance is defined as the frequency at
w hich the im aginary part of Y is z ero, then
and for rb! < +,
(2)
Then , a t res onan ce,
Y = rb~.
(3)
Thus , th is is a res onant im pedance trans form er, s ince by vary ing
bl and ad jus ting the LC-circu it to mak e Im ( Y) = O, the input conduc-
tance Re( Y) can be made to vary over a w ide range. Figure 2.3 illus -
tra tes graphically w hat is involved . The Re ( 17) = g moves up and
dow n the curve as bl is v an ed .
10
LINEAR THEORY OF HIGH-Q TR TUBES [S EC.2.2
S im ilarly , let us cons id er the circuit of Fig. 2 .4 w here an output
circuit cons is ting of th e s hunt s us ceptan ce bz and the load con ductance
1
2
FIG. 2 .4 .—Resonant impedance t ransformer
with ou tpu t cir cu it .
g2 has been added . The input
adm ittance Y w hen the circuit is
tuned to res cm ance [Im ( Y) = O]is
()
e(Y) = g = rh~ + g, $
‘, (4)
w here (r + g,/ b~)b, < ~ and
b;>> g;. Equation (4) could als o
repre s en t an id ea l tran s forme r cir-
cuit w ith voltage s tepup and s tepdow n ratios of bl and bz , respectively.
Let us now exam ine the frequency res pons e of the circuit of Fig. 24
in the vicin ity of res ona nce.
.
lm(yJ = b=b ’– (r+ ~ ’ ; t ( i ~ +’)”
(5)
w here X’ = — bJ (g~ + b;) and r’ = gj,’(g~ + b;). If th is is res tricted
to the region w h ere b; >> g;, then
t)= b,-x~.
(6)
At res onan ce , b = O, and
The Q of a s im ple s eries -res onant circuit is given by
(7)
(8)
A parallel-res onan t circuit having L, C, and G all in s hunt is d es cribed by
(9)
In th e circu its u nd er d is cu s sion th ere is obviou s ly n eith er a s imple s eries -
IYear resonance ,
the behavior of the s us ceptance curve is at leas t s im ilar to that in a para l-
lel-res onant circuit.
How e ver, s in ce it is n ot obviou s ju st w h at pa rticu la r
L, C,
or G should be us ed to get an expres s ion for the Q of the circuit,
further inves tigation into the nature of the quantity defined by Q s hould
be m ad e.
It is pos s ible to define Q in a number of w ay s all of w hich are
equivalent. The am plitude of os cilla tion of a freely os cilla ting s ys tem
SEC.2,2]
T .UMPED-CONSTANT TRANSFORMER ,T
11
w ill d ecreas e exponentia lly w ith a tim e cons tant equal to 2Q/ ti, w her Q
is defined as in Eqs . (8) or (9). Alterna tively , Q may be defined as
% times the ra tio of the energy s tored to the energy
d k s ipa ted p er cy cle . In th e p ara llel circu it, os cilla tin g
w ith a frequency w / 27rand am plitud e V, th e en ergy
s tored per cy cle is +CV2. Th e en ergy d is s ipa ted per
cy cle is 2 irGV2 / 2W,a nd Q = cW / G, a s before.
Finally,
the frequency varia tion of the s us ceptance or react-
ance of an os cil a ting circu it around its natural or
res onan t frequency can be s tud ied . The parallel-
res on an t circuit of Fig. 2 .5 has an admittan ce
o
1
Y
“B
G
L
FIG. 2.5.—Para llel-
resonan t circuit .
‘=G+4”C-$)=G+4-$
(lo)
w here a; = (LC)-’. By us ing Eq. (9) and the approximation that
(m – u) <<co,
Y= G+j2QGk .
~o
(11)
Let Im ( Y) = b; then from Eq. (10), a t res onance,
db
udb
d (ln u) = da
— = 2UC = 2QG,
or
(12)
(13)
With Eq, (13) as a bas is , an equ ivalent d efin ition of Q may be s et up
for the more complex circuit of Fig, 2 .4 . If the d eri~-ative of Eq. (6)
w ith res pect to In a is tak en, then
db adb
= ~, + (wb:b, + bobz)(bo + bz) – bob,(ubi + b,), (1+)
— . .
d (ln u) du (b, + b,)’
where
~ = Ib,l = b,, ‘$$ = lb,l = bz,
and
db,
—~o
bob;
cob(=u-=—
dw
Au (bl + bJ 2”
Then by the us e of Eq. (7) for b,, and
(15)
(16)
12
LINEAR THEORY OF IIKJH-Q TR TUBES
[SEC. 2.2
The Q of the circuit is d efined by Eq. (13) w here the tota l conductance
G = YO + rb~ + gz (bJ bz)’, and
Q=, l ,
(
C ;+ r+;
2
)
(17)
w here YO is the conductance of the line or generator connected to the
circu it a t term in als 1 -1 .
Equation (17) m ay be rew ritten
(
“+r+$ .+ +$.++,,
2
*U
(18)
thus defin ing the “inpu t,” ‘( ou tpu t,” and “unloaded” Q’s . On th is
basis ,
1
.$ +;:
z – .
w here the s ubs cripts ind ica te that the res onant circu it is loaded by the
genera tor on ly (Q~J , or by the generator and a load (QLJ.
Next, let us cons id er w hat happens if the capacitor C in Fig. 24 is
s hort-circu ited . Th is w ould
+I!zl13:h:z:
reak d ow n upon the applica tion
w ou ld requ ire z e ro su s ta in ing volt-
1
age, Fig. 2 .6 .
The res is tance ~
FIQ. 2.6.—Circuit of Fig. 2.4 with the
capacita nce short-circuited.
may be n eglected s in ce the circu it
is no longer res onant. The ra tio
of the pow er delivered to gz to the ava ilable pow er from the genera tor
w ill be determ ined . The input adm ittance to the circu it is
y = j~l + (92 + 3772)(–W.
92 + j(b2 – b.)
For bl and bz large
The pow er abs orbed in g~ is
(19)
(20)
()
‘=[’+g’($zb’’’=
SEC.23]
CAVITY RES ON ATORS
13
This pow er is k now n as the direct-coupled lea kage pow e r to d is tinguis h it
from the leak age pow er due to the voltage d rop acros s the d is charge.
The d irect-coupling a ttenua tion
D
expres s ed in d ecibels is 10 log,~ of the
ra tio of P of Eq. (21) to the m axim um pow er ava ilable;
(22)
As a las t example, the ins ertion los s of the circuit in Fig. 2.4 w ill be
calcu lated , w ith the as s umption of a current gen erator w ith unit in ternal
admittance.
At res onance, the input onductance of the circuit is given
by Eq. (4). The pow er trans ferred to the load is
()
‘=’+’ii’’+’b’l’”
(23)
The ins ertion los s expres sed as the ratio of the actual to the available
pow er is th e reciproca l of th e tra nsm is s ion ,
~-,= [1+4)2+4’
()
,’”
492 F2
(24)
Thus , Eqs . (4 ),
format ion ra tio,
(18), (22), and (20) ind icate that the im pedance trans -
QLZ, nsertion IOS S , and d irect-couplin g a tten ua tion a ll
increas e w ith the s quare of the co pling s us ceptances .
It is , th erefore ,
neces s ary in any practical d es ign to comprom is e betw een maximum
tolera ble in s ertion los s a nd m in imum trans forma tion ra tio.
2 ,3 . Cavity Res onators .—The circuit analy zed in Sec. 2 .1 is a th r-
oughly practical circu it and can be us ed w ith little m od ifica tion up to
frequencies of the ord er of 100 Me/ s ee. At higher frequencies , rad iation
los s es from open-w ire circuits becom e exces s ive, and at the s am e tim e it
becomes pra ctica l to u s e res on an t tra nsm is s ion lin es or ca vities in stea d of
conventional LC-circuits . Although it is d ifficult to obtain a Q of m ore
than a few hund red w ith lum ped cons tants , it is not d ifficult to ach ieve an
unload ed Q of 2000 to 10,000, and practica l d es igns exis t for res onators
w ith Q’s of 50,000 or m ore. As a res u lt, it is pos s ible to us e large trans -
forma tion ra tios w ith ou t pa y in g th e penalty of e xce s s ive ly la rge in s ertion
losses.
Mos t m icrow ave TR tubes (A <50 cm ) us e s ome form of res onant
cavity as a voltage and impedance trans form er, The 1ow -Q res onant
iris es u sed in ba nd pa s s ‘1 ’R tu bes con s titu te a tra ns ition al grou p betw e en
14
LINEAR THEORY OF HIGH-Q TR TUBES
[S ~C. 23
lu mped -cons tan t and d is tribu ted -cons tan circu its and w il be d is cus s ed
in Chap. 3 . The remainder of th is chapter w ill d ea l w ith the linear
properties of h igh-Q ‘1’R tu bes and w ith d eta iled d es cription s of various
tubes .
Res onant cavities have been d is cus s ed by a number of au thors , and
com plete mathematical ana ly s es exis t for a large num ber of d ifferen t
geom etrica l s hapes and m od es of os cilla tion w h ich gi e the res onant fre-
quen t y Q and equiva len t s hun t or s eries res is t an te. In the follow ing
s ections , a k now led ge of m icrow a ve circu itry w ill be pres um ed , and , pri-
m arily on the bas is of trans mis s ion line ana ly s is , the rela tion betw een
various cavity param eters and the functions of the TR tube w ill be ind i-
ca ted . Becaus e the m ethod s of hand ling lum ped -cons tun t circu its are s o
h ighly perfected and w idely unders tood ,
equi~-alent lum ped-cons tant
circu its w ill be d eveloped for TR-tu be res onant ca vities .
In the des ign of a TR-tube cavity , a number of factors mus t be c n-
s id ered s im ultaneous ly . The m ode of os cilla tion and the s hape of the
cavity mus t be s uch that i is c nven ien t to place a s hort s park gap at a
poin t of m axim um voltage,
mm
(a )
(b)
FIG. 27,-Cross sect iom of
cavities.
s o th at w h en th e ga p fires th e d irect-cou plin g
attenuation trill be a maxim um .
For in -
s tance, it w ould be d ifficu lt to s atis fy thes e
cond ition s in th e !f’Eoll-mod e of os cilla tion ,
The ra tio betw een the gap voltage and the
exciting volta ge s hould be large.
S in ce th e
load ed Q and the s tepup ra tio vary by
the s am e factors in a given ca ity d es ign ,
and s ince extrem ely large va lues of Q are
und es irable becaus e of ins tability in tuning, a com prom is e m us t be m ad e
betw e en the tw o.
Although the actual s hapes of m os t TR cavities are fa irly com pli-
ca ted , they can be cons id ered as mod ifica tions of a cavity mad e of a
;es onau t lengt of rectangu lar w a veguid e opera ting in the !f’EOl-m od e
and coupled through large s hunt s us cepta nces to the load and gen ra tor,
Fig. 2 .7a . In order to reduce the break dow n voltage to a low enough
va lue to be us ed , a pa ir of pos ts are placed acros s the cavity a t a poin t
of m aximum voltage to form a s park gap, Fig.
2.7b.
The pos ts add a
s hun t ca pa cita nce a cros s th e ca vity w h ich ca us es th e res on an t frequ en cy
to be low er than if there w ere no pos ts pres en t.
Impedance Transforma tion .—Let us cons id er the res onant m od e of a
len gth of los s le s s tra nsm is s ion lin e of ch ara cteris tic a dm itta nce YO s h ort-
circu ited a t the far end and s hun ted by a com pa ra tively large s us cepta nce
B, a t the poin t a -a , Fig. 2 .8 . The inpu t s us ceptance w ill be
Yi = jB1 – ‘jYo Cot 2;,
(25)
SEC.2.3]
CAVITY RESONATORS 15
w here 1 is the length of the line. For s im plicity it is as s um ed that the
guide w avelength is equal to the air w avelength . By ad jus ting either
B , or 1 the input s us ceptance can be m ade z ero at any given w avelength .
~i;~j {@q
B,
FIG. 2S, -Transmit -
FIG. 29.-Equiva-
sion line with shunt len t cir cu it of Fig. 2.8
susceptance.
near resonance .
If B , is large, Y , w ill be z ero for 27rl/ h = (m r t ,) w here, i small. The
impedance of a s hort-circu ited tra nsm is s ion lin e is
(26)
(27)
In other w ords , the reactance of a s hort-circuited length of line varies
linearly around z ero w ith w avelength . This , of cours e, is jus t lik e the
varia tion in rea cta nce of a s eries LC-ci cu it near res on an ce; and for sm all
va lues of AA/ XO, a s hort-circu ited length of transm is s ion line can be
res onant circuit. Thus , an equ i-
valent circuit for Fig. 2 .8 can be
draw n in as s how n Fig. 2 ,9 . The
frequency res pons e of the circuit
m ay be analy zed as in Fig. 2.10
w here it has been as sum ed that BI
is an inductive s us ceptance. The
frequency for w hich the input
susceptance Yi is z ero w ill fa ll to
the left or to the right of the pole,
depend ing upon w hether B1 is an
inductive or a capacitive s us -
ceptance. In the vicin ity of jo, if
FIC+.2-10.—Frequency r esponss of cir cu it
of F ig. 2.9.
B is la rge, the s us cepta nce w ill va ry nearly linearly through z ero, w h ich is
s im ila r to th e va ria tion of a s imple pa ra llel-r s on an t circu it.
The circuit of Fig. 2“8 is a t w e-term inal netw ork , and as s uch can be
u sed on ly as a s hunt or s eries elem ent.
This is us efu l for ATR tubes and
further applications are d is cus s ed in Chap. 4 . For a TR tube a four-
term inal netw ork through w h ich pow er is trans mitted is required . This
16
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC. 2.3
may be accomplis hed by coupling the cavity to an outpu t load by a
s u s cepta nce B z, Fig. 2 .lla .
Theinpu t s us ceptance Yimay be w ritten as
Y, =jBI+ Y,
(I3 + jBz) + jYo tan 61
YO + j(G2 + @3J tan @
G,Y,(l + tan’ Pl) + jBJYo – YOtan’& – B2 tan 01), (28)
= jBl +.Yo
(Y , – B, tan i31)2+ (G, tan i31)2
w here ~ = %/ h . If the imaginary part is s e t equa l to z ero the s olu tion
for tan B1,
where B1 and B2 are large com pared w ith Yo, is
B, + B,
tan@ =YO-.
BIB,
(29)
The rea l part of Yt = G + jB, w ith B1 and B,>> Yo, is
G,Y,(l + tan’ ,81)
()
z
G = ‘0 (YO – B2 tan d l)z + (G2 tan ~l)z = ‘2 ~ “
(30)
Equations (29) and (30) are to be compared w ith Eqs . (7 ) and (4)
w h ich give th e id en tica l res ults for th e lum ped -con sta nt circu it. Altern a-’
LIJ
~ t anh j91/2
(a )
(b)
F IG. 2.1 1.—Transmission lin e with t wo
coupling susceptances.
tiveiy , a m ore exa ct equ iva len t cir-
cu it can be draw n by us ing the
equ iva len t T-s ection for a length of
lin@ Fig. 2 .1 lb, and the s am e rela -
tions w ill be found at res onance.
Cavity Los ses .—The calculat ions
thus far have neglected the pow er
d is s ipa ted w ith in the cavity its elf.
If the cavity is not too los s y , the
net e ffect of d is s ipa tion in the w a lls
can be repres en ted by a lum ped res is tance s hun ted acros s the cavity
at the poin t of m aximum voltage. It can be defined as
1
—= Reh=
(voltage)’
G.,
2~ X energy los t per s ee’
(31)
where
\
Energy los t per s ec = # \B]’ da
(32)
and 8 is the s k in depth , f th re fe quency ,” and B the m agnetic field at the
s urface of the cavity . The voltage is the line in tegra l of the electric
1Guillem in, Comm un icationNetworks, Wile y , New York , 1 935.
f!.Ec.2.3]
CAVITY RES ONATORS
17
ds 1 is
s ection of the cavity . The path of in tegration us ually chos en for th is
in tegral is one that gives a m axim um of voltage w ithout us ing an extrem e
path . If Eqs . (31), (32), and (33) are com bined ,
(34)
Equation (34) is the equiva lent s hunt res is tance that w ould have to be
laced acros s the res ona tor along the particu lar path of in tegration in
rd er to produce the s am e effect as the d is s ipation in the cavity w alls .
It s hould be poin ted out that s ince the “inductive” and “ capacitive”
e lements a re h op ele s s ly in term in gled , th e equ iva len t s e rie s res is ta nce R,,
if ca lcu la ted by a s im ila r proced ure, w ill b e rela ted to th e s hun t res is ta nce
by R, = RJA, where A may be larger than Q2 by as much as a factor
f 2 .1
Th is me thod of ca lcu la ting R., has been applied to m os t of the s im pler
geom etric s hapes and to m os t of the m odes of os cilla tion . The cavities
f TR tubes are us ually s o com plica ted geom etrically that the m ethod
becom es extrem ely com plica ted , and all d es ign w ork is bas ed on experi-
m ental y d eterm ined v lues of a quantity proportiona l to R.h. Such
values are ob ained by m eas uring the input conductance of a cavity at
re s onan ce (1 ? = O).
It is , therefore, of in teres t to s ee how th is m eas ured
cond uctance varies w it the coupling to the cavity .
Let us refer again to the s im ple line cavity of Fig. 2 .11, and calculate
the input adm ittance Yi. The as sum ption now is that the trans mis s ion
line form ing the cavity has a propagation factor 7 = a + j/ 3 w here the
ttenuation cons tant a is s mall. Then
Y
gz + jb, + tanh y l
z= 1 + (g2 + jb,) tan h -y l’
(35)
w here gz = GJYO, and bz = B.J Yo. Expa nd in g ta nh yl ,
w here 6 = L?l. If B1 a d Bz >> Yo, and al <<1, the cavity w ill be nearly
half w avelength long. If th is is s o,
tanh Y1 = al + je,
(37)
@=7r+c.
1W. W. Hansen,Lecture Seriesat Radiatio Laboratory ,RL Report T-2 ,
18
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.2.3
The s ubs titu tion of Eq. (37) in to Eq. (35) gives
Y [g, + al + j(t + b,)l[l + gzcd – bzc – j(gx + bzal)lm (38)
—=
Y, (1 + g,al – A)’ + (g,e + b,at)’
For res onance, the imaginary part of Eq. (38) mus t ‘equal –bl. To
s atis fy th is , it is found that, if al << ba>> gz
Finally , the s olu tion for the real part is
(39)
Thus , at the input term inals , there is a tota l conductance compos ed
of the load cond uctance trans form ed through tw o coupling s us ceptan ces
and a quantity that m ay be various ly in terpreted as the s hunt conduct-
ance or the s e ies res is tance of the cavity trans form ed through the input
coup ing. The form of th is equation is identical w ith that of Eq. (4)
for th e lumped -con s ta nt circu i .
Finally , let us find the conductance at the cen ter of the cavity .
At res onance, the im aginary part of the adm ittance is z ero and Eq. (37)
can be w ritten as
If th is is put back into Eq. (35), it is found that at res onance the con-
ductance at the center of the cavity look ing tow ard the output term inal
is
G
–@+&’
Z–22
(40)
The tota l conductan e at the cen ter, inc ud ing both input and output
term inals and as sum ing a m atched generator is
G
1+*”
=ffl+T;
Yo
(41)
Thus , the quantity cd can be defined a the s hunt conductance of the
cavity , and the tota l conduc ance-load ing of the cavity is the s im ple
s um of the external and avity conductance, each trans form ed by a
cons tant appropria te to the reference plane chos en.
Equation (39) as serts that at its res onant frequency , the cavity and
its load m ay be replaced by an equivalent conductance.
If this con-
SEC.2.3]
CAVITY RESONA TORAS
19
d ucta nce Gi is equ al to th e gen era tor con du cta nce YO, th e pow er d elivered
by the genera tor is a m axim um s ince the reflection coefficien t
~= Yo– Gi
Y, + Gi
is z ero. How ever, G~ is the s um of the trans form d cavity and load
conductance; and it is the pow er d elivered to the load that is of in teres t.
The net pow er flow into the cavity and its load is given by
P = Ph.(1 – r’). (42)
The fraction of thk pow er del vered to the load conductance is
!1
)
,”
92~,
P,=P
()
~ 2 + gcb;
2 ~2
and the ins ertion los s in d ecibels is given by
[
01
,”
l+ b?9c +92 –
L =
10 log,o
b’
()
bl 2
492 &
(44)
Th is equation is identical in form w ith that of Eq. (24) for the lum ped -
cons tant circuit .
Calculation of Q.—As has been ind ica ted at the beginning of th is
s ection , the calcula tion of QOfor a cavity of s im ple d es ign, s uch a s a right
cy lin der, is a s traightforw a rd proced ure, and form ula s a re a vailable for
a number of d ifferent d es igns . 1
Th es e h ave been d erived by calcula ting
the ra tio of the energy s to ed to the energy d is s ipa ted per cy cle. How -
ever, the quantity of d irect in teres t is ot th is ra tio but the rate of change
of input adm ittance w ith frequency (or alternatively , the varia tion of
ins ertion los s w i h frequency ). Therefore, let Q
w ay a s b efore ,
Q=~:”
Th e problem , th erefore, is to d eterm in e
udb/ d~.
For conven ien ce, variables are changed from
be defined in the s am e
(13)
u to k = 2T/ A = @/ c.
This is d one becaus e in m icrow a ve experim ents w a velength is the varia-
ble that can e meas ured convenien tl . It can be s how n that the
deriva tive of the input adm ittance of a s ection of transm is s ion line
:Vol. 11, Chap. 5, and the referencesthere cited.
20
LI.VEA Ii THEORY OF HIGH-C? l’Ii TCBES
[SEC. 23
term inated in an admittance }’.., is
1
d }’,.
()
~?
1 d l’out
—=j~l ~
1 + (j}-,. ‘ d (ln k )
+ 1 + (jl’...)i d (ln k )’
(45)
~vhere K = 2W &, and k fl is the ~va veltm gth in the transm is s ion line und er
cons id era tion, and all admi tances have been norm alized w ith res pect to
}’.,’
For w aveguide f a high-pas s ty pe, & and A are rela ted by
(46)
}vhe re X , is th e cu toff ;v av ele rlgth .
TJYOoth er u s efu l rela tion s a re
(48)
It can lx- s een from Fig. 2 . I la that 1-.,,, = g, + jh, and at res onance
}’ti = g – ~bl (the reference plane is j~l>t to the right of b]); hence
()
), 2
If the rela tions hips g = g, ~
+ g,b; and
ancf I“; = I-,. + ~bl are s ubs titlltcd into I;(I. (,50),
I
SEC. 2,3]
CAVITY RES ONATORS
21
w here n is the num ber of electrica l ha lf w avelengths m os t nearly equal
to the length of the cavity .
To d eterm ine Q, Eq. (13) is u s ed , and for the load ed Q
1 d Im ( Y,)
Q“=Em
b~mr
“[1 +’4)2+ ’4(: ’
[
10
1 2
QL, = ?!!
~ ;+g+9c .
1
(52)
Th is expres sion is com plete ly ana logous to the corres pond ing one for
th e lumped -con sta nt circu it, Eq. (1 7).
If the coupling s us ceptances are large, then Eqs . (51) ind ica te tha t
the cond uctance w ill change s low ly w ith frequency , rela tive to the ra te
a t w h ich th es us cepta nce ch an ges .
Th ere fore, it is u s ua l to a pp roxima te
a res onant cavity by a s im ple para llel-res onan t circu it w ith a cons tan t
cond uctance equal to the actua l va lue of the circu it a t res onance, and to
choose L and C to”give the s am e Q as he actua l circu it.
In ord in a ry
ca vitie s th is a pp rox irn a tio n is s u fficien tl y a ccu ra te to p re d ict th e p erform -
ance a t frequencies d ifferen t fro the res onan t frequency by Au/ u = 3 / Q,
d es pite the fact tha t the ad mittance has a pole a t a frequency rela tively
clos e to the res on an t frequen cy ins tea d of a t in fin ity .
Voltage Transformation Ra tio.—Th e volta ge tran sform ation ra tio of a
res onan t cavity us ed for a TR tube is of cons id erable im portance s ince
it is one of the factors tha t d eterm ine the amoun t of leak age pow er
rea hin g th e cry s ta l d etector. Tw o tra ns for-
m ation ra tios are of in teres t. Th6 firs t ra tio
refers to the behavior of the res onant cavity
and is the ra tio betw een a voltage applied to
its term ina ls and the voltage acros s the gap
bejore a spark has jorm ed . The s econd is the
ra tio of the voltage d rop of the d is charge
main ta ined acros s the gap to the voltage
appearing acros s the load . Although both of
thes e quantities have to d o w ith leak age
pow er, they are functions of the linear properties of the cavity and ,
th ere fore , w ill b e d is cu s s ed h ere .
Let u s cons id er t e cas e of a s im ple s ection of resonan t line w ith no
s park -gap pos ts , Fig. 2 .12 . At the plane i-i, the pow er flow ing to the
righ t is u ~G~;s im ilarly , a t the plan e O-O the pow e r flow in g to th e righ t is
II~GO. If there are no los ses betw een the tw o planes , the tw o quan tities
ii 10
I
I
v i
i,”
o
b,l
Ibz
,
!.i i.
F IG 212.-Reson an t lin ewit h
susceptances b, and bx.
22
LINEAR THEORY OF HIGH-Q TR TUBES
mus t be equa l. If Eq. (39) is us ed for Gi,
Pi=v:[G,(;)2+b;alYo]
If the cavity los ses are as sum ed to be negligible (cd = O) then
and
Vo
– = b,,
Vi
[SEC.2.3
(53)
(54)
w hich is the voltage s tepup ratio from plane -z ’ to plane O-O.
Cons id er how ~avity d k s ipation a ffe ts thk ratio. Practical d es ign
con sid era tion s gen era lly require that at the input term ina ls to the cavity
the apparen t hunt conductance be of the order of one-th ird the load
conductance. Th is amounts to abou t a 30 per cent pow er los s in the
o
m
----
jbl I
J
----
k;
o
FIG. 2.13.—Equiv-
a len t circu it of ha lf
of lin e in F ig. 2.12.
ca vity a nd , th ere fore, Pi w ill be about 15 per cent
grea ter than PO becaus e of los s through the firs t half
of the ca vity .
If the center of the cavity O-O is chos en as the
reference plane, Th4ven in’s theorem m ay be us ed to
replace the actual generator to the left of i-i by an
equivalen t one at O-O. The equivalent generator
has an internal adm ittance Y’ obtained by open-
circu itin g th e a ctu al cu rren t gen era tor a nd ob s erv in g
the adm ittance s een look ing to the left from 04
The intens ity of. the new curren t s ource equals the
cu rren t flow in g th rou gh a s h ort circu it a cros s O-O.
Equa tion (4 o) gives th e equ iva len t gen era tor a dm itta nce
To obta in the s hort-circu it current through O-O, the various incid ent
and reflected w aves are added , Fig. 2 .13 . If the currenteflect ion coefE-
Cient r’l = (Y — YO)/ ( Y + Yo), then the to al curren t at O-O oan be
s how n to be 1101 = 1/ bl for bl large. Now , the voltage at the inpu t
term in als is th e cu rren t I d ivid ed by the tota l conductance or
I
Vi =
()
2“
l+gcb; +gz :
SEC. 2.3]
CAVITY RES ’ONA TOES
23
The voltage at the cen ter of the cavity is found in a s im ilar manner,
I
1
““=Gl
1
–+$+$+:
b:
and
Vo
—.
b
v;
1,
(54)
w hich is the s am e res u lt that w as obta ined w hen cavity d is s ipa tion w as
neglected . Thus , it is s een that the voltage s tepup is proportiona l to the
squ are root of the input Q (s im ilarly the voltage s tepd ow n is proportiona l
to the s quare root of the output Q).
Th is cou ld have been anticipa ted
on a con serva tion -of-en ergy ba sis , s in ce the adm ittan ce tran sform ation
is proportional to the external Q.
(a)
(b)
FIG. 2,14.—Cavity with capacit ive pos t s and equ iva len t cir cu it .
A practical TR tube w ill d iffer from this cavity in that it w ill have a
pair of pos ts acros s the guide at a voltage maximum to form a small
s park gap, Fig. 2 .14a. The gap, of cours e, add s a capacitive load acros s
the cavity . How ever, m ore deta ile exam ination ind ica tes that there is
an inductive reacta ce in each of the pos ts form ing the gap and , there-
fore, the equiva len t circu it is s im ilar to that of Fig. 2“14b. The net
s us ceptance acros s he cen ter of the cavity is
jz)o = –j(x. – xc)–’.
In a s m ilar manner i can be s how n that the voltage s tepup ra tio
from the external term inals to the cen ter of the cavity is proportiona l
to the corres pond ing external Q. How ever, the voltage acros s the gap v.
is greater than the cavity voltage Vo by a factor
and the total trans form ation ra tio is
(55)
v=
b.
–= b,—.
v,
b. – b.
(56)
24
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.23
The Q of s uch a cavity can be s how n to be
Q.,= 21~+’)K1(;~+’o,
(
)
;+ $+9,
1
(57)
27r
‘0 “f b, and b,>> b,.
‘here ‘1 = ‘an -’ F, = 5 – 31
Direct-cou plin g A tten ua tion .—Du rin g th e tra nsm ittin g period th ere is
a d is charge acros s the gap w h ich for all practica l purpos es m ay be, con-
Y++y ’
(a) (b)
FJ~ . 2.15 .—Cavity with shor t -circu ited pos t and equiva len t circu it .
CEKl
(a) (b)
FSQ.
2.16.—(a)Magnet ic field in a cavity with shor t -circu ited post . (b) Cylin&lca l
ca vit y wit h two ou tpu t lin es.
s id ered to have zero dy nam ic impedance. S ince the d is charge on ly
s hort-circu its the capacitor X. in Fig. 2 .14 , the tota l s us ceptance acros s
the guide is not in iin ite, bu t is equal to ‘jb.. As a res ult, the a ttenu-
ation betw een the input and the output term inals w ill be large, bu t fin ite.
To ca lcula te the attenuation , a ll voltages and adm ittances are referred
to the center of the cavity , Fig. 2“150 . Tow ard the left from the
pos t, there is an adm ittance Y =
l/ b~ – jbJ2 , and tow ard the right
Y’ =
g,/b:
– jbo/ 2 and , therefore, the circu it is that of Fig. 2 .15b. The
ratio of the pow er delivered to the load , gz~b~, to the available pow er is
Thus , th e d irect-coup led
P
4g*
P-
— = b:b;(bo + b.)’”
(58)
pow e r is invers ely proportiona l to the prod uct
SEC.2.4]
LOOP- AND IRIS -CO UPLED CAVIT IES 25
of the external Q’s , and it a ls o varies invers ely w ith the s quare of the pos t
5UsCeptanCebL .
A qualita tive but us eful concept of d irect-coupling attenuation
as s um es that the cavity s hort-circu ited by the pos t, Fig. 2 .16a, m ay be
thought of as tw o w aveguides in para llel that are bey ond cutoff a t the
opera ting frequency . The incid en t pow er is exponentia lly attenuated
betw e en the input a d ou tput term inals of the ca vity , and the attenuation
increas es w ith the d iam eter of the center pos t. Th is , of cours e, is s im ply
a res tatem ent of the fact that the attenuation increas es w ith the pos t
s us cepta nce. If a cy lind rical ca vity is con sid ered , Fig. 2 .16b, it becom es
apparen t that the attenuation d ecreas es rapid ly as the angle a betw een
the input and the output lines is m ade les s than 180°.
2 .4 . Com paris on of Loop-coupled and Ins -coupled Cavities .-In the
analy s is of res onant cavities thus far, it has been as s umed that the
externa l cavities have been connected to the res onant s tructure by direct
in du ctive or capa cit v e couplin g.
That is , it has been as s umed that
there is no mutual reactance be-
tw e en the couplings and the res o-
nant c i r c u it. The equivalent
circuit as sum ed m ay be either the
s im ple one in S ec. 2-1 or the m ore
exact one s how n in Fig. 2 .llb.
A better repres enta tion of the
m
92
F IG. 2,17.—Equ iva 1en t cir cu it of TR t ube
including losses.
TR tube is s how n in Fig. 2.17 w here b, and b~ are the coupling s us -
ceptances , bO is the equivalent capacitive s us ceptance of the gap and
pos ts acros s the cavity , g. is t e s hunt conductance of the cavity . If
b = blbO/ (2bl X bo), and b! is s im ila rly d efin ed for bz and if bl and bg are
large,
(59)
All th es e ca lcu la tion s a nd equ iva len t circu its a re ba s ed on th e a s s ump-
tion that no m utual couplings exis t betw e en b, and
bz
and the res t of the
circuit. This cond ition is s atis fied if th in ind uctive or capacitive iris es
are used for bl and bz , Fig. 2 .18u.1
How ever, coupling to a cavity can be
done equally w ell by means of a loop link ing the magnetic field of the
cavity , Fig. 2 .18b. If th is is done, it is neces sary to cons ider the m utual
coupling betw een loop and cavity , and the equivalent circuit may be
1F or equiva lent circu it s of var ious obstaclea in wavegu idea , see “Wave Gu id
H an dbook,” RL Repor t No. 432/7/44, a nd Vol. 10 of th is ser ies.
26 LINEAR THEORY OF HIGH-Q TR TUBES
[Sm . 24
draw n as in Fig. 2 .19 . It has been s how n by W. W. Hans en l that the
trans form ed conductance s een at the inpu t term inals varies invers ely
w ith th e s qua re of th e m utual con du cta nce
Ml
and Mz for
bl
and
bz
large,
(a)
EkG.2 .18.—Ir is -coup led cavity (a ) and loopcoup led cavity
(b, = l/ JJ . The mutu l inductance is proportiona l to
and at res ona nce
Gi = G (A/Zi)2 + G~(ze/zi)’
(b)
(b).
the loop area
(60)
w h ere Gi is th e in put con ducta nce, A is the area of the cavity in a plane
para lle l to th e E vector, Z1 and 2.
are the areas of the inpu t and out-
-lJN~@’2 %:%!!::;:::::::
s ions for Q and d irect ‘coupling
w h ich are com pletely ana logous
F1o. 2 .19 .—Equ ivalent circu it of loop -
to th os e for th e iris -coupled ca vity
coupled cavity.
ca n b e d erived .
Although a deta iled d is cus s ion of m ethod s for coupling to cavities
w ill be res erved for a later s ection , it is of in teres t to mak e a s imple ‘
(a)
(b)
(c)
Fm . 2.2C.-Met hod s of couplin g t o a ca vit y.
com paris on betw een loop and ins coupling. T ere are three cas es to be
considered:
1 . If the coupling iris is a s m all circular hole in a thin pla te, Fig. 220a,
the s us ceptance is ind uctive and varies nearly as
d-g.
1W. W. Hansen ,J . App. Ph gm , 9, 654 t o 603 (1938).
SEC.2.5]
METHODS OF TUNING
27
2 . If the iris is s ymmetrica l, of th ty pe s how n in Fig. 2.20b, th e
s us ceptan ce is ind uctive and va ries nearly as d–z.
3 . If the coupling is a small loop, Fig. 2 .20c, the inductance is pro-
port ona l to its length and the s us ceptance, then , varies as d –l.
The adm ittance trans formation ra tio N in thes e three cas es may be
tabu la ted as in Table 2“1 .
TABLE 2 1.—ADMITTANCETRANSFORMATIONRATIO N FORTHREECASES
coupling
N va ries a s
Circular ir is
bz, d-6
Symmet r ica l induct ive ir is
b,, d -,
Small loop
b,, d -,
It s hou ld be poin ted ou t tha t thes e varia tions are for sm all loops or
iris es . For iris es it is further as sum ed tha t the m eta l pla te is very th in .
As the open ing of the iris or the length of the loop is m ad e larger, the ra te
of change of b w ith d b ecome s s low e r.
The ra tes ind ica ted in the las t
colum n m ay be d eceptive becau se, a lthough the tolera nce on the circu lar
iris is the m os t s evere , a round hole m ay be made to much clos er toler-
a nces tha n is pos s ible w ith th e oth er s tru ctu res .
A s ymmetrica l inductive iris is m ore d ifficu lt to mak e to accura te
tolerances ; bu t m os t d ifficu lt of a ll is the loop w hich is made of fa irly
th ick w ire, to give it rigid ity , bu t is ben t on a rad ius w hich is on ly a few
tim es the th ick nes s of the w ire. Des pite th is d ifficu lty , it w a s pos s ib le
to mak e coupling loops for 0-cm TR tubes in w hich the adm ittance
trans form ation ra tio w as held to a tolerance of about +10 er cen t.
2 .6 . Method s of Tun ing.-It is us ua lly requ ired that a given TR
tube opera te anyw here w ith in a band of frequencies t a t is w id e com -
pa red w ith its bandw id th (Aw >> a / Q).
Th e re s onan t circu it, th ere fore ,
mus t be made tunable. From a cons id era tion of Fig. 2“17 it is s een
that varia tion of either the gap capacitance or the cavity inductance
change s th e re sonant frequency .
It is not d es irable to tune by vary ing
the coupling s us ceptances s ince the ins ertion los s and leak age pow er
change rapid ly w h ile the tun ing ra te rem ains very s low .
Variation of the gap capacitance is a conven ien t m ethod of tuning
if the m echanica l d es ign of the tube perm its a mechanica l motion to be
trans m itted in to the low -pres s ure region w h ere the s pa rk gap is loca ted .
S evera l TR tubes have been des igned w ith s uch a tun ing s y s tem . The
h igh-frequency end of the tuning range is genera lly lim ited by the leak -
age pow er, w h ich increas es w ith the gap length . It i us ua lly pos s ible in
th is w ay to get a tuning range of 10 to 15 per cen t and s till maintain
sa tis fa ctory leakage pow er le ve ls .
The inductance of the circu it m ay be changed by a variety of m echan-
ica l s chem es . Bas ica lly , w hat is d es ired is to change the m agnetic field
s trength in a given region , and thus change the energy s torage r the
28
LINEAR THEORY OF HIGH-Q R T1’ ES [SEC.25
inductance.
A vane acros s a w aveguid e acts as an inductive lumped
s us ceptance, Fig. 2 ,21, becaus e it caus es a local concentra tion of the
magnetic field . Thus , the cavity can be made tunable as s how n in
Fig. 222. S lid ing iris es w hich continually m ak e ood contact w ith the
n ,
Magneticines(H)
kl~ , 2 .21.—Waveguide with induct ive vane .
g o
-,
u ,,
~~
Inductive
Variablenductive
coupling
tuningirises
irises
F IC. 2.22.—Va ria ble in du ct ive ir ises
for t u ning a cavit y.
top and the bottom of the guide pres en t a des ign problem w hich is
m echanica lly very d ifficult. Figure 223 s hom x an equivalent s cheme
commonly us ed w ith cell-ty pe TR tubes , In tubes of th is ty pe the gap
and low -pres s ure region are confined w ith in a glas s envelope w hos e
d iameter is small compared w ith the cavity d iameter. .4 m etal s lug,
Met
slug
(a)
(b)
FIG.223.-Meta l slu s for t un in g a TR ca vity.
us ually a s crew , is pus hed in to the cavity .
Th is adds a lum ped induct-
ance in parallel w ith the res t of the circu it, and the frequency increases
as the slug is pushed in to the cavity.
A change in the cavity d iameter has
an equiva lent effect, and in fact, the s lug m ay be cons id ered s im ply as a
partia l change in the equivalent cavity d iam eter.
SEC.2.6]
EQUIVALENT-CIRCUIT CALCULATIONS
29
A third m ethod of tuning involves changing the total circu it capaci-
tance by means of a metal s lug that can be moved in and out rad ially ,
but w hich is ins ulated from the cavity , Fig. 2 .23b. Although the geo-
m etric capacitance of the s lug does not vary w ith pos ition , the electric
field varies from a maximum at the center to zero at the outs id e of the
cavity , The d is placement curren ts flow ing through the capacitance
betw een the s lug and cavity increas e as the s lug is moved tow ard the
center.
Moving the capacitive slug toward the center decreases the resonant
frequency of the cavity.
A method that is mark ed ly d ifferen t from thos e jus t d es cribed
em ploy s an auxiliary cavity tuned by one of thes e m eth d s , and coupled
to the main TR cavity n s uch a w ay as to act as a variable eus ceptance
in parallel w ith it. The s us ceptance an tak e on pos itive or negative
va lues as the auxiliary cavity is tuned to h igher or low e r frequencies than
the incid ent frequency . In general, th is s cheme introduces a certain
amount of exces s los s in to the circu it. It has the advantage, how ever,
that a precis e tuning mechanism may be built in to it w hich may be
calibra ted . Th is is not generally pos s ible in the TR cavity .
The tw o
catities may be butted together and coupled by an iris , or they may be
joined by a trans mis sion line about k / 2 long and coupled either by loops
or b y iris e s .
2 .6 . Equ ivalent-circu it Ca lcu la tion s . Inse?tion Los s .—In previou s
s ections it w as s how n t at a res onant cavity cou ld be repres en ted to a
good approximation by an equiva- 1A
len t parallel-res onant circuit. The ‘
pla ne of referen ce is arbitrary ; bu t
it is genera lly conven ien t to refer
all adm ittances to the input ter-
Sm
inals . Th is is ind ica ted ~in Fig. ‘
2 .24 w here all adm ittances have
=or T
been normaliz ed w ith res pect to Fm. 224.-Cavity and equ ivalen t circu it
Y,, g: = gJ ~ is th e a ppa ren t ca vity
r e fe r r ed to termina ls AA.
conducta nce, g~ = g&/bJ 2 k the apparen t load conductance, and b is
the input s us ceptance. On the bas is of th is s imple circu it, a number of
u sefu l rela tion s hips in volvin g Q, in sertion los s , an d in pu t s ta nd in g-w a ve
ra tio m ay be d erived .
Th e tran sm ism”on T of the circuit is the ra tio of the pow er d is s ipa ted
in aL to the Dow er available from the genera tor.
Th e in sertion loss L
.—
w ill be d efin ed as
– 10 loglo T,
T = (1 + 9.%)’ + b“
w h ere the generator is as sum ed to have unit in ternal
(61)
conductance.
30 LINEAR THEORY OF HIGH-Q TR TUBES [SEC.2.6
Cam’ty
Q.—In S ec. 2 .2 an expres s ion for Q w as derived . Equation (52)
m ay be rew ritten in the follow ing form s:
‘0 =&d(:k)b
1
—= Qo&l
QLI = 2(9;+ I) ~(lnk)
1’
(62)
1 db
Qo -&_+-.
~2=2(g:+l+ g.)_=
w here Q’ is the unloaded Q of the cavity ; QL1 is the Q of the cavity loaded
only at its input term inals by a matched genera tor; and QL2 is the Q of
the cavity loaded at both the input and outpu t term ina ls .
The s tand ing w ave s et up in a transm is s ion line by a d is continuity
is equal to the sum of the incident and the refl cted w aves .
Th e ra tio
of the maximum voltage to the m inimum voltage of the s tand ing w ave is
the ataru lin g-w au e ratio T , and is d efined by
(63)
w h ere r is the voltage reflection coefficien t, For the cavity w h os e input
a tilttance is
r=
/ rl =
If th is is s ubs titu ted
Y = (g. + g:) + jb ,
YO– Y=
1 – [(9L + d) + ~bl,
Y,+Y
v’(1 – g. – g;)’ + b’.
v’(1 + g.+ g:)’+ b’
in to Eq. ( 3),
(64)
N(1 +g. +g:)’+ f)’+ <(1 – g. – g;)’ +b’
(65)
‘=ti(l+g ~+g:)’+b’ -~(l-g. -g:)’ +bz”
Exam ination of Eq. (61) ind icates that the pow er to the load g. fa lls
to half its maximum value w hen Ibl = (1 + gL + g.), and for th is cond i-
tion the s tand ing-w a ve ratio w ill be
(1 + g. + g:) + <1 + (gL -t 9:)2.
‘}’ = (1 + gL + 9:) – %“1 + (9L + 9:)2
If the input s tand ing-w ave ratio at res onance is
(66)
1
rg= g-l=
(gL + g:)’
S rw .2.6]
EQUIVALENT-CIRCUIT C’ALCULA TIONS 31
then
(67)
It s hou ld be noted tha t a s ubs titu tion of l/ @ for ~ res ults in the id entica l
equation.
S im ilarly , Eq. (65) m ay bes olved forb, and
b=-
(68)
Figure 2 .2 is a plot of the s tand ing-w ave ra tio agains t frequency ,
m eas ured at the input of a ty pica l TR cavity w ith no output load ing.
A curve of b, calcu la ted from the
data by means of Eq. (6 ) s s uper-
10-
imposed.
The curve of b is a
9 -
s tra igh t line over the range con-
s id ered , w hich is w hat w ou ld be
obta ined from a s imple parallel-
resonan t circuit .
Optimum Coupling. —Maximum
pow e r is d elivered to th e loa d g~ for
a give n g;w hen gL = 1 + g:.
Simi-
larly , a red uction in g: res ults in an
increas e in T. It is genera lly nec-
es s ary , how ever, to mak e the bes t 1
-
p os s ib le comp rom is e b etw e en lea k -
age pow e r and ins ertion los s .
-2 -1
Lea k age p owe r w ill b e d is cu s s ed
A f Mc\sec
in d eta il in Ch ap. 5; h ow e ver, it has
a lread y been s een that the d irect-
coupled pow er varies invers ely as
F]Q. 2 .25.—Input s tanding-wave ra t io
the prod u t of th e input and outpu t
r, and susceptance b for a 1B27 TR cavit y;
@ = a’, = 1.30, fO = 3260 Me/see, QO =
Q’s for a given tube and cavity , and z~cu # = I91o.
it w ill be s een la ter tha t the arc
lea ka ge pow e r a nd s pik e lea ka ge en ergy a re s ubs ta ntia lly in depen den t of
the input Q, but vary invers ely w ith the ou tp t Q.
It is im portant to choos e the bes t opera ting poin t for a certa in s peci-
fi d ins ertion los s tha t w ill give us able values of d irect-coupled and arc
leak age pow er, and s pik e leak age energy . Figure 2 .26 is a plot of in s er-
tion los s L in db vs . g. for various values of g:. It is obvious that there
are an in fin ite num ber of com b nations of
9L
and g: that w ill give the
s am e los s . S ince the arc leakage pow er and s pik e energy increas e w ith
increas ing g’, on ly values of g~ ~ (1 + gj) w ill be chos en .
32
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.2.6
Let us in ves tiga te the con dition s that give m axim um d irect-cou plin g
attenuation for a given va lue of L.
In Eq. (61) let b = O and subs titu te
the follow ing quantities : g: = N~., g~ = N1/ N2. Then s olve for the
prod uct N1N2 wh ich is proportion al to the d irecbcou plin g a ttenu ation,
N,N2 =
N;
2
––l– Nlgcf2
T
-“ ‘6’)
If th e de riv at v e d(NIN,)/dNl k s et equal to z ero, a s olu tion for the poin ts
FIG.
~o
1
OL
2
3
I
1
Max.directcouplingattenuation
-1
~ -2
, , <
[/ 1
I ~
r
&
0
%’
(l+ Lre+9L)2
-3
/
.4~LJ I
2.26.—P lot of in ser tion loss in decibels a s a fu nct ion of g~ for va riou s va lu es of
9 ‘6
of m axim um or m in im um d irect-coupling attenuation for a given va lue
of low -level tra nsm is s ion may be obta in ed ,
d(N,N,)
4(2-$) +;(1-+)=” ’70)
=N; +N; :+Nl~
dN,
The roots of th is equation are mos t eas ily found by as s um ing s pecific
va lu es of T , and then us ing Hom er’s m ethod or s om e s im ilar approxim a-
tion . on ly pos itive, rea l roots are of in teres t. Inves tiga tion s how s that
thes e roots d o ind eed corres pond to a m axim um value of NINZJ and , there-
fore , repre s en t max imum a ttenua tion .
The s e solu tion s -a re p lotte d in Fig.
2 .26 s uperim pos ed on the los s con tours as the locus of poin ts giving m axi-
mum d ire ct -c oupling a tte nua tion .
For va lues of g: >0 .1 , the optimum
coupling cond ition lies s om ew h ere bet w e en “ equal” coupling (Nl = N2),
and “matched -ou tpu t” coupling (g& = 1 + g: or Na = 1 + Nlg,).
SEC.2.6]
EQUIVALENT CIRCUIT CALCULATIONS
33
For bes t perform ance in the receiving period it is d es irab e to us e a
“matched-output”
coupling s ince varia tions in the load cond uctance gh
caus e the leas t chang of T in th is region .
Th is is im portan t becaus e
of the com para tively large varia tions that are found in the adm ittance
of cry s ta l d etectors . The conductance s pread may be as large as 4 to 1
(from g. = YO/ 2 to 2Yo), even a fter the cry s ta l moun t has been des igned
to m inim iz e th is s pread . In Table 2“2 the ins ertion los s L in d e cib els
and rela tive leak age pow er are lis ted corres pond ing to a cry sta l con -
ductance g= = Y,/ 2 , Y ,, 2 Y ,. The leak a e pow er has been s epara ted
in to d irect-coupled pow er, and gas (fla t or s pik e) leak age pow er.
Th e
la tter is s im ply proportiona l to Nil w h i e the form er is proportiona l to
(NIN,)-’.
TABLE2 ,2.—COMPARISONF1NSEETIONos s , GAS LEAKAGEPOWER,ANDDIB~CT-
COUPLEDPOWERFORTHREE DIFEEEENTCOUPLINGCONDITIONS
Allad jus ted to L = –1 .25dbforg. = 1
In ser t ion loss db
Gas leakage power
Direct -coupled power
i
%0 Matched
Equal
&latched
Matched
~ou-
qual
Matched
Matched
~ou-
‘qua’ Matched
cOu-
input
output
input output input
pling
pling
output
pling
— — —
.—
0.5
–2 .46 –2.14 –1 .76
0.375 0.5
0.666
0.57
0.5
0.58
1
–1 .25 –1.25 –1 25
0.75 1 1.33
1.15 1
1.16
2
–1,0
–1.06 –1 .76
1.5 2
2,66 2.3
2
2.32
Exam ination of Ta ble 2 .2 ind ica tes tha t the d irect-coupled pow e r is a
rather ins ens itive function of the particu lar coupling. The ins ertion
los s und rgoes the larges t excurs ions Trith m atched -inpu t coupling.
Con vers ely , th elea ka ge pow e ris s m alles t for m atch ed -in pu t and larges t
TABLE2.3.—SUMMARYOF FORMULASFOR COUPLINGTHROUGHA TR CAVITY
Inpu t s t anding-
wave r at io
T
Q.,
“ c
QL I
Qo
h fa t ched inpu t
1
l–g:=l–2p
1–T
d=—
2
2
1–T
?:
l+g:–2– T
Equa l coup ling
3fatchcxl output
1+9=2 (>-1)
1 + 2g:
()
–2
1+;
= (1 –p)’
(1 +g:)-’ = 1 –2?p
~
—
1–<T
9:
1–T
2+g:–
271 + d
2
9:
(1 - W)
—
9:
l+g:–
—
1–T
2 – ~–T
l+g; –
34
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC. 2.7
for matched -output coupling. Equal coupling has the advantage of
eas e of mechan ical cons truction if the line to the r ceiver is of the s ame
ty pe as the trans mitt r line (s am e s iz e coaxia l line or w aveguid e), s ince
the tube can be m ade s ymmetrica l.
S pecia Ca .s es .-A few s pecia l form ulas m ay be derived for the three
couplings jus t d es cribed and the res ults are s how n in Table 2 ,3 .
2 .7 . Electrom agnetic Calcula tions of Cavities . -Although the bas ic
phenomena of the res onant cavity are extrem ely s im ple, the exact
calcula tion of the res onan t frequency Q voltage-s t pup ra tio, and
equ ivalent s hunt conductance becom es very d ifficu lt w hen practi a l
s hapes of cavities Wus t be ana ly zed .
Fa irly s tra igh tforw a rd m eth od s
~f a na ly z in g cy lin d rica l, s p he rica l, a nd s im ila r ca vitie s h av e b ee n d eriv ed
by a num ber of authors . 1 ,2 For TR cavities or k ly s tron cavities (rhum ba-
trons ), the field s can no longer be expres s ed by s imple functions , bu t
mus t be compounded out of a s um of many d ifferent m odes , s o ad jus ted
as to s a tis fy the boundary cond itions that tangentia l E is z ero at the
meta l w a lls .
At the pres en t tim e, an exact s olu tion has not been obtained for the
cy lind rical cavity w ith conical pos ts .
x tremely a ccu ra te ca lcu la tion s
have been made, how ever, in w hich the pos ts w ere as s umed to be right
circu la r cy lin ders , a nd wh ere s uita ble m ea ns of es tim atin g th e equ iva len t
d iameter of the cy linder w ere determ ined .3 ,4J By thes e means it has
been pos s ible to ca lcula te the res onant frequency w ith an error of les s
than 1 per cen t.
The m athematica l techniques us ed in thes e calcu la tions w ill not be
d is cus s d here s ince they are long and involved . The s olu tions obtained ,
how ever, give the res onan t frequency in term s of an effective para llel
L
and C, w here the C is a function of the s ta tic capacitance of the pos t,
and L is as socia ted w ith the energy s torage in he annular ring betw een
A m ore recen t and ad vanced m ethod in the art of treating cy lind rica l
res onant cavities has been us ed by N. Marcuvitz of the Rad iation Labora-
tory . Th is methodh c ns id ers the cavity as c mpos ed of s evera l rad ia l
trans mis s ion lines of various im ped ances (heights ) and lengths (rad ii).
Although th is method has not been applied to TR cavities , its us e w ould
1W. W. Han sen , J ou r. App. Physics 9, 654 (1938); 10,38 (1939).
z S . A. Sch elk unoff, E lect romagn et ic Waues, Van Nost ra nd, N , Y., 1943.
3H, A. Bethe, R. E. Marshak, J . Schwinger ,
“ Theoret ica l Result s on the TR
Box)” NDRC Repor t D1-116, J an. 20, 1943.
4H. A. Bethe, R. E. Ivlarshak, J . Schwinger , “ Theory of the TR Box, ” NDRC
Repor t 14-128, May 14, 1943.
5 J , S chwinger ,
“Theoret ica l Trea tment of a Cylindr ical TR Box, ” RL Group
Report 43-8/26/42,
s Vol. 8, Chap. 8,
SEC.2.8]
CELL-TYPE TR TUBES 35
re su lt in great ma thema tica l s imp lifica tion , w hen rad ia l-transmis s ion -line
charts become availab le .
The coupling betw een the cavity and an external load or s ource of
pow er m ay tak e any of s evera l form s .
It may be a small hole in the w all
of the avity , a loop, or a capacitive probe.
The firs t tw o, the hole and
the loop, are us ed almos t exclus ively in TR cavities . The small hole or
iris is equ ivalent to the large s hunt ind ucti e s us ceptances in the equiv-
alent circu its of S ees . 2 .1 and 2.2; the loop has been briefly d es cribed in
S ec. 23.
The ca lculation of the pow er flow through an iris involves the m atch-
ing of three field s : the unperturbed field in the cavity , the unperturbed
field in the w aveguide or s pace into w hich the iris a llow s pow er to flow ,
and the field in the immed ia te vicinity of the iris .
Here again , the
m athem atical com plica tions grow roughly exponentia lly w ith the s iz e
of the hole. If the hole is very small, then it can be as s umed that the
field in the cavity and w aveguide are completely und is turbed by the
pres ence of the hole, except in its im med ia te vicin ity . Furtherm ore, it
can be as s umed that the tangentia l H w ill be cons tant in magnitude
and phas e over the entire w indow .
With thes e lim iting as sum ptions ,
it has been pos s ible to ca lcu la te correctly the load ing and frequency
s hift ca us ed by ind uctive iris es in TR cavities .1 ,23 ,4
Loop coupling, although bas ica ily very s im ple, is com plica ted by the
fin ite th ick nes s of the w ire and the s tand ing w ave along the loop. As a
res ult, n o accu ra te s olutions exis t for th is problem .
2.8 . Cell-ty pe TR Tubes . Tube Ty pes .—The cell-t pe TR tube is a
unit cons is ting of a s park gap in a low -pres s ure gas eous a tm osphere,
enclos ed in a glas s envelope. Electrodes are brought ou t through the
glas s for connecting to an external cavity , w h ich in com bina tion w ith the
TR tube is a res onant circuit. The tube is placed in the cavitv s o that
there is a m axim um voltage acros s the gap.
One of the earlies t 10-cm m icrow ave TR tubes is s how n in Fig. 2 .27.
It w as developed by J. L. Law s on at the Rad iation Labora tory , and con-
s is ted of a s park gap in a small glas s tube w hich plugged in to a cavity .
The leak age pow e r of th is tube w a s und oubted ly high, and becaus e of the
small gas volume its life w as s hort; how ever, it had only to protect a
ground ed -grid -triod e firs t d etector, w h ich it d id . The firs t “m od ern”
]H. A , Be the , “Lumped Cons tan tsfor Small Irises ,” RL Report 43 -22 ,Lfar. 22 ,
1943.
z H. A. Bethe, “Theory of Side Window sin Waveguides , ’]RL Report 199,Apr. 4 ,
1943
3H, A, Bethe, “Excita tion of Cavit ies thr ugh Windo\ vs , RL Report 202,Apr. 9 ,
1943.
4H. A , Be the , “Theory of Diffraction by SmallHoles ,” RL Report 128 ,Jan . 2?3 ,
1942.
36
LINEAR THEORY OF HTGH-Q TR TUBES [SEC. 2.8
m icrow ave TR tube w as the s o-ca lled s oft Su tton tube d eveloped by the
s im ple exped ien t of adm itting gas in to a Sutton reflex k ly s tron tube
and us ing it, cavity and a ll, a s a TR tube. One cavity and three tubes
w ere us ed to tune the th ree band s 9 .1 cm + 1 per cen t, 10 cm + 1 per
cen t, and 10 .7 cm ~ 1 per cen t. The tubes w ere id en tica l except tha t
FIG. 2.27.—Early 10-cm TR tube.
they w e re pretuned by vary ing the
gap s pacing before they w ere
evacuated.
The 721 .4 TR tube and la ter
the 724A tube, w ere engineered
by a group under A. L. Samuel a t
th e B ell Teleph on e La bora tories . 1
Thes e tw o tubes are us ed in the
9 -cm to 1l-cm and 3. l-cm to 3 .5 -
cm band s res pectively , and ,
together w it h the 1B27 tube
d eveloped coopera tively by the
Rad ia tion Labora tory and S y l-
vania Electrica l Products Com -
pany , are the mos t w id ely us ed
m icrow ave cell-ty pe TR tubes .
They are illus tra ted in Fig. 2 .28 .
The s park gap is formed betw een
the sm all en ds of tw o copper con es .
The cones are d raw n from “th in
copper s heet and have circu lar
flanges a t their bas es . A cy lind er
of low -los s gla ss s epa ra tes th e tw o
flanges . In ord er to mak e a bu t
s ea l betw e en the gla ss and the copper, it is n eces s ary to balance th e s tra ins
by s im ulta neou sly s ea ling gla ss cy lin ders to th e ba ck s of th e flanges , as in
Fig. 2 .29 . After the d is k s ea ls have been m ade, the k eep-a live electrod e
is s ea led in a t one end , the tube is pretuned and evacua t d , and the other
end is s ea led off.
Tw o other m icrow ave cell-ty pe TR tubes tha t have been us ed at
longer w avelengths (about 25 cm ) are the 1B23 tube and the 1B40 tube.
The s park gap in the 1B23 tube, Fig. 2 .30 , is betw een the ins id e of the cone
and the w ire electrod e. The 1B40 tube is clifferen t from any of the other
tubes in th is group, in that it has no r-f electrod es w ith in the glas s
envelope. It is u s ed w it a cavity s uch as tha t s how n in Fig. 2 .31 , and
an electrodeless d is charge is s truck betw een the tw o cy lind ers of the
1Samuel,Mccrae, and Mum foral,“Gas Dis cha rgeTR sw itch,” 13TLMM-42_14@_
2 6, Apr 1 7, 19 42 .
SEC.
28]
CELL-T YPE TR TUBES
37
externa l cavity . Although th is s im plifies the d es ign , the leak age pow er
of th is tube is very large and is tolerable on ly in certa in s pecia l applica -
.-
FIG.228.-TR t ubes t ypes lB
27.724 B, 721B.
tions . The cons truction is very s im ple for it involves on ly Kovar-gla s s
seals .
The cell-ty pe TR tubes have the advantage tha t they m ay be us ed
in a variety of circu its and cavitieq
and over a w id e range of frequencies
With s uitable cavities the 1B27 tube
has been us ed at w a velengths ranging
I
from 8 cm to 13 cm . The 721B, 724B, Cow er
1B23 , and 1B40 tubes are jixed -tuned ‘Ianges
lass
By vary ing the s pacing each
ers
tubes .
is ad jus ted to res onate at a s pecified
frequency in a cavity of s tandard
d im ens ions . Once the, tube is s ea led
FIG.2.29.—Firsts tagein as s embling
cell-typeTR tube. Glas scy lind ersare
off, no further ad ju s tm ents of gap
s ealedsimultaneous lyo both s idesof
s acing can be made, and the com -
the f langes.
plete TR as s em bly is tuned by inductive or capacitive s lugs in the
externa l cavity as d es cribed in S ec. 2“5 . The 1B27 is a tunable
tube. The gap s pacing may be varied by means of a d ifferen tia l s crew
mechanism tha t m oves one of the cones in or ou t. The cone is s ea led , of
38 LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.28
cours e, to maintain a low -pres s ure region around the gap. In a given
cavity , it is pos s ib le to tune th 1B27 tube from 10 to 15 per cen .
FIG. 2.30.—1B23 TR
tube.
keep-alive
electrode
Fx~. 2 .31.—1B4O TR tube.
The critica l d im ens ions of the 721B, 724B, and 1B27 tubes are s how n
in Fig. 2 .32 . Thes e d im ens ions are the glas s d iam eter, th d is tance
+D3+
9
t-- %-4
FIG.2.32.—Critical dimen-
UiOnSf i’21B, 724B, and 1B27
t ubes given in Table 2.4.
betw e en flanges , the cone angle, the gap s pa c-
ing, the cone d iam eter, and the flange d iam -
eters . Table 2 .4 gives the d im ens ions of thes e
th ree tu be s .
The us e of h igh-Q cavities w ith larg
adm itta nce tra ns forma tion ra tios re qu ires th at
the los ses in the cavity be held to a m in im um .
The glas s cy lind er betw e en the d is k s of the TR
tube is in a region of mod era tely h igh field .
The d ielectric los s in the gltm s can m ak e a con-
s id erable con tribu tion to the effective s hun t
conductance gc of the cavity . Corn ing 707
glas s has the low es t d ielectric los s of any of
the common glas s es . Only fu s ed quartz and
Corn ing “Vicor” 709 glas s , w h ich is abou t 90
per cen t quartz , have low er los s es . Thes e ,
how ever, cannot be s ea led to copper becaus e
of th eir h igh m eltin g poin ts an d low coefficien ts of expa ns ion . In Ta ble 2 “5
SEC.2.8]
CELL-TYPE TR TUBES
39
TABLE 24.-CRITICAL DIMENSIONSOF CELL-TYPE TR TUBES AS INDICATEDIN FIG.
232
Dimen sion s a re in In ch es
Dimensions
721B
D,
1*
D,
1 ++
D,
1***
D, 0.075
9
0.030
18°
; 0 .825
t 0.030
I
724B
0.372
0 .622max .
0.615 min.
0.622 max.
0.615 m in .
0.020
0 030
18°
0.410
0 030
1B27
;*&
1 062
I.000
0.125
o.oo2t00.035
18°
0.670
0.030
the com plex d ielectric cons tan t c = c’ + jc” is given for Corn ing 707 glas s
a nd 7 05 gla s s .
TABLE2.5 .—COMPLEXDIELECTRICCONSTANTOF 707 AND705 GLASSES
707glass
705glass
A
e’ t“/ t’
t’
C“/ E’
25 cm
4.0 0.0019 4 72 0.0047
10 cm
4.0 0.0019 4 .72
3.2cm
0.0052
3.99
0 .0021 4 .71
0.0061
The’ copper flanges extend ing bey ond the glas s are m ad e th in s o tha t
they can be d eform ed by the clamping rings of the cavity , and can als o
be pres s ed tigh tly agains t the cavity s hou ld er w ithou t break ing the glas s
s ea l. Th is a llow s the res is tance of the con tact betw een the flanges and
the cavity to be held to a m inimum .
Cavities ad Tuni g.—The TR cavity m os t common ly us ed in the
3 -cm and lo-cm band s is illus tra ted in Fig. 2 .33. It is cy lind rica l, and
opera tes in w hat m ay be d es cribed as a m od ified TEO1o-m ode.
There
is no varia tion of the field w ith angle, and except in the vicin ity of the
pos ts , there is no varia tion of E between the top and the bottom of the
Cavity.
For a given tube, the heigh t h of the cavity is us ua lly main ta ined
con s ta nt, a nd th e d iamete r D is va ried to m a ke ca vities for va riou s tuning
ranges . To perm it the tube to be connected in to the cavity , the cavity
is s plit in to tw o h alves a lon g a d iametral pla ne.
S in ce th e lin es of cu rre nt
flow are rad ial on the top and bottom faces , the break betw een the tw o
40
LINEAR THEORY OF HIGH-Q TR TLIBES [SEC.2+3
ha lves of the cavity d oes not cu t any curren t lines , and therefore there are
no los s es from rad ia tion or from Poor co ta cts .
S ince the curren t flow in the top and
otto faces is rad ia l, an in tim ate con -
tact mus t be m ade betw een the tube
flanges and the cavity in ord er to hold
to a m in imum the ‘R los s e s a t th e j oin t.
Th is is d on e by exertin g en ou gh pres s ure
to d eform the flange and caus e it to
flow agains t the cavity . Figure ‘2 .34
s how s the deta ils of tw o s uch arrange-
m en ts . In Fig. 2 .34a the clam ping ring
A is d raw n dow n agains t the flange by
s ix s crew s s paced around the circum -
ference. Th is m ak es an excellen t con -
tact, bu t it is d ifficu lt to replace tubes
qu ick ly in s uch a cavity , Figure 2.34b
s how s an alterna tive m ethod w herein
a clam ping nut B forces a ring C agains t
a neoprene gas k et D, w hich in turn
pres s es aga ins t t e tube flange. The
ga s k et, b y virtu e of its flexibility , forces
th e fla nge to mak e good contact w ith
the cavity d es pite any high s pots on he
cavity or m is alignment betw een the ring and the cavity . The s crew -
clamping mechan ism is comm on ly us ed on the 1B27 and 724B TR tubes ,
T
6 Eqbally spaced screws
I
I
B
(a )
(b)
FIG.2.34.—Methods of clamping cell-typeTR tutw into cavit ies ,
except tha t it has been found unneces sary to us e the gas ket on the 724B,
pres umably beoaus e of the small flange d iameter. In the 1B27 tube (or
SEC.2.8]
CELL-TYPE TR TUBES
41
the 72 lB , fa ilure to us e the gas ket m ay res ult in an increas e of ins ertion
los s of 1 or
2
db.
The fixed -tuned tubes (721B,
724 and 1B23) can each be char-
acterized by a curve w hich gives
the res onan t w avelength as a
function of cavity d iam eter. Fig-
ures 2.35 and 2“36 s how thes e
curves for the tubes , 721B and
724 . Figures 2’37 and 2“38 s how
aty pica l ca vity and a tuning cu rve
for the 1B23 tube. The curves
a re n om in al, a nd p rod u ction tu be s
lie w ith in a band les s than +0.5
per cen t a r o u n d the average
curve. The tubes are all pretuned
in a s tandard cavity by changing
the gap spacing before the tube
is s ealed off until res on ance is ob-
ta ined at a s tandard frequency .
Th is m eans that if the one d iam -
~ 11-
&
:E
>UIIJ
= .E
g
g
9
1.6
1 .8 2 .0 2 .2 2 .4
2 .6
Cavity diameter Din inches
FIG. 2.35.—Tun in g cha ra ct er ist ics of
721B TR tube as a funct ion of cavity diam-
eter . The cavity is loop-coupled to a
loaded Q of 300.
eter or glas s th ick nes s (for ins tance) varies from tube to tube, a lthough
$44”
0.50 0.55
0.60
0.65 0.70
Cavity diam. D in inches
Fm. 2 .36.—Tuning character is t ics of 724B
TR t ube a e a fu nct ion of ca vit y diamet er . Th e
cavity is ir is -coupkxf to a QL*of 200.
t
T
*
1
F IQ. 2.37.-Csvit y for 1B23 TR tubes .
42
LINEAR THEORY OF HIGH-Q TR TUBEIS
[SEC. 2%
th e tu ning will be correct a t the s tand ard frequency , for d iam eters larger
or smal er than the s tandard cavity the s lope of the A vs . D curve w ill
Diameter and height of cavity A in inches
F1~. 238.-Tun ing cu rve for 1B23 TR
tube for cavity shown in Fig. 237. (Data
are from Western M ectric Co.)
va ry and the s prea d w ill in creas e.
Figure 2 .39 s how s the tun ing
effect of inductive tuning plugs on
th e res on an t w a velen gth of ca vities
of various d iameters . Tw o plugs ,
d iametrica lly oppos ite , a re in s erte d
equal d is tances for thes e cu rves .
Th e mech an ica l d es ign o in d uctive
tun ing plugs is d ifficu lt. Figure
2 .40 s how s tw o pos s ib le cons truc-
tions . The tuning s crew in Fig.
2 .40a is required to m ak e good con -
ta ct on ly s om ewh e re n ea r th e ca vity
w all, a s i n d i c a t e d . Its tuning
range, how ever, is small. I the %-in . s crew s s how n in Fig. 2 .39 w ere
replaced by +-in . s crew s , the tuning range (AX/ k ) w ou ld be on ly abou t 2
to 3 per cen t, as compared w ith
the 10 to 15 per cen t obta ined
w ith the large s crew s .
Th e s crew
show n in Fig. 240b completely
f lls the s pace betw e en the top and
the bottom of the cavity , and the
tuning ranges ind icated are ob-
ta ined . To be eff ective, how ever,
the s crew mus t mak e a good elec-
trica l con tact w ith the cavity a t
its inner- end, as s how n in the
drawing.
Th is is a d ifficu lt con -
d ition to s a tis fy . The threads in
th e cavity w all on ly s pan abou t
15° to 20° and they lack precis ion
for, in ord er to facilita te prod uc-
tion , they are tapped rather than
mach ine cu t. Furthermore, be
caus e the thread s m us t be s ilver-
p la ted , it is not pos s ible to s pecify
a tight i beca us e th e pla ting jams
th e th rea ds , an d m ak es it d ifficu lt
12
E
.
~ 11
a
H
a+
~6>,,
;
d
: 10
* ?38,,
s
T
&
:9
* 1.91,,
2
z
8
0 0 .2
0 .4 0 ,6
.8
Plugnsefilon-d in inches
F rQ. 2.39.—Tun ing characteristicsof
721B TR tube as a funct ion of plug inser -
tion, QLZ = 300.
or even im pos s ible to turn the s crew s by hand . As a res u lt, w hen the
lock nut is loos ened , th res onan t w a velength of the cavity m ay jum p ba ck
and forth erra tica lly as the con tact changes , and , therefore, m ak e it very
SEC. !2.8]
CELL-TYPE TR TUBES
43
Must make contacthere
(a)
Cavi
F1~. 2.40.—Induct ive tuning screws.
Section “AA”
/ - 4 $&s$a;d ~A
FIG.2.41.—Expanding induct ive tuning screw.
7
Insertion into cavity 1in inches
FIG.242.-Ca pa cit ive t un in g d ug in 2.16-in . diamet er 1B 7 cavity.
44
LINEAR THEORY OF HIGH-Q TR TUBES [SEC.24
d ifficu lt to tune the cavity to a new w avelength . Thes e effects become
w ors e as the rad ial travel of the tuning s crew increas es .
In 10-cm tubes
thes e effects are pronounced , w hereas in 3 -c tubes they are hard ly
noticeable.
In order to overcom e this c n tact trouble, a num ber of s chem es have
been cons id ered . It is pos s ible to us e s pring load ing, but in order to
m aintain con s an t pres s ure on th e
s crew , the s pring m us t be s evera l
tim es as long as the maximum
trave of the s crew . This mak es
the ca vity a ss em bly very large and
bulk y . Figure 241 s how s an ex-
pand ing tuning s crew that has
been us ed s ucces s fu lly . It a llow s
a continuous ly variable pres s ure
to be exerted betw een the end of
num
Kovar
Glass
13.0
12,5
12.0
11.5
11.0
E
.: 10.5
f
a
#
9.5
9,0
8.5
8.0
\
A
\ B
\
\
[/
\
\
\
\
\
c
.
\
\
\
\\
\
.
F
‘\
~..
u-u
7.5 ~
024681
Turns of tuning screw
Increasing gap spacing ——————
243.
Fxa. 24.4.
Fm. 2 .43.—Differen t ia l tun ing-screw mechan ism for IB27 TR tube,
F IG.2 .44.-Tun ing r auge of 1B27 TR tube in va r iou s cavit ies: Cu rve A, coaxial cavity;
Curve B, cavity 2.150” ID on 11” X 3“ wavcgu ide; Curve C, 1.800” ID cav ity looP-
coupledto i“ coaxialline; Curve D, 1.550” ID ca vit y loop-cou pled t o ;” coa xia l lin e;
Curve E, 1.400” ID ATR C8VitYon 11” X 3“ gu ide; Curve F 1.400” ID cavity on
1}” X 3“ gu ide.
the s crew and the cavity , and thus perm its the opera tor to loos en it ta
the poin t w here it can jus t be turned by hand and s till maintain a good
con tact during rota tion .
Figure 2.42 ind icates the tuning ranges w hich can be obtained w ith a
apacitive tuning s lug. S ince no electrical con tacts are involved , the
tuning is very smooth. No measurements of the los s in troduced by the
SEC. 243]
CELLATYPE TR TUBES
45
curre ts in the s lug, or by the pres ence of the poly s ty rene s leeve around
thes lug have been m ade, bu t cas ua l obs erva tions ind ica te that they are
not e xce s s iv e.
Capacitive tuning s lugs have found very little us e thus far, partly
becaus e of the m echanica l-d es ign d ifficu lties as socia ted w ith getting a
s mooth d riving m echanism on the poly s ty rene rod , and partly becaus e
of the adven of the TR tube w hich has an ad jus table gap.
Thes e tuning d ifficu lties are avoid ed in the 1B27 tube w hich is
tuned by vary ing the gap s pacing w ith the m echanis m s how n in Fig. 2 .43 .
The a lum inum s hell w hich carries the tuning mechanism is cem ented
to the glas s cy linder s ea led to the back of one of the d is k s . Sm ooth
J-1.000’~1
FIG. 2,45.—TR tube in coaxia l cavity.
tun ing, w ithou t the neces s ity of us ing lock nu ts to s ecure a given s ettin ,
is obta ined o er a range of 10 to 15 per cen t in a given cavity .
Figure
2.44 s how s the tuning characteris tics of the 1B27 tube in cavities of
various d iameters D. Exam ination of the curves s how s tha t the cavity
d iam eter requ ired to tune to a w avelength of 13 cm w ould be about
2 .5 in . How everj in certa in ligh tw eight a irborne radar equ ipm ent, the
s pace and w eight a llotted to a TR cavity to tune to 13 cm w ere extrem ely
small.
The cavity s how n in Fig. 2 . 5 w a s d es igned for th is applica tion .
It m ay be cons id ered either as a ca acitance-load ed coaxia l cavity or as
a fold ed TEOIO-cavity . It is on ly lfi in . ID by 1 in . long, bu t it tunes
over the range ind ica ted in Fig. 2 .44 accord ing to the Curve A. It is
a lmos t im pos s ible to fabrica te s uch a cavity as a s plit un it, w ith the
parting line a lw a ys para llel to the current flow . It w a s therefore d ecid ed
to mak e the cavity a “plug-in” ty pe. The tw o flanges on the 1B27 tube
46
LINEAR THEORY OF HIGH-Q TR TUBES [SEC.2.9
have, a d ifference in d iameter of & in. Th is a llow s the tube to be
ins erted from the end A, Fig. 2 .45 , and have its large flange clam ped
at th is end by a s u itable ring, w h ile the sm aller flange is forced in to the
s pring fingers at B. If. thes e ingers are properly tem pered they w ill
d eform the tube flange and mak e a good co tact. A tube can be ins erted
in to a cavity of th is ty pe on ly a few tim es before its small flange is
permanen tly d eform ed and w ill no longer m ak e good contact. Th is is
objectionab e for labora tory u’s e; bu t w here the life of the complete
equ ipment is on ly tw o or three tim es that of a
w
w
TR tube, th is is not a s erious d efect.
The unloaded Q of the coaxia l cavity is on ly
about one half that of the conven tiona l cavity .
As a res ult, either higher leak age pow e r for a given
ins ertion los s com pared w ith a TEolO-cavity , or
m ore ins etilon los s for a given leak age pow e r m us t
Fm. 2.46.— Mod ified be accepted . In h igh-perform ance equ ipm ents ,
flange for us e in Plw in th is defin itely ru les out the coaxia l cavity ; bu t
cavity.
w here w eight and s iz e are of param ount im port-
ance, the los s in perform ance (about l+ d b) can be accepted .
An im proved des ign for a plug-in tube has been reported by the
Britis h . In th is d es ign the small d is k on the TR tube is form ed as
s how n in Fig. 2 .46 . The ben t-over s mall d is k is s tronger than the s traight
ty pe and pres en ts a grea ter area to the con tact fingers .
2 .9 . Tun fng Tem pera ture Com pens ation .-Military rad ar equ ipm ent
m us t opera te at m axim um efficiency und er a grea t variety of cond itions .
In particu lar, a irborne equ ipm ent m us t be s ubjected to tem pera tures
ranging from – 55°C to 100”C. This im pos es the firs t requ irem nt on
com ponen ts —they m us t not break or otherw is e fa il becaus e of extrem e
tem pera tures . The next requ irem ent im pos ed is that every com ponen t
mu s t funct ion elect rica lly over a tem pera ture range from about — 15°C to
100”C. There is no clear lim it on the low -tem pera ture poin t; th is lim it
is es tim a ted by as s um ing tha t the average tem perature rise w ith in an
opera tin g ra da r equ ipmen t is 4 0°C ove r th e extern al ambien t tempera tu re.
The characteris tics of a TR tube w hich are tempera ture s ens itive,
are tun ing, leak age pow e r, and recovery tim e.
The leak age pow er and
the recovery tim e w ill be d is cus s ed in Chap. 5 . Except a t the s tart
of the opera tion , it is undes irable and often im pos s ible to tune the TR
tube in an aircra ft. Th is in itia l tuneup us ua lly o curs on the ground
w here the tem pera ture may be w idely d ifferen t from the tem pera ture
under w h ich the plane opera tes w hen aloft. The change of tem p ra ture
changes the res onant frequency of both the TR cavity and the trans -
m itter. It is requ ired , of cours e, that the tw o frequencies either rem ain
cons tan t or change by the s am e am ount.
SEC. 2.9]
TUN IN G TEMPERATURE COMPEN SATION
47
The magnetron transm itter us ed at m icrow ave frequencies is in
a lmos t a ll ca s e s of a ll-coppe r con s tru ction .
As its tem pera tu re ch an ges ,
therefore, it expands in all d imens ions by an amount d eterm ined by the
coefficien t of expans ion of the m etal.
If a ll the linear d im ens ions of a
res onant s tructure are m ultiplied by a cons tan t, its res onant w a velength
is m ultiplied by the s am e factor; therefore a copper m agnetron changes
frequency at a rate of 16 parts pe m illion per “G-the frequency d ecreas es
a s th e tempera tu re in crea s es .
For eas e of m achining, cavities for cell TR tubes are us ually m ade of
bras s . The tem pera ture coefficient of bras s is not much d ifferent from
that of copper, va y ing from about 17 to 20 parts per m illion per “C.
The glas s cy l nd er betw e en the copper d is k s has a m uch low e r coefficient
of expans ion (3 .1 X l@/ °C) than copper, and , therefore, the d is tance
betw een the flanges is practica lly independen t of temperature. The
copper cones , of cours e, expand w ith tem pera ture and , therefore, the gap
betw een them decreas es . S ince the externa l cavity expand s at about the
s ame rate as a copper cavity , and the gap decreases w ith in crea s in g tem -
perature and thus increas es the capacitance load ing, the res onant fre-
quency of the TR tube decreas es fas ter w ith increas ing temperature
than d oes the res onant frequency of the m agnetr n .
The problem involved may be s tated in the follow ing w ay . Let the
height of the cavity be h, the length of the pos ts 1 , the gap le gth 6, the
coe5cien t of expans on of the cavity a ., and that f the glas s a~. Then
at s om e tem pera ture to,
&o=h– 21.
(71)
At any other tempera ture to + At, if the cavity w ere all copper
& = (1 + a.At)(h – 21).
(72)
For thk i s am e temperature, the gap in the TR cavity is
Y’ = (1 + aOAt)h – 2(1 + a.At)l.
(73)
The d ifference betw e en the tw o,
8’ – Y’ = h(a, – ag)At,
(74)
is the amount by w hich the cones in the cell TR tube mus t be pulled
apart at (fo + At) in order to tune th is tube to the s ame frequency as
that of an a ll-copper cavity at th is tem perature.
In the 721B and 724B TR tubes the gap s pacing is compens a ted by
proper s haping of the d is k betw een the bas e of the cone and the ins id e
of the glas s . Th is is a purely empirica l proc s s , bu t it is k now n that
a lm os t any temperaturetu ing curve w hich is d es ired can be obta ined
by giving the d is k the appropria te in itia l curva ture. The 1B27 TR
tube has one of its cones expos ed to the a tmos phere and connected to a
48
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC. 2.9
tu nin g-s crew mech an ism , Fig. 2 .4 3.
The tem pera ture coefficien t of th is
tuning mechanism may be us ed to m ak e the proper corre tion to the
cavity . Let the length of the s crew (from the cone to the firs t thread
-in the hous ing) be 1. and its coefficient be a.; the length of the hous ing
from the glas s to the firs t thread be h and its coefficien t ah; and us e th~
s am e quantities for the glas s cy linder i~ and a~.
The motion of the end
F]Q. 2.47.
TR tube temperature ‘W
—Tuning-temperature characteristics of 721A TR t ube. A compa rison
of fla t a n d wr ir dded disk s, mea su r ed in a br ass ca vit y.
is m ade
of the s crew rela tive to the d is k (as sum ing the copper is eas ily d eform ed )
is
A = (l@ag + l~a~ – l,a ,)At.
(75)
If A is pos itive and equal to Y – 8“, as given by Eq. (74), the cavity w ill
e properly compens a ted . The hous ing s hell of the 1B27 tube mus t be
light s ince it is cem ented to the glas s . Th is automatically res tricts
the choice of materia l to s om e grade of alum inum w ith an a of about
23 X 10-’/ OC. The length m aybe
{~~~~a cons idera tions . s neAn
va ried w ith in rea s onab le lim its , bu t
it is ba sica lly res tricted by m ech an -
Eq. (75) mus t be pos itive, a , < ah.
Kovar w ithan a of on ly 5 X 10-’/ OC
is a s uitable m ateria l for the s crew .
(a) (b)
After a reas onable m echanical ar-
FIG. 2.4S,—Compar ison of pla in (a )
rangemen t of the tuning meoh n ism
and tempera tu re-compensa t ed (b) TR-
has been made, even if the tun ing-
tube cones.
tem perature curve w h ich res ults is
either over- or und ercom pens ated , it can be corrected by proper s haping
of th e d is k w h ich carries th e s ta tiona ry con e.
Figure 2.47 s how s the d ifference in tem perature-tuning character-
is tics betw een a fla t d is k and a d is k w hich has a w rink le, Fig. 2 .48 . The
w rink led d is k, in add ition to giving a lm os t the s am e tuning s lope as an
a ll-copper cavi y , has almos t no hy s teres is , w hereas the fla t d k k has
SEC. 2.10]
CAVITY COUPLIN GS
49
both a very large tun ing-temperature s lope and hy steres is . If the d is k
w ere perfectly fla t betw een the s ea ls , it cou ld e ually w e ll buck le in or
ou t w ith an increas e in tem pera ture.
On the other hand , if it has an
in itia l concave curva ure (s een from the gap), it tend s to becom e even
m ore concave at h igher temperatures , and thus pu lls the gap apart and
gives the proper s ign to the s lope of the tuning curve. If the d k k is
s im ply bow ed the cones m ove in the d es ired d irection , bu t there is con-
s id erable hy s teres is in the m otion . The w rink led d is k s how n in Fig. 2 .48
overcom es th is objection and gives the perform ance s how n in Fig. 2 .47 .
Figure 2 .49 s how s the tem pera ture-tuning curves of a 1B27 TR tube
in a bras s cavity tuned to s evera l d ifferent freq encies .
The couplings
to a 1B27 cavity are normally
ad jus ted to mak e QM about 350.
Und er thes e cond itions the band -
w id th (to ha lf-pow er transmis s ion )
is 9 Me/ s ee at AO= 9.5 cm . Com -
paris on of th e tube cha ra cte ris tics
w ith that of a copper cavity a t a
tempera ture ris e of 60°C above
the in itia l tuning tem pera ture in -
d icates that the TR and mag-
Tempwatureaboveambient°C
10 20 30 40 50 60 70 80
. -o
r’
.
y=.---.:y .: :
“d>- AllCUCav’v~0=9’5
z
=
u -5
>.
.
m>. u ~
2
%’
\
z
t -10
k~~9.8 Cm
FIQ. 2.49,—Tun ing-t emper a tu r e cu rve
1B27 TR t ube.
of
netron cavities w ill cliffer in frequency by abou t 2 to 4 hIc/ s ec.
Th e
detuning los s es are o the ord er of 0 .7 to 2 .3 d b.
2 .10 . Cavity Couplings . -Thus far in the equ ivalent-circuit calcula -
tions the couplings to a cavity have been characterized by a s us ceptance
in the cas e of the iris , or by a reactance and mutua l inductance in the
cas e of a loop. In practice thes e quantities are almos t never m eas ured
d irectly , and are on ly of academ ic in teres t to the engineer. once a
particu lar TR tube and external cavity have been chos en , then on ly the
couplings rem ain to be ad jus ted in ord er to get the d es ired ins ertion los s
in the d es ired manner (equa l coupling, matched input, and s o forth ).
Thus , in ord er to ad jus t the coupling to the proper va lue it is neces s ary
to m ea ure the input adm ittance at res onance, firs t w ith no load to
d eterm ine the va lue of g: and then w ith the proper ou tpu t load to d eter-
m ine (g: + g~). Thes e tw o meas urem ents , plus a m eas urem ent of Q,
comp le te ly s p ecify th e low -le ve l p rop ertie s of th e ca vity .
The s e mea sure -
m en ts are not enough, how ev r, to d eterm ine the coupling s us ceptances
bl or bz .
Equ ation (7 6) is th e expres s ion for th e Q of a n iris -cou pled ca vity
( )
L, =A ; + # + g c’,
1 2
(76)
It is pos s ible to m eas ure QL or Q~Z d irectly and then to compute QO;
50
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.2.10
how ever, no meas urem ents made at the externa l term ina ls (inpu t or
ou tpu t ) can define the m agnitudes of b1 and bz un les s either g. or A is
known. The s hape and capacitive load ing o the cavity d eterm ine the
cons tan t, A. In particu larly s im ple cas es , a a for a cavity m ade of a res ~
nant length of rectangu lar w a vegu id e, the iris s us ceptan ce m ay be found
in various handbook s , 1 or computed from the length of the cavity and
its propagation cons tan t. In principle, th is can s till be d one in cavities
of even m ore com plica ted s hape, bu t the m athem atica l com plica tions are
~ Cavity
(a)
u
(b)
I
*+!i$l-
(c)
FIO.2 .50 .—Methods of coupling a cavity to a coaxia l line ; (a) ser ies (ir is ) coupling, (b) loop
coupling, (c) capacit ive (probe) coupling.
s o grea t as to d s courage s uch compu ta tions . As a res u lt, the data
ava ilable cons is t of curves of the apparen t s hun t conductance g: of a
given TR cavity coupled to transm ission lines of a given type as a function
of the d im ens ions of the iris or loop.
The frequency of opera tion and the ty pe of s et unde cons id era tion
determ ine w hether a TR cavity is to be coupled to a coaxia l or to a w ave-
gu id e tra nsm is s ion lin e. Figu re 2 .5 0 llu s tra tes th ree m eth od s of cou plin g
a cavity to a coaxia l line. Figure 250a s how s s eries , or iris , coupling
in w h ich the ou ter cond uctor is cu t s o tha t the trans mis s ion-line curren t
is in terrupted by the cavity . Figure 2.50b s h ow s a loop -cou ple d ca vity
in w hich the curren t in the loop s ts up a magnetic field tha t couples to
tha t of the cavity . Figure 2 .50c is a capacitance-coupled cavity in w h ich
1 (1 avegu ide Hand ook, ” RL Repor t 43-2/7/44 and “ Waveguide HandboOk
Su pplemen t,” RL Repor t No. 41-1/23/45; a lso Vol. 10, Ra dia tion La bora tor y Ser ies.
SEC.2.10]
CAVITY COUPLINGS
51
the probe acts as an antenna and the voltage d op a long it excites the E
field in the cavity . The firs t tw o are fa irly common m ethod s of coupling;
but the las t one has never been us ed on any m icrow ave TR cavities ,
s ince the electric field in the ou ter portions of the cavity , w here a probe
can be ins erted , is s o w eak
coupling.
th at it is d ifficu lt to ob ta in ‘s u fficie ntly -tigh t
(c)
F IG. 2,51.—h Iet hods, of cou plin g a TR, cawt y t o a r ecta ngu la r wa vegu lde; (a ) ser ies
couphng, (b) shunt rouplmg, (c) feed-through coupling ,
F igure 2. 1 shows th ree common methods of coupling TR cavit ies
to rectangula r wavegu ides. F igure 2.51a shows ser ies coupling in which
the cavity is moun ted on the broad face of the wavegu ide, so tha t t ,he
coupling hole in terrupts the longitud inal line curren t.
Figure 2 .5 1b
illus tra tes the s o-ca lled s hun t coupling in w h ich the cavity is mounted
cm the narrow face of the gu ide s o that he cou plin g h ole in terru pts th e
vertica l curren ts in t e w all. 1 Figure 2 ,51c is the s o-ca lled “feed -
‘ For :1 more complete discussion of the meaning of “ser ies “ and “shunt “
cOl1-
n ect ion s t o wa vegu ir les, sw ~h ap 7 of t his volume,
E=G. & G. LIBRARY
us VEGAS BRANCH
52
LINEAR THEORY OF HIGH-Q TR TUBES [SEC. 2-10
through”
coupling in w hich the cavity is mounted on the end of the
w a veguid e and , therefore, the coupling is of the ty pe d is cu ss ed in S ec. !2 ,2 .
At 10 cm , the couplings illus trated in Figs . 2 .50a and and Figs .
2.51b and c have found the w ides t us e.
At 3 cm , coaxia l lines , becaus e
of their com paratively high attenuation are never us ed as m ain trans -
m is s ion lines , and the 724 ‘1’R tube has been us ed exclus ively w ith the
couplings s how n in Fig. 2.51a and
An iris cut in to a cavity as s how n in Fig. 2 .51 acts as an inductive
1 .0
~ 0.9
-
; 0.8
-
:: 0.7
: 0.6
.5 0.5
-
z
g 0.4
~ 0!3
-
&
~ 0.2
~ 0.1 -
0
0 0.10,20.30 .40.50.60.7 0.80,9
6 in inch s
FIG. 2.52.—Reflection coefficient of induc-
t ive a nd ca pa cit ive ir ises in wavegu id e 0.400
in . by 0,900 in , at A = 3.2 cm.
s us ce~tance if its height is equal
h
the cavity w ere made of a s ection
of w a veguid e of the ty pe d is cus sed
in Sec. 2 .2 , the iris es could be
m ade either capacitive or induc-
the top and bottom , or from the
s id es . The s us ceptance res ulting
from a given opening 6 betw een
the iris es is much greater for an
inductive than for a capacitive
iris . For th is reas on larger open-
ings and les s critical m echanical
tolerances are allow a ble w ith in-
ductive iris es . Firz -ure 2.52 is a
com paris on of the reflection coefficient of s ymmetrica l capacitive and
inductive iris es & in. th ick in w aveguid e 1 in . by 0,5 in. by 50-m il w all a t
k = 3.2 cm .l
The coupling iris betw een a circul r TEO1@-cavity and a w aveguide
(as s een in Fig. 251a) w hich is m ade by s licing off a s egm ent of the cavity ,
is rectangular. Its height h is a lw ay s equal to that of the cavity , w hile
its length 1 is determ ined by the d is tance from the center at w hich the
s ice is made.
The length of the hole for any practical TR-cavity
coupling is les s than a half w avelength; it is of the order of A/ 1 , and ,
therefore, it acts as an inductive s us ceptance w ho e m agnitude varies
invers ely w ith 1 . The actual s us ceptance of the hole varies not only
w ith its length , but a ls o w ith its th ick nes s .
An iris of z ero th ick nes s
appears as a pure shunt s us ceptance acros s the guide.
If the th ick -
nes s t # O, then the equivalent circuit is that s how n in Fig. 2.53.2
Figure 254 is a plot of the variation of B. and B, as ’a function of t
w ith d = 0.375 in ., a = 0.900 in ., and = 0.400 in . at A = 3.20 cm .
I ~~w aveg~id~Ha nd book Supplemen t,“
RI , Report h“o. 41-1 / 23/ 45.
2“WaveguirleHand book Supplem ent,”
‘rhe discuss iona nd examples will be for
r ou nd h oles, bu t t he gen er al a pplica tion t o r ect an gu la r or ellipt ica l h oles is va lid.
SBC. 2.10]
CAVITY COUPLINGS
53
Let us now exam ine the input s us ceptance to th is netw ork term ina ted
in a cond uctance g,
y = _j& , (Q – jhJ( –jbb)
g – j(t). + b,)
gb, – j(gz + b: + bab~).
= –jb. + b, –- ~ + ~ljo + bt)z
Fort = O,b, = c@ andb~ = –2 .3 , Y = g –j4 .~; bu ta tt = 0.020in .,
bb = –28, and bu = –2.7, Y
0.83g – j5. 13. Thus , the apparen t
Reference planes
m
-L”
-?-
~t~
o
1 1
0
FIG. 2.53.—Equivfi lent ci rcui t of th ick ir is .
s u s cepta nce h as been in crea s ed b y a bou t 10 p er cen t, a nd th e con du cta nce
tra ns form a tion th rou gh th e h ole is a bou t 1 .2 ; th eref ore th e d iam eter of th e
0.8-
h=%”
8r
?
0.7-
87
I
~b
(s5
\
,:
:O\ \ {q
9
;4
In
g3
\
~ Z!J%
z=
+2
=1
\
&
BbJYox 0.1
: !,~
o
0 0.02 0 .04 0 .06 0 .08 0 .10
:750 .8 0 .9
1 .0 1 .1
l.’!
Holehickness - tinches
Wtndow length 1 in inches
FIQ. 2 .54.—Var ia t ion of ser ies and
FIG.2.55.—Conductance of 721 TR cavity,
shun t suscep t ances of a 0.375-in . hole
2.67-in . ID, sh u nt -cou pled t o 1~ in . by 3 in .
in a diaphragm across a wavegu ide
wavegu id e a s a fu n ct ion of win dow len gt h 1,
0.406in. by 0.900in . a t X 3.2 cm. A = 10.7 cm, Qo = 2500.
hole requ ired to prod uce a certa in oupling to a cavity m us t be increas ed
w ith increa sing th ick nes s of the h ole.
For s evera l d ifferen t cou pli g s ch em es th e follow ing cu rves s how the
vs ria tion in equiva len t cavity conductance w ith the varia tion in s iz e
54
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.210
of the coupling w indow . Figure 2.55 s how s the varia tion for a 721A TR
cavity , 2 .67-in . ID, coupled to the narrow s id e of I+in . by 3-in . w ave-
guide at X = 10.7 cm . The thick nes s of the iris w as that of the gu ide
w all, 0 .080 in . Figure 256 s how s the coupling of the s ame cavity to a
1#-in . coaxia l line by m eans of an
iris ; the equivalent cavity con -
ductance g. is plotted agains t the
ch ord 1 of th e in ters ectin g circles .
Figure 2.57 ill s trates a 721A
cavity iris -coupled to a ~-in .
1 .0
0.8
I____!?
o “
\
cavity
~; 0.6
0.4
@ ;,,
0 .2
0
0.7
0.8 0.9 1.0
1inches
FIG.2 ,56.—Conductance of a 721
TR cavit y, 2.67-in . ID, ir is -coupled
to 1&in . by l-in . diameter coaxia l
line, A = 10.7 cm, QO= 2500.
T
TR tube
line
ductor
FIG. 257.~Dimension s of 721 TR cavit y,
ir i%cou pled t o
coa xia l lin e; d = 1.439”
for u ’. = 0.30; d = 1.219” for g’c = 0.10;
Qo = 2500.
coaxia l line, m eas ured at A = 9.4 cm .
Figure 2.58 gives g: vs . 1 , a t 8 .5
cm and 10.7 cm , for 1B27 cavities coupled to the narrow s id e of a I+-in .
b y 3 -in . w a vegu id e.
Figure 2.59 s how s the effect of placing a s heet ~ in . th ick of d ielectric
0 .4
0.3
m
AB
“-” 0.2
0.1
0
0.6
0.8 1,0
1.2
Window length (t) in inches
FIG. 2.58.—Transformed cav-
it y conduct ance g’. vs . coupling-
window length 1 in 1B27 cavit ies
on n ar row side of 1}-in . by 3-in .
waveguide.
Curve A is for A =
S 5 cm, cavit y d iamet er of 1 40”,
window thickness of 0.040”;
Cu rve B is for X = 10,7 cm,
ca vit y diamet er 2,15”, win dow
th icknees 0.080”; Qo = 3000.
(,’
=- 3.5) ~ver the iris of a 1B27 TR cavity ;
it a ls o s how s the frequency s ens itivity of
the coupling. With in the accuracy of the
e xp eriment, th e cu rv es a re s tra igh t lin es a nd
thus ind icate that the effective coupling
s us ceptance of the irk increas es as the
s quare root of the w avelength , s ince
g: = b~g,. This is unexpected , s ince it w ould
have been pred icted that an inductive
s us ceptance w ou 1d vary d irectly w ith
wavelength.
In Sees . 2 .1 and 2“2 it has been s een
that the coupling s us ceptances caus e the
loaded cavity to res onate at a frequency
d ifferen t from that of the unload ed cavity .
Ind uctive iris es caus e the load ed cavity to
res ona te at a low er frequency than the un loaded cavity . Capacitive
iris es or loop couplings caus e the loaded cavity to res ona te at a higher
SEC. 2.11]
DIRECT-COUPLING ATTENUATION
55
frequ en cy tha n th e u nloa ded ca vity .
Figure 2 .6 0 in dica tes th e ch ange i
res onant w avelength of a 721A cavity as a function of the orien ta tion
of the loops . When the plane of the loop is a t 90° to the magnetic field ,
the coupling is a m in imum . The frequency s h ift is of the order of
~ per cen t w hen QLZ is 250 and QOis 2500. Meas urements on a 724A-
tube cavity coupled for matched input w ith inductive iris es give the
;~* ~~
9.8 10.0 10.2 10.4 10.6 108 11.0 112 0
0 .2 0.4 0 .6 0,8 1,0
Wavelengthincm
cm @
FIG. 2.59.—Frequency sen sit ivit y of ir is
FXG,2.60,—Effect of loop coupling
cou plin g t o ca vity on en d of 1}-in . by 3-in .
on ca vity reson an t wa velen gt h for a
wa vegu ide a nd effect of polygla s sh eet pla ced 721A TR tu be; ca vity 1.S75” diamet er
ove r t he ir is.
cou pled t o a 72-ohm coa xia l lin e by a
loop $ in . h y ~ in . made of ~-in . wire.
Th e a ngle of or ien ta tion is d.
res u lts tabula ted below , w here 11 and 12 are the lengths of the input
and outpu t w indow s . The w avelength s h ift is about 1* per cen t from
th e l w es t to th e h igh es t loa ded Q; th e w a velen gth in crea s es w ith in crea s ed
loading.
TABLE2.6 .—MEASUREMENTSN724A-TuBECAVITYCOUPLEDFORMATCHEDINPUT
WITH INDUCTIVEIRISES
l,, in .
I
1,, in .
I
A, cm
I QL2
0.23
0.216 3 .13 320
0.275
0 .244 3 .205
178
0.315
0.275 3 .23 133
2 .1 1. Direct-cou plin g Atten ua t on . -Direct-cou plin g a tten ua tion wa s
d is cus sed in S ees . 2 .2 and 2 .7 , w here it w as s how n that the attenuation is
proportional to the product of the input and outpu t Q’s and to (bo + b.)’
where b& is the s us ceptance of the pos t acros s the cavity and bo is th e
s u acep ta nce of th e ca vity in du cta nce.
The ord er of m agnitude of th is a ttenuation in I&cm . TR tubes loaded
to Q~2 = 300 is 60 db. How ever, if the TR tube is connected as s how n
in Fig. 2 .61 and its impedance is very small compared w ith the line
56
LINEAR THEORY OF HIGH-Q TR TUBES [SEC.2.11
im pedance, then the ra tio of the available pow er to the d irect-coupled
pow er is 4 tim es as great as if the TR tube w ere connected d irectly acros s
the genera tor term inals . Thus , becaus e the critica l quantity is the leak -
age pow er w hen the TR tube is us e as in Fig. 2“61 , it is cus tomary to us e
th is n ew d efin ition for d irect-cou plin g a tten ua tion (lea k age pow er/ tra ns -
m itter pow er) and the value of 60 db quoted above s hould now read 66 db.
The d irect-coupled leak age pow er w ith 106 w a tts trans mitted is 0.25
w atts if the a ttenuation is 66 db. Experience has s how n that 10 -cm
s ilicon cry s ta l d etectors w iths tand
pu ls es of 5 to 10 w atts for s hort
tim es , bu t they s how a s tead y s low
deteriora tion at leak age pow ers of
the ord er of 0 .15 to 0 .2 w att. It
Q
Antenna
1
1
TR tube
Generator
G2
FxG.2.61.—TRtube
connect ion for dir ect -
coupling att enuation.
)“
‘-c
21A
% Sutton cones
2 60
cones=
Ig
15°
m
* 1-
~
D
: 50
40
t--l 875’*
o
0 .1 0 .2 0 .3
0 .4
Average cone diam. in inches D
FIG. 2.62.—Direct-coupIing att enuation
a s a fu nct ion of m ea n post diamet er .
thus becomes apparen t that TR tubes for h igh-pow er radar s ets need
d irect-coupling attenuation greater than 66 d b.
R. L. McCreery has m ad e a s eries of m eas urem en ts of the attenua ti n
through a 721A cavity and through a Su tton -tube cavity .’ Figure 2 .62
is a curve of the attenuation , in a cavity of 1 .875-in . d iameter w ith tw o
con ica l pos ts s h ort-circu ited a cros s th e ga p, aga in st th e a vera ge d iam eter
D. The cavity w as coupled to give a value of Q., of
320
w hen the gap
betw een the pos ts w as ad jus ted to produce res onance at A = 9.1 era ;
the ins ertion los s w as about 1 db. The a ttenuation m eas ured is the
ins ertion los s of the cavity , and the d irect-coupling attenuation in a
s ys tem w ould be 6 db greater.
Although it w ou ld appear that the TR-tube cones s hould be made
large in ord er to get optimum perform ance, it mus t be recalled that the
us e of a larger pos t has one of tw o effects : (1) If the gap capacitance and ,
therefore, cavity d iam eter are to be k ept cons tant, the gap length m us t
be increas ed , and th is increas es the arc leak age pow er (s ee Chap. 5 ); (2)
If the gap length is k ept cons tant, the capacitance is increas ed , and the
cavity d iam eter m us t be d ecreas ed to res onate at a given frequency ; th is
1R. L. McCreery , “Direct Coup l ng iu the TR Box ,”RL Report No. 352 ,Nov . 3 ,
1942.
SEC.2.11]
DIR ECT -CO [J PLIiVG AT TENUAT ION
.
s erious ly res tricts the h igh-frequency tuning range.
A com prom is e
betw een the tw o m us t be effected , and h is torica lly , the 721A, w h ich w as
already in production at the tim e
“:o&
of thes e measurements , s eemed to ~ ~loo
be a reasonable compromis e .
Measurem ents of h igh-level
leak age pow er as a function of Z ~ ~ ‘--”
tran sm itter-p ow e r le ve l h av e b een
made on 721A TR tubes in a num -
100 200 300 400 500
ber of d iffere nt ca vitie s .’
Figure
Transm issionulsepowerin kw
FIG. 2.63.—Direct -coupling at tenuat ion
2.63 is a plot of s uch data . Table through 721A TR cavity on waveg.ide
2 .7 compare s th e d irect-couplin g
E-plane T; X = 10,7 cm, QO= 2000, L =
– 1.54 db. The slope of the curve gives a
a tenuation through 721A TR value of t he d]r ect cou plin g a tt en ua tion of
cavities coupled in s evera l w a ys .
6%8db.
Values are corrected to QO= 2000, L = – 1.5 d b, m atched input.
TABLE 2.7.—DIRECT-COUPLINGATTENUATIONTHROUGH721A TR CAVITIES
CORRECTEDTO Q, = 2000, L = –1.5 DB,g: + W = 1
A
10.22
10.22
10.75
10.75
10.75
10,75
10,8
10.8
10.8
10.8
Original conditions
QO
2550
2463
2000
2200
2160
2180
2000
2000
2065
2065
db
L
0.95
1.15
1.54
1,54
2 .2
2,14
0.74
0.74
1.34
1.34
1
1
1
1
1
1
1
1
Corrected
db
attenuation
66.9
68
68.6
68.6
66,8
66.8
67
67.7
68.4
69
Method of coupling
Iris on ~“ coa xia l
Shunt T on ~“ coaxia l
E -pla ne wavegu ide T
E -pla n e wavegu ide T
Shunt Ton ~“ coa xia l
Shunt T on ~“ coaxia l
Ir is on ~“ coa xia l
Ir is on ~“ coa xia l
E -pla ne wavegu ide T
E -pla n e wavegu ide T
In the cours e of a s eries of m eas urem ents of leak age pow er through a
721A TR tube, it w as obs erved that the leak ge pow er measured w as
dependen t upon the ins ertion of the inductive tuning s lugs if they com-
pl tely filled th e ca vity (>in . s crew s in a n +&-in .-h igh ca vity ); bu t sma ller
tuning s crew s (&in . d ia .) had no effect on the leak age pow er.
Figure 2 .64 illus tra tes a cavity tha t w as d eveloped for the 721 ATR
tube for us e at line pow ers f the ord er of 500 kw or greater. It is
larger in d iam eter than the us ual cavity us ed to tune over the range from
1L. D. SmuUin, “ Meesurementa of 721A TR-Tube Leakage Power ,” RL Repor t
No. 249, Ma r. 9, 1943,
58
LINEAR TH.??ORY OF HIGH-Q TR TIJBES [SEC.211
10.3 to 11 .1 cm (3 .25 in . compared w ith 2 .67 in . ) but fou tuning s lugs ,
tw o of w hich are fixed , are us ed to tune over th is s ame range. The effec-
tivenes s of th is arrangem ent is ind ica t d in Fig. 2 .65 w h ich com pares the
leak age pow er through the large cavity w ith the s tandard cavit . The
quantity plotted is the average rectified cry s ta l current prod uced by the
leak age pow e r S ince the d uty factor is 1 / 2000, the peak rectified current
is of the ord er of 10 m a or grea ter.
Th e d egree of s atu ration of th e cry s ta l
is ind ica ted by the curve of leak age pow er through the 2 .67-in . cavity ,
w ith plugs clear ou t, agains t line pow er. The leak age pow er through
the large cavity is plotted agains t plug ins ertion for a cons tant line pow e r
of 690 k w . It can be s een that the l ak age pow er at w avelengths betw een
Movable tuning screw
\
Fixed tuning scr w
?
F IG. 2.64.—La rge ca vit y for 721A TR t ube.
Plug. insertion z in inches
o 62 0.4
0 .6 0 .8
:
.—
B
a
C8
P
A
:7 ---
A- --t
766
%
~
~5
11:1 “4 I
&
g4
10”7 10!3
23
0
200
400
600 800
Pulse line power in kw
FIG. 2.65.—Comparison of leakage
power t h rough 2.67-in .. a nd 3.25-in .-
diamet er ca vit ies. Cu rve A shows
i vs. p for 2.67-in. cavity at X = 11.1
cm ; Cu rve B show i vs. z at 690 kw.
11.1 and 10.3 cm is w ell below that of the smaller cavity w ith no tuning
plugs at the s am e pow er level. S ince the small cavity had a meas ured
d irect-coupling attenuation of 66 d b, and the large cavity , w h en tuned to
10.7 cm and w ith a line pow er of 690 k w , had a leak age pow er corres pond -
ing to that through the smaller one at a line pow er of 110 kw , its d irect-
coupling attenuation is greate by 7 .9 db, or is equal to about 74 db.
Harrrw n ic.s .-Th e tran sm is s ion characteris tics of the fired TR cavity
a t frequencies higher than the fundam enta l or carrier frequency of the
trans mitter are of cons id erable im porta ce. S ideband frequencies for
m icros econd pu ls es are res tricted to a rela tively few megacy cles per
s econd above or below the carrier, and are attenuated to the s am e exten t
as the carrier in pas sing through the fired cavity . Harm onics , how ever,
are not n eces s arily a tte uated to the s am e exten t.
S ince the tw o “w a ve-
guides”
around the s hort-circu ited cen ter pos t of the TR cavity are no
SEC.2.12]
INTEGRAL-CAVITY 1’R I’UBES 59
longer small compared w ith A/ 2 for the s econd or third harmonics , it
w ould be expected that there w ould be relatively little d ire t-coupling
a tten ua tion a t th es e h igh er fre qu en cies .
Unfortunately , no quantita tive data are available to illus trate th is .
When the cavity is coupled to a w aveguid e, there is no w ay of d eterm in-
ing in w hat m od es the harm onics are propagating, s ince they m ay choos e
any or all of four or five d ifferen t m od es d epend ing upon the s hape of the
exciting feed and upon various obs tacles in the guide.
It is therefore
d angerou s to s y nth es iz e th e operatin g con dition s by feed ing in s igna ls at
thes e harmonic frequencies and m eas uring the attenuation d irectly
becaus e thes e s y n thes iz ed cond itions may be d ifferen t from actual
opera ting cond itions by as m uch as 10 db.
Tes ts made on a 1B27 TR cavity normally tuned to 10.7 cm in a
2.15-in . ID cavity ind icated as little as 6-d b attenuation at a w a velength
of 5 cm . If thes e meas urem ents are ty pica l, the pu ls ed magnetron is an
exceptiona lly good os cilla tor, s ince m eas urem ents of actua l harm onic
leak age pow erl have given maximum values of a few tenths of a w att
w hen the pu ls e pow er at the nom ina l frequency w as 50 k w .
If the harm onic leak age pow er becom es exces s ive, there is little that
can be done to the cavity to reduce th is pow er. Cry sta l m ixers for h igh-
ow e r 10-cm rad ar s ets us ually have harm onic-s uppres s or chok es built
in to them . Abou 10 to 20 db of protection can be obtained in th is w ay .
Difficu lty w ith h armon ic bu rn ou t of cry s ta ls h as been en cou ntered on ly in
the h ighes t-pow e r s ets , w h ere it has been rem ed ied by the us e of a pre-TR
tube (s ee Chap. 4).
2 .12. In tegra l-cavity TR Tubes .—The cell TR tubes d is cus s ed in
S ec. 2 .10 are com para tively inexpens ive to m anufacture, and they have
the ad vantage f being ad aptab e for us e in a variety of d ifferent cavities
and circu its . As the frequency increas es , the tube becom es s m aller; bu t,
becaus e of the requ irem ents for s trength , the thick nes s of the glas s
cy lind er s epara ting the tw o d is k s rem ains cons tan t and , cons equently ,
occupies an incr as ingly larger fraction of the volume of the cavity .
This res ults in d ielectric los ses w hich increas e rapid ly as frequency
increas es . A further cons equence of the pres ence of the glas s is that it
ad ds a proportiona tely grea ter capa citive load ing to th e ca vity at high er
frequencies , and thus forces the s park -gap capacitance to be red uced by
increas ing the gap for a given cavity d iam eter.
Or if the gap is k ept
cons tan t, the ca ity d iam eter mus t be reduced to k eep the res onant
frequency cons tan t, thus increas ing the copper los s es . In any cas e, a
cell tube is practically ou t of the ques tion f r us e in the 1 .25-cm region;
and in the 3-cm band it is jus t us able, QObeing about 1500 or les s .
1B. Cor k, “ Tr an sm iea ion of H igh er H armon ics t hr ou gh a TR Ca vit y,” RL Repor t
No. 361, J a n. 11, 1943.
60
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.212
S ince the exces s los s res ults m ain ly fr m the pres ence of the glas s in a
region of h igh ele tric field s , th e obviou s s tep is eith er to rem ove the glas s
en tirely , or to place it w here the field is w eak , tha t is a t the ou ter d iam -
eter of the cavity . F@re 2 .66 s how s an early 3 -cm TR tube bu ilt by
Wm . Pres ton of the Rad ia tion Labora tory early in 1942 . It cons is ts
of a res onan t length of w aveguide w ith a s park gap at the cen ter, and
the coupling iris es covered by glas s w indow s . At the tim e th is tube w as
ade, it w as not pos s ible to s ea l the fla t w indow s in to the cavity and
therefore, it w as neces s ary to w ax them in place. As a res u lt, w hen the
724A cell TR tube w a s d eveloped , further w ork on th is tube w as d ropped .
As in teres t in the 1 .25 -cm band d eveloped , it becam e obvious tha t a
cell tube w ou ld be quite im practica l.
A group at the Wes tinghous e
Res earch Labora tories , under the d irection of S . Kras ik and D. Alpert,
F IG. 266.-(3ld 3-cm TR t ube.
d eveloped an in tegra l cavity by a new techn ique. 1 The glas s w as s ea led
d irectly to a Kovar ring, and the com bination then s old ered to the copper
cavity . At the tim e the tube w as firs t d emons tra ted there w ere no
1 .25 -cm rad ar s ets rea dy f r prod uction; bu t 3 -cm s ets w e re experien cin g
cons id erable d ifficu lty w ith the 724A TR tube in the form of cry s ta l
burnout, s hort tube life , and frequent tube break age. It w a s, therefore,
reques ted tha t a s im ilar in tegra l-cavity tube be d eveloped for 3 cm .
The Wes tinghous e group made s uch a tube, and J . B . Wies ner and F. L.
McMillan of the Rad ia tion Labora tory perfected leak age-pow er char-
acteris tics . Th is tube w as the 1B24 and w as pu t in to production by the
Wes tinghous e Electric Co. a t Bloom fie ld , N. J ., and the S y lvan ia
Electric Products Co. at S a lem , Mas s . The 1 .25 -cm tube w as d eveloped
at a s low er pace under the join t efforts of the Wes tinghous e Res earch
group and C. W . Zabel, a t the Rad ia tion Labora tory . Its pr duction
1D . A1per t, ‘(Kova r t o Gla ss Disc Sea ls, Some Applica tion s in Micr o-Wave Equ ip-
m en t, TR Box Gr ou p Repor t No. 1,” Resea rch Repor t SR 19$, West in gn oum Ra ea rch
Laboratories.
SEC. 2.121
INTEGRAL-CA VITY TR TUBES
61
form is k now n a8 the 1B26 and w as m ade by Wes tinghous e and Sy lvan ia .
Figure 2 .67 s how s thes e tw o tubes .
At the reques t of ihe Navy Bureau of Sh ips , H. . McCarthy of
S y lvania made a s im ila r ube, th 1B50, to opera te in the 4 -cm re ion .
Before en tering in to a deta il d d es cription of thes e three tubes , the
genera l characteris tics w h ich favor the us e of the in tegra l-cavity over
los s es becom e exces s ive in the cell tube. The 724 has a (?o of abou t
1500 , w hereas tha t of the 1B24 is 3000 or more. Becaus e the glas s
d iameter of the 724 tube is not very much smaller than the cavity
d
d iam eter, there is little room for inductive tun ing s crew s and the m axi-
mum tuning range obta inable in an ord inary cavity is 2 to 3 per cen t. A
double-m ode cavity tha t can be tuned over a 12 per cen t band has been
d es igned for us e as an .4TR s w itch (s ee Chap. 4) bu t it w as never applied
to a TR sw itch .
The in tegra l-cavity tubes are capacitance-tuned . This is d one by
vary ing the gap s pacing by m eans of a d ifferen tia l s crew w hich acts
on the back of one of the cones , a s in the IB27 . The res u lting tun ing
range is of the ord er of 10 to 15 per cen t of the nom inal frequency .
The 724 tube is not very large, and the cavity in to w hich it mus t fit
has a number of sma ll parts a ll of w h ich mus t be as s embled at once.
Under extrem e cond itions of m ilitary s ervice , even the s im ples t repair
‘ob becom es an in tolerable burd en; and complica ted tas k s are either
~oorly execu ted or not perform ed at a ll, It w as fe t tha t the us e of an
62
LINEAR THEORY OF HIGH-Q Tit. TUBES
[$Ec. 2.12
integral-cavity tube, mounted in s om e s imple manner betw een tw o
w avegu id e chok e connectors , w ould grea tly im prove the eas e of m ain-
tenance of the radar equ ipm ent, and that the ultim ate in TR des ign
w ould e ach ieved w hen it w ould be pos s ible for a “cham berm aid w ith
FIG.26 8.-Cut-aw ay view of t he 1B24 t ube.
boxing gloves ” to change tubes
in the field s ucces s fu lly . A final
a dva nta ge of th e in tegra l-ca vity
tube is that it is pos s ible to add
an external gas res ervoir to it in
order to increas e its life. Th is is
hard ly pos s ible, in the cell tube
becaus e of the w ay it is clamped
in to its ca vity .
The fact that Q, is h igher for
a n in tegra l-ca vit y TR tu be pe rm its
loos er coupling (larger coupling
s us ceptances ) w ith a cons equen t
increas e of the trans form ation
ratio s o that for a given insertion
los s , if a ll other factors are equ al,
the h igh-level leak age pow e r w ill
be smaller than that from a cell
TR tube.
To offs et thes e advantages
there is the obvious fact that the
in tegra l-cavity tube is m ore com -
plica ted and more expens ive to
mak e. The cavity for he cell
tube is a permanent part of the
duplexer, and is not throw n aw ay
w henever a tube is replaced ; but
the en tire cavity and tuning
me chan ism of th e in tegra l-ca vity
tube are s crapped each tim e a
tube is d is carded . Although this
w ould be an im portant econom ic
cons id eration in norm al peace-tim e undertak ings , the life of the 1B24
integral-cavity tube is s evera l tim es that of the 724, and therefore, the
cos t peT houT of operation of the tw o are roughly equal.
Figure 2,68 is a cut-aw ay view of the 1B2-I tube, w hich s how s the
tuning m echan is m , cavity , coupling w ind ow , k eep-a live electrod e, and
gas res ervoir. The 1B26 , except for a 90° change of pos ition of the
res ervoir, is a s ca led -dow n vers ion of the 1B24. The cavity is m ade ou t
SEC.2.121
INTEGRAL-CA VZTY TR TUBES
63
of an oxy gen -free, h igh -con du ctivity (OFHC) copper or s elen ium copper
block , w ith the con es s ilver-s old ered in place as s how n , and the w ind ow s
s et in to the face. The block its elf has both faces parallel and they are
of th e p rop er d iam eter to a ct a s th e cover for a w a vegu id e ch ok e con nector.
Glass
ft adder
(a)
\/
CuBJock
(b)
FIG. z .69.—Methods of seal ing glass windows into copper blocks .
The w in dow s are glas s d is k s s ea led in to Kova r rings w h ich are in turn
s oft-s old ered to the block . The origina l w ind ow s w ere m ad e as s how n in
Fig. 2 .69a . The Kovar d is k w as fla t. As a res u lt, it s oon becam e
apparen t tha t w hen the copper
cooled , a fter s old ering, it con -
tracted enough either to s qu ez e
the Kovar and thus crack the
glas s , or els e to caus e the s old er
to flow bey ond its ela s tic lim it
w ith the res ult tha t w hen the tube
w a s w a rm ed up aga in the s old er
crack ed and a llow ed the tube to
leak . The w rink led Kovar d is k
s h w n in Fiz . 2 .69b a llow s the
ou ter d iam eter of the Kovar to be
s queez ed w ithou t crack ing the
glas s , and the bevel on the edge,
w ith s old er con fined to the top as
s how n , preven ts th e ty pe of s old er
le ak ju s t d e s crib ed .
Th e w ind ow s are m ad e by s ea l-
ing glas s d is k s to the oxid iz ed
Kovar ring in an induction hea t-
ing coil. A eu tectic s oft s old er,
67 per cen t tin and 33 per cen t
lead , w ith a melting poin t of
1 80 ”C, or a pu re tin s old er, is u s ed
to s old er the Kovar to the copper.
Th is is th e fin al a s s em bly opera tion
tun ing. Becaus e of the d ifficu lt{
on the tube before fina l exhaus t and
w encoun tered in itia lly , it is now
requ ired that a tube w iths tand a t leas t fifty c.vcles of half-hour period s
a t the extrem e tem pera tures of —4 0”C and 100”C w ithou t leak ing.
64
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.212
The 1B50 , Fig. 2“70 , is m ade s om ew hat d ifferently in that its body is
fabrica ted out of three pieces of s teel: a cavity block , and tw o cover
pla tes S ince the d iam eter of the cover pla tes mus t be 2% in . to match
the connector chok es , if the tube had been m ade of a s olid piece of copper
it w ould have been very heavy and expens ive. S teel has the advantage
that after heating it d oes not becom e dead s oft as copper d oes , and there-
fore, it can be us ed in rela tively th in s ections . Its coefficien t of therm al
expans ion is only 10 X 10–e/ OC as compared w ith 16 X l&G/ OC for
copper, w hich m ak es it eas ier to s old er the w indow s in place.
In fact,
they are hard -s old ered to the block in th is tube and can w iths tand over
100 of the temper ture cy cles d e-
s cribed . A s teel cavity w ould have
a very low Qo. To overcom e this ,
th e ca vity is copper-pla ted an d th en
heated in a hy drogen atm os phere
w h ich ca us es the copper to flow and
Windo
F IG, 271.-Over la ppin g ga p of 1B50 TR FIG. 272.-CV221 (Br it ish ) 3-cm in tegr al-
tube.
ca vit y TR t ube.
form a homog neous s urface over the s teel. The gap of the 1B50, Fig.
.71 , is d ifferen t from the gap of the other tw o tubes . In ord er to mak e a
tube w hos e leak age pow er d oes not vary w ith tuning, the cones are m ade
to overlap, s o that the gap s pacing rem ains cons tant as the tube is tuned .
The us e of an overlapping gap im pos es s evere requirem ents on the tuning
m echanism . In order to m ak e the tuning curve sm ooth , it is neces s ary
to res trict the w obble of the m ovable cone to les s than 0.0002 in .
Figure 2.72 s how s a Britis h 3-cm , in tegra l-cavity TR tube, C~221 .
The bod y is copper and the w indow s are s im ilar to thos e in the 1B24.
Tuning is accom plis hed by s queez ing the s trut m echanis m s how n below
the tube, and thus moving the low er cone up or dow n.
In Ta ble 2% s ome of th e more importa nt electrica l low - evel ch ara cter-
is tics are lis ted , Thes e tubes all have equal input and output couplings
and , if they are term ina ted by a matched receiver, the input voltage
s tand ing-w ave ratio w ill be 1.2 to 1 .3 . They are des igned to be m ounted
etw een w a vegu id e chok e connectors as s how n in Fi . 273, and the bod y
Slsc. 2.12]
INTEGRAL-CA VI TY TR TUBES
65
TABLE 28-b3W-LEVEL CHARA-RISTICS OF 1B26, 1B24, AND 1B50 TR-Tu zEs
I
I Minimum tuning range I
Mc/zec
Insertion
Waveguide
‘be ‘0” 10SS(db)
QL
flf
sise,in.
max
min
—
1B26
1.4
220
24,580
23,420
* X * X 0.040 wall
1B24
1.2
300
9,600
8,500
1 x + x 0.050wall
1B50 1.2
7,100
6,000
1+ X * X 0,064 wall
d iameter is large enough to allo the us e of a pres s uriz ing gas k et as
s how n in th e illu s tra tion .
r
F IG. 2.73.—In tegr al-ca vit y TR t ube
moun ted between wavegu id e ch ok e con-
nectors.
FIG. 2.74.—Tun ingcu rve for 1B24 TR
tube. (D&z are from the SUlvaniaEledrti
Produ cls Co.)
Table 2 .9 gives the critica l d im ens ions of the three tubes .
TARLE 29.-CIt IT1CAL DIMENSIONSOF 1B26, 1B24, 1B50 TR TUBES
—
Dimension
I
1B26
I
1B24
IB50
Cavity diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ‘ 0.250”
0 .500” 0.725”
Cavity heigh t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.238” 0,454” 0.525”
Window diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.148”
0.333” 0,494”
Cone tip diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 002” 0.004”
Cone separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.,, ., ..,.
0.006”
Cone travel.................,.. . . . . . . . . . . . .
0.009” 0,018”
0.070”
COne angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36°
36” 36°
Body diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1,015” 1.760”
2.625”
Figures 2 .74 and 2.75 are tuning curves for the 1B24 and 1B26 TR
tubes.
The num ber of m egacy cles per s econd per turn is fa ir~y high and ,
therefore, in ord er to ens ure smooth tuning w ith little back las h , the
66
LINEAR THEORY OF HIGH-Q TR TUBES
[SEC.2.12
differential tuning screw must be s prin g-loa ded a s in dica ted in Fig. 2 .68.
The 1B50 has a s im ilarly s haped tuning curve.
The s h ift of res onant frequency w ith tem erature in a 1B24 TR tube
is s how n in Fig. 2-76 , w ith a curve for an all-copper cavity s uperim pos ed ,
and lines w hich ind ica te the detun ing that w ill caus e ~ db and 1 db los s .
The 1B24 and 1B26 tubes are of a ll-copper cons truction except for the
tuning mechanism . By proper choice of materia ls for the s hell and the
Turns of tuning screw counterclockwise
TR tube temperature in ‘C
o
0 20 40
60 80 100 1:
1 -
\
\
2 - \
\
3 -
\
\
\
4 -
\
All-copper ~1
5
cavity
\
!0
FIG. 2.75.—Average tun ing curve for FIG. 2 6.-Typica l t emperatu r~tun ing
1B26 TR tube. (Da a me from We&W-
curve for a IB24 TR tube. (Data are
houseEledrti Corporation.) from West i@ouse Ele&ic Corporation.)
Th e init ia l t un ing was at 9380 Mc /see, an d
QL2 = 300.
two screws, the combina t ion can be made to move the cone at a ra te
near ly equal to that of an a ll-copper cav ty. The 1B50 has a steel cav ty
with copper cones and diaphragm. Its over -a ll tuning changes at a
ra e of approximate y —0.22 NIc/sec/°C. At 6500 Nlc/sec an all-copper
cavity changes at – 0.10 &Ic/sec/°C. With a r ise of 80°C, the TR cavity
will r esona te a t a fr equency about 9.6 Me/see lower than the fr equency
of the copper cavity; and if ~Lz = 250, the s ignal los s w ill be increas ed by
about db.
CHAPT R 3
BAND AS TR TUBES
BY WALLACE C. CA DWEL
3.1 . In troduction . -Early in the d evelopm en t of m icrow ave radar it
becam e evid en t tha t the pres ence of numerous tun ing ad jus tm en ts on
the r-f com ponen ts s erious ly hand icapped m axim um s ys tem efficiency .
Although thes e con trols pres umably a llow ed the s et to be tuned to its
peak s ens itivity , the complica ted tune-up proces s tha t w as neces s ary
becaus e of the in teraction of the various con trols us ua lly res u lted in a
m is tun ing of the s ets , w ith s ens itivity dow n by 10 to 40 db. Early s ets
had the follow ing ad jus tm en ts : m agnetron im pedance tuner, TR phas e
s h ifter (to provid e ATR action), TR tuning, tw o tuning ad jus tm en ts
on the cry s ta l, four on the loca l os cilla tor, and an antenna tuner. By
1943 many of thes e con trols had been elim ina ted by carefu l d es ign of
r-f com ponen ts , s o tha t their im pedance w as w ith in abou t 10 per cen t of
line im pedance in a 10 to 20 per cen t frequency band . Even tua lly , a
ty pica l s et had on ly t e follow ing r-f tuning con trols : TR and ATR
tun ing, Ioca l-os cilla t or tu n ing, and loca l-os cilla tor couplin g t o th e cry s ta l.
The ad ven t of the therm ally tuned loca l-os cilla tor and au tom atic-fre-
quency -con trol circu its elim ina ted that manual ad jus tm en t, and the
loca l-os cilla tor coupling cou ld be s et once for a given tube, and then
ignored . Th is left on ly the TR and the ATR tuning ad jus tm en ts .
Thes e elemen ts w ith load ed Q’s of 200 to 400 w ere s till very s ens itive
to transm itter frequency , and it w as not uncommon to find ra ar s ets
in the field w ith s ens itivities 6 to 12 d b d ow n from optim um perform ance
m erely becaus e of poor TR tuning.
The combina tion of the tunable-cavity magnetron , the ban -pas s
TR tube, the 1ow -Q ATR tube, and the therm ally tuned loca l-os cilla tor
tube m ad e pos s ib le a (‘s ingle-k nob” tunable rad ar.
The firs t and mos t
obvious ad van tage of s uch a s et is its opera tiona l s implicity . S econd ,
the s im ple tuning ad jus tm en t a llow s s election of an opera ting frequen t y
that w ill m in im ize in terference from other radars and from enem y
jamming.
Th is frequency may be changed m ore or les s con tinuous ly
w ithou t in terrupting egu lar opera tion , and in tentional r-f jam ming
becom es a lmos t imp s s ib le . The ability to ad jus t frequency during
opera tion m ak es it pos s ib le to learn m ore abou t a particu lar target by
obs erving its am plitude as a function of frequency . Echoes from targets
67
68
BANDPASS TR TUBES
[SEC. 3.1
s uch as corner reflectors , cliffs , or battles hips , ha ve m ore or les s ch arac-
te ris tic fre quency dependencie s .
Thus the need or jus tification for a low -Q or bandpa s TR tube is
obvious.
His torica lly , its d evelopm ent w a s the res ult of other require-
men t s .
In 1941, the developm ent of a h igh- ow er 10-cm s earch s et to
operate a levels in exces s of 500 kw w as undertak en at the Rad ia tion
Labora tory . TR tubes w ere on ly in their in fancy , and it w as not
believed that the s oft Sutton tube (high-Q) cou ld be us ed at s uch high
powers .
As a res ult, A. Longacre and his group d eveloped the s o-ca lled
“beetle” T tube w hich w as s im ply a Iow -Q res onant s lit enclos ed in a
glas a bu bble, and d es ign ed to be clamped betw e en tw o s ection s of l~-in .-
by -3 -in . w avegu ide. Thes e tubes had large leak age pow ers , but s ince
they w e re required on ly to protect therm ion ic d iod e d etectors , they w e re
adequate. Tw o of thes e tubes w ere us ed in tandem ; the firs t reduc d
the pow er incident on the s econd .
Thes e tubes w ere turned over to the
Genera l Electric Co. for further d evelopm ent and m anufacture. M. D.
Fis ke of that com pany us ed s evera l low -Q r s onant iris es to form a band -
pas s s tructure and began to w ork on th is conception . Meanw h ile, it was
d is covered that the 721A TR tube w as able to protect cry s ta ls a t pow ers
in exces s of 500 kw . Becau e of th is , a las t-m inute change w as made in
the high-pow e r s y s tem s jus t bei g pr d uced by ins ta lling d uplexers w ith
721A TR and ATR tubes , and w ith cry s ta l m ixers .
Thus , the original incentive for producing low -Q TR tubes , that s ,
h igh pow er, w as rem ved ; but in te es t in the bandpas s fea tures of the
tube w as arous ed , and Fis ke and his group continued their w ork under
an OSRD d evelopm en t con tra ct, s pon sored by the Rad iation Labora tory .
The culm ina tion of th is w ork w as the in troduction of four TR tubes
des igned for us e in the 3-cm and 10-cm bands , tw o pre-TR tubes , and
nine low -Q ATR tubes for us e in the 1 .25-, 3 -, and 10-cm band s .
The TR
and pre-TR tubes w ill be d is cus s ed in th is chapter, and the ATR tubes
w ill be d is cus sed in Chap. 4 .
The techniques that w ere us ed to develop a bandpas s TR tube
centered firs t around the fact that the reflections from sm all, id entical,
im pedance d is continuities s p ced h/ 4 apart a long a trans mis sion line
tend to cancel each other, and , s econd ly , around the des ign of a glas s -
covered res ona nt w ind ow wh os e frequency ca n be accu ra tely con trolled ,
and w hich is able to w iths tand the action of an intens e r-f gas d is charge
along one face. In the bandpas s TR tube, there are a number (2 or 3)
of res ona nt s lits (elem ents ) s pa ced one-qua rter guid e w a velen gth along a
pie e of w a vegu id e; the ends of the guide are clos ed off by glas s -covered
w indow s. The s lits and w indow s are all tuned to the s ame res onan t
frequency . The loaded Q of the elem ents is us ually of the order of 10,
and that of the w indow s 2 to 5, as com pa ed w ith 300 for a ty p ca l high-Q
tube.
SEC.3.1]
.
q
INTRODUCTION
FIG.3.1.—At h r ee -gap bandpas s TR tube.
69
F IQ. 3.2.—A two-ga p bm dpass TR t ube.
70
B NDPASS TR TUBES
[SEC.3.2
The development of a y des ired bandpas s characteris tic is a com -
para tively s im ple as k . It becom es d ifficult only w h enthe leak age-pow e r
requirement impos ed upon a TR tube has to be cons id ered . The , s ince
m in im um leakage -pow er and max mum bandw id th are not obtained by
the s ame des ign, comprom is es mus t be made in order to get the bes t
over-a ll performance. This chapter w ill d is cus s the low -level d es ign
con s id e ra tion s , and th e leakage pow er, or h igh -le ve l cha racte ris tics , w ill b e
cons id ered in Chap. 6 .
At the beginning of th is d is cus s ion , it is important to cons id er the
phy sica l form of a bandpas s TR tube.
Figure 3 1 s how s a ty pica l three-
gap tube. A cliff erent s hape of gap is us ed in the tw o-gap ty pe’ s how n
in Fi . 3 .2 .
In the follow ing s ections the s ingle-elem ent circu it and then the
m ultiple-elem ent circuit w ill be pres en ted . Thes e w ill s erve as an in tro-
duction to the experim enta l data and to the final d is cus s ion of ach ieve-
m ents to d ate, and of problem s s till pend ing s olution,
THEORETICAL CONSIDERATIONS
3.2 . Res onant Elements .—Let us cons id er a thin d iaphragm w ith a
rectangular open ing s old ered into a w aveguide as s how n in Fig. 33a.
The s iz e of the open ing may be chos en s o that nearly all the energy of a
(a) Rectangular slot
(d) Dumbell
(g) Posts and diaphragms
Glass
(b) Window
(c) Tilted rectangular slot
(e.) Dumbell-pointed posts
(f) Dumbell-pointed
posts-tunable
(h) Truncated cones and
(i) Circular hole-post
diaphragm
(j) Crescent
FIG. 3 3.—>lisce llaueous rexanant e lements in rectangular guide,
SEC. 3.2]
RES ONANT LEMENTS
71
given frequency incid en t cm the d iaphragm is trans mitted through the
d iaphragm . Elem en ts of a grea t variety of s hapes may be made to
resonate.
The rectangu lar s lot m ay be tilted w ith res pect to the gu ide
or it may be filled w ith d ielectric. A res onant elemen t of the dumbbell
ty pe may be made w ith a number of varia tions . In elem en ts of s om e
ty pes , pos ts or cones are us ed w hich enable the res onan t elemen t to be
tuned c nven ien tly . A variety of elem en ts are s how n in Fig. 3 .3 .
To us e the elem en ts of Fig. 3 .3 in complica ted combina tions , it is
d es irable to k now the dependence of res onan t frequency on the geo-
m etrica l param eters of the elem en ts , as w ell as to k n w the frequency
d epend ence of transm is s ion or reflection . Moreover, the energy los t
currents in the d ielectric s hou ld be k now n.
Unfortuna tely , even the
s im ples t of the res onan t elemen ts—
the rectangular s lot—has not been
ana ly zed theoretica lly to the exten t of
obta in ing a numerica l res u lt. The
problem may be a ttack ed by find ing
m
G
c
Y.
experim en ta lly th e equ iva len t circu it
~+
of the res onan t elem ent. Th is equ iv-
a len t circu i s erves as the bas is for
x
ca lcu la tion s on th e more complica ted
FrG. 34 .-An equ iv ale nt circu it of a
m ultiple-elem en t circu it. An equ iva-
res onantelemen t,
len t circu it w ill be as sum ed , its behavior ana ly zed , and the as sum ption
verified by com pa ris on w ith experim en ta l d ata .
F r ana ly s is the res onan t elem en t may be regard ed as a lumped
inductance, capacitance, and conductance shunted acros s the line as
s how n in Fig. 3 .4 .
Th e s u s ce pta nce B of the equ ivalent circu it of the res onan t elem en t
may be defin d by
The frequency w h ere B = O is the res onan t angular frequency m ,
The loaded QL, is d efined (S ec. 22) by
(1)
(2)
w h ere M and w l are the frequencies w h ere the s us ceptance equa ls plus and
m inus the tota l conductance. They are given by
72
BANDPASS TR TUBES
[SEC.3.2
1
@2c — —
= +(21’o + G),
UJJ
(3)
1
d — —
= –(2Y0 + q.
u IL
If the pos itive roots of Eqs . (3) are chos en ,
(JL2 = ~oc
2% + G“
(4)
S ome inves tigators ’ have us ed a s ligh tly clifferen t defin ition of QL2.
They have d efined
QL2 . #.-
fJ2
— d
(5)
w h ere u; and u{ are the frequencies for w h ich half the pow er is reflected .
Th is d efin ition is s om ew hat d ifferent from Eq. (4) if the conductance
of the res onant elem ent is not z ero.
Equation (3) gives the frequencies
at w hich half of the pow er is transm itted b the res onant elem ent, and
thes e frequencies are not the s ame as W;and u;. To es timate the magni-
tude of incons is tency that m ight be expected , the pow er reflection at w
w ill be computed . It is given by
B=2YO+G.
(6)
The adm ittance look ing from left to right at X-X in the circu it of Fig. 3 .4
is given , a t CM,by
Y= Yo+G+j(2Yo+G).
(7)
The re fle ction coe fficie nt is
G +j(2Y0 + G)
‘=–2YO+ G+.7’(2YO+ G)’
(8)
from w hich the fraction of the pow er reflected i
~
l~lz = ; + ‘2
2(2% + G)z”
(9)
The res onant elem ents d is cus sed in th is chapter us ually have a value of
G les s than 0.1 YO. This m eans a d ifference from half-pow er reflection
of about 0 .2 per cen t.
Th e effect of cond ucta nce in the res ona nt elem en t,
th erefore, m ay be con sid ered to be sm all, and eith er d efin ition of Q~2may
be app lie d .
I ee Ref. (4) in the bibliography at the en d of the chapter .
Hereafte r superscr ipt
n umber s r efer t o t his bibliogr a phy.
SEC. 3.2]
RESONANT ELEMENTS
The equation for the circuit of Fig. 3 ,4 , rela ting
frequency in term s of QLZ, is
()
2~L,(2% + G) ‘+ “
Als o, th e pow e r reflec ed h as alread y been obta in ed
Irl’ = (2Y,Gj2 )~i B’”
73
th e s us cepta nce to
(9a)
It is often us efu l to have an expres s ion for B in term s of s ince it is r
tha t is obta ined by measuremen t. It is eas ily found that
[
1
= (Y8+YoG)(T–1)2 – T@ ‘ ,
r~l.
r
(lo)
A meas urem nt of r a t the res onant frequency , that is , a t the frequency
for w h ich B = O, can be us ed to determ ine G,
G = Y,(r – 1),
rzl.
(11)
In Fig. 3 .5 are s how n curves repres en ting Eq. (9a) for G/ Y, = O and
G/ Y , = 0 .3 . Such a large value of G is not ty pica l for the res onant
0 .8 1 .6 2 .2
B/ Y .
FIG. 35 .-The absolu te mag-
ni tude o the reflect ion coefficient
a s a fu nct ion of su scept an ce of a
single resonan t circuit .
Waw+length in cm
FIG. 36.-l3ompa rison of exper imen ta l da ta
with a theore tica l resonant -circu it curve .
elem en ts d is cus sed in th is chapter. The large va lue w as chos en to give
better portra yal of the cu rves .
In Fig. 3 .6 th e ca lcu la ted reflection coefficien t is plotted a s a fu nction
of w avelength to com pare w ith data tak en on a res onan t elem en t.
Th e
ca lcula tio s w ere m ade us ing the va lues of the res onan t frequency and
the Q~2 obta ined from the experimen ta l curve. The data for Q.* w ere
tak en at r = 2 or \rl = 0.33; therefore the theoretica l and experim enta l
74
BANDPAS S TR TUBES
[k%c. 3.2
curves s hou ld m atch at the res onant frequency , except for the fact that
los s w as neglected , and their w id th s hou ld be the s ame at Irl = 0 .33.
The fact that the experim enta l poin ts lie clos ely on the theoretica l curve
ind icates tha t, over the frequency range of the curve, the phy s ica l s truc-
ture is w ell repres en ted by the as sum ed circu it as far as reflections are
concerned.
Throughout th is d is cus s ion of the s ingle res onant elem en t, an equ iv-
a len t circu it has been cons id ered from the s tandpoin t of the reflection
ch ara cteris tics of the elem en t. To u nd ers ta nd the ga s-d is ch arge p oper-
ties of the elem ent, it is im portan t to k now the electric field in the gap
in term s of the voltage in the gu id e. For the s imple circu it, if the
capacitance w ere as s umed to be concen tra ted in the gap, the voltage
acros s the gap w ould be the s ame as a ros s the w aveguid e. How ever, a
rough meas urement on a gap of the pos t ty pe s eem s to ind icate that the
ra tio of the voltage acros s the gap to the voltage acros s the guide is abou t
II
Lp
m l
q
~
Iy
/
L
c
1P
Llll 4
FIG.3.7.—Equivalent circu it of resonant gap .
ten . Th is m eas urem ent w as m ade by placing a pla tin iz ed -glas s res is tor
a cros s th e ga p a nd mea s urin g th e s ta nd in g-wa v e ra tio a t res on an ce.
Th e
res is tance of the pla tin iz ed -glas s res is tor a t t e m icrow a ve frequency
w a s tak en to be the d -c res is tance.
Fu rth erm ore, it is k now n from th eory
and from experim ent that a pos t in the plane of the electric field in w a ve-
gu id e behaves as an inductance s hunted acros s the line. n a res onant
elem en t of the pos t ty pe, the inductance of the pos t w ould be xpected
to be in s eries w ith the capacitan e of the gap. Both the rough experi-
m ent and the ana ly s is of the res onant elem ent in term s of s im pler s truc-
tu res lea ds to an expecta tion of a s tepu p of gap volta ge over guid e volta ge.
It is w ell to as s ume a very s im ple circu it to es tim ate the s tepup in
voltage. In Fig. 3 .7 L, is the inductance of each pos t, and L is the
inducta ce as s ocia ted w ith the magnetic-energy s torage due to the
narrow ing of the gu id e. It is as s umed tha t there i no mutua l coupling
be tween L and L,.
The d is charge, or gas break dow n , ta kes pla ce acros s
the cond ens er C. The ra tio betw een the voltage acros s the gap and the
voltage acros s the gu id e m ay be calcu lated for tw o s pecia l cas es .
In the
S nc. 3.2]
RESONANT ELEMENTS 75
fired cond ition the gap circu it m ay be repres en ted s in Fig. 3“8a and
for the unfired cond ition as in Fig. 3“8b.
The ratio @’/ cl for Fig. 3 .Sa is
E
Zox x z ,
..-=
e #z :(x + x,)’+ x;x’
“ x, ~=”
In the unfired cas e and w here X = uLI and X. = 2aLp at res onance, the
ratio E/ e for Fig. 3 .8b may be w ritten as
E
x
–= x+x,’
s ince XC = — (X + XP), a t res onance.
In the firs t cas e, it w as as s umed that the gap w as brok en dow n and
that as a res ult, th gap voltage w as held cons tant. In the s econd
(a)
(b)
FIG.3S.-Circuit of r eson an t ga p for (a ) firedcondition;(b) unfired.
cas e, the gap is not fired and interes t is in the gap voltage corres pond ing
to given fixed line voltage. The Q of the circu it of Fig. 3 .8b is giv n by
()
=:X; XP2=KX;2XP.
.
Let us now as sum e that the gap w ill ioniz e at s om e defin ite voltage .?,
that th is voltage is proportional to the gap s pacing g, and that X, m g~a,
~vherea is the area of the end of the pos t,
Th en a t res onan ce,
g = k aXc = ka(X + x.),
and the critical line voltage w ill be
~=~ x
X+xp
= liaX.
This equ tion ind icates that for a fixed res onant frequency , the
critica l, or b reakdow n , voltage E is proportional to the area of the end s
of the pos ts and the reactance X of the inductive iris .
~xam ina tion of
the equation for Q s how s that if X is held cons tant, the loaded Q can be
red uced by m ak ing XP smaller w ithout a ffecting l?.
S in ce 1 ?is a m ea s ure
of the s pik e energy , it s hou ld be pos s ible, by proper s haping of the elec-
trodes , to obtain a m inim um value of Q for a given s pik e energy .
76
BANDPASS TR TUBES
[SEC. 3.3
The as s umptions and calculations made above are only the mos t
elementary s ince they do not tak e into account mutual in teraction
betw een the field s of the inductive iris es and the pos ts , nor do they
cons ider the relative magnitude of the “s tray” capacitance and the
“lum ped” capacitance of the gap.
How ever, for a res onant iris of thk
ty pe acros s a w aveguid e, the deta iled s olution of the boundary -va lue
problem has never been carried out, and it is , therefore, neces s ary to
approach the problem from the m uch s im pler poin t of view us ed here..
3 .3 . Multiple Res onant Elem ents in Waveguides .-S evera l m ethods
of naly s is and repres enta tion have been us ed in the analy s is of the
problem of circu its contain ing more th n one res onant element. As an
introd uction to this problem , a s im plified m eth od of calcula tin g th e pow e r
reflection and th e ins ertion los s of
th e th ree-elemen t circu it s h ow n in
3j%p2j>fl
m “’;p;E’’’”ca lcu”u”
tlon s , a hne a quarter-w avelength
long betw een the elements is as -
3 2
1
s umed to be independent of fre-
FIG. 39.-Three resonantelementss epara-
quency . Let the s us ceptance of
ted by quarterw avelengthsf line.
the end elements be aB, and the
s us ceptance of the center element be B. The follow ing equations us e
normalized adm ittances , that is , ~ = Y/ Yo.
If YI, vZ, and ~S are regarded as the adm ittances look ing from left to
righ t at the appropria te term inals as s how n in Fig. 3 .9 ,
y l = 1 + jab,
(12)
y2=jb+~=jb +--&=
l–~bz+jb
1 + jab l+ jab “
(13)
and
1 – abz + j(2ab – azba)
y~=jab+~=
l–ab’+jb “
(14)
By the us e of
~=1–y3
1 + Y3’
th e reflection coefficie nt is th en
j(b – 2ab + a2b3)
r = 2 – 2ab2 + j(b + 2ab – a2b3)’
Th e reflected pow er b ecome s
]rlz =
bz (l – 2a + azb’)’
4 + b2(l – 2ci + ~zbz )z”
(15)
(16)
8Ec. 3.31
MULT IPLE RE90NANT ELEMENTS
77
It is con ven ien t to d etine pow e r los s L a s th e re cip roca l of th e tra nsm itted
p ow er expres s ed in d ecib els , th us
L = 10 log, ,
Inpu t pow er .
Outpu t pow e r
(17)
If the e are no res is tive los s es in the circu it, the los s may be w ri ten in
~erm s of th e reflected p ow er,
1
— .
L = 1010g’O 1 – lrl’
(18)
For th e ca s e u nd er con s id era tion
[ 1
== 10 log,, 1 +~(1 –2a+a2b2)’ .
(19)
If Cz=l,
[
1
L=lolog,o 1+:(1 –bz )?
(20)
Ifa =$ ,
.( )
=lologl” 1+
(21)
If the circu it is compos ed of
m ore than tw o elem en ts w ith
quarte r-w avelength s epara tion be -
tw een elem en ts , z ero los s occurs
for va lues of b of the ind ivid ua l
elemen ts other than zero. Be-
tw e en z eros th e los s ma y b e s ign ifi-
can t; the grea er the number of
elemen ts , the larger may be the
los s . It s hou ld be obs erved that
the z eros can be elim ina ted by
proper ch oice of th e s us cepta nces
for the various elem en ts . For the
w’
1 I—AYA
@Ei!EElc
1 I-A%
D
-1 !--%
circu it of Fig. 39 it can be s een
L
from Eq. (19) tha t the los s has a
s ingle z ero on ly w hen a = +.
Th e
--l t-- ‘Y4
los s curve obta ined for a = + is
ana logous to the los s cu rve for a
critica lly c o u p 1e d d ou ble-tu ned
circu it. For a number of partic-
F IG. 3. 10,—MuIt ip le-elemen t r es onan t
ular circu its s how n in 17ig. 3 .10 ,
are g iven ill Table 3 .1 .
Table 3 .1 pres en ts the reflected
pow er and the ra tio of inpu t pow er to o[ltpu t pow er as a function of b .
78
BA.VDPASS TR TIBES
I
[SEC.3.3
0
0.2 0 .4 0 .6
0 .8
1,0
1 ,2
1 .4
B/ Y O
I
I
1.6
1.8
F IG. 3.1 1,—l)a ndpa ss ch ar act cr ist iw a ccor din g t o t he >Implc t h eor y for t he cir cu it s of
FIG. 310.
‘~ABLIL!1 .-THE REFLEITur ] I’(JJVERixl>THEliATIOSor.’~NI)CT~’C\ YEIIOOIJTJ ,Lr
POWER,EXPRESSEDN TERMSOF b FORSBVER.4LNICLTIELEMEXT’IR,ITIT.
E lem en ts a rc sepa ra ted by a qu :wt er wa ~elen gt h of lin e for t he fr rqt lcn (.j
cor rr spon dln g t o b = O. T}IC fr equ en cy r fepen (lcn ce of th e lin e len gth
is ncglcctcd,
I
Iuput pojver
Cir cu it of F ig. 310 Iteflcctw lpo!vt,r
ou t pu t p [)lvcr
I
I
.4
II
c
1)
E
b?
.l+b~
b,
4+b~
b,
64 + bG
b,
i36 + b’
l+g
SEC.3,3]
MULTIPLE RESONANT ELEMENTS
79
For the circu its of Table 3“1, Fig. 311 gives los s as a function of b.
It is in teres ting to note that a cond ition can als o be found for a four-
elem ent circuit w hich m ak es the los s characteris tic a m onoton ica lly
in crea s in g fu nction of b. For the four-elem ent circuit the s us ceptance
of the tw o end elem ents s hould be 1/ (1 + @) tim es the s us ceptance of
th e cen tra l e lemen ts .
The im portance of the m agnitudes and the phas es of both reflected
and transm itted w aves becom es clear in the d is cus s ion of m icrow ave
duplexers in Chap. 7 and in Vol. 16.
Th e criterion of tra nsm is s ion ba nd -
F1~. 3.12.—Reflect ion coefficient and t ransmission coefficient for circuit C of Table 3 .1 .
w id th of the TR tube m ay be cons id ered to depend on the ty pe of d uplexer
in w hich the tube is us ed .
From Eq. (15) and the expres s ion for the trans mis s ion coefficien t in
voltage,
(22)
Th e re fle ction coefficien t a nd th e tra nsm is s ion coe fficie nt ca n b e p re s en te d
as a polar plot on a Sm ith chart. Thes e quantities are s how n in Figs . 3 .12
and 3.13 for tw o three-elem ent circuits (C and D of Table 31). The
s us ceptance is ind ica ted a long the curve. The phas e of the reflection
coefficien t is m eas ured at the elem ent neares t the generator; the phas e
of the trans mis s ion coefficient is m eas ured at the elem ent neares t the
load , w ith res pect to the phas e of the incid ent w ave at the elem ent
neares t the genera tor.
The transm is s ion coefficien t is rotated through 180° corres pond ing
to tw o quart r w avelengths of line at m idband . In Fig. 3 .12 only values
80
BANDPAS S TR TUBES
[SEC.
3.4
of the reflection and transm is s ion coe5cien ts for pos itive B were
plotted s ince the curve is s ymmetrica l about B = O. It s hould be
obs erved that for B YO betw e en z ero and 1.2 , the angle of the reflection
coefficien t for the three-equal~lem ent cas e varies betw een the lim its
270° >0> 180° and – 30°< @< OO; for the unequal elem ents the
range is 90° > 0 > 20°. Although neither of the circu its p s s es s es a
90”
1.0
270°
FIQ.3.
13.—Reflection coefficient an d tran smission coefficient for circuit D of Table 3.1,
s imple res onance behavior it s eem s more lik ely that, in the us e of the
TR tube in the duplexer, the unequal-elem ent tube could be im proved
at the band edges by m atching elem ents .
3 .4 . Wave Equilibrium Calcu lations . -By an equilibrium m ethod of
ana ly s is , an expres s ion can be obta ined for the los s of a netw ork com -
pos ed of an arbitrary num ber of iden tica l s hunt elem ents equally s paced
along a trans mis sion line; and the frequent y dependence of the s pacing
betw een elem ents need not be neglected The pres en ta tion below w as
firs t us ed by FNk e and WarnerT and la ter genera liz ed by Marcus .’
SEC.3 .4]
WAVE EQUILIBRIUM CALCULATIONS
81
In Fig. 3 .14 are s how n shunt elem ents w ith arbitrary s pacings 6P
along a tra nsm is s ion lin e.
To obta in either the reflection or the trans -
m is s ion from this com plica ted s y s tem , the m ultiple reflections cou ld be
cons id ered , and the appropria te s um tak en of the s ucces s ive reflected and
transm itted w aves at the ind ividual elem ents of the s y s tem . Th is
becom es very complica ted for more than tw o elem ents . A s impler
m ethod and the one adopted here rela tes the tota l traveling-w ave am pli-
tud es proceed ing in each d irection on each s ection of line in the equ i-
librium s ta te to the am plitudes on the ad jacen t s ections of line.
Let A, and BP repres en t the voltage am plitud es of w a ves traveling
in the forw a rd and back w ard d irections at a reference pos ition jus t a fter
the pth elem ent. Let t.and r, be the reflection and trans mis s ion coeffi-
cien ts for a w ave advancing upon the pth elem ent from the left, $ and
--11-
- p-l— p -
:i3iii:m:E:
1
2 P-1 P Ptl N-1 N
FIG. 3. 14.—N lumped elemen t s spaced a t a r bit r ar y in t er va ls a long a t r an smis sion lin e.
r; the coefficien ts for a w ave advancing from the righ t. The electrica l
line length betw een the (p – l)th and the pth elem ent is O-, = 2U ~
9
w here lP–I is the d is tance s epara ting the elem en ts .
The tota l voltage
w a ve advancing in the forw a rd d irection can be w ritten
(23)
if it is rem em bered that A ~, A ~–1, and BP are all m eas ured at the s ame
ins tant of tim e; bu t the on tribution t A ~ from A ~_1 w a s m ad e earlier
by a tim e interva l corres pond ing to ff~l, hence the negative s ign . For
the w a ve in the negative d irection ,
From Eqs . (23) and (24), B may be elim inated by s olving Eq. (23), fo
BW,, substituting Bp~.i in to Eq. (23), s olving Eq. (24} f r BP and then
putting B, back in Eq. (23). The res ult is
Ap+I +
[(
p+rj+i
)
%+11:+1 e-je. _
t;+l
1
h]
~
“ ltp #8rb.l)A*l =
+
rpttil
O. (25)
82
BANDPASS TR TUBES
[SEC,3.4
This equation may be s im plified by as s um ing that the elem nts are
all id en tica l and are id entica lly s paced .
If p=T, r;= T’, t.=t; =t,
and OP= 0, are pu t in to Eq. (25), it becom es
[
~ , + (r?-’ – p)pe _ @
f-t
t
1
A, + A*1 = o.
(26)
For the n elements of Fig. 3 .14 , p runs from 1 to n – 1. To obta in the
n ratios A 1/Ao, . . . , A “/A o requires one m ore equa tion . An ad ditional
equa tion is provid ed by the bound ary cond ition that no w a ve is incident
from the right, B. = O. From Eq. (23),
As = te-ieA._l.
(27)
The general s olu tion of Eq. (26) is given by
A, = Me a + Ne–~”,
(28)
p rovid ed th at
@ — (m/ — ~2)e-le
cos h a =
2t q
(29)
From Eq. (28)
A,= M+N,
and from Eqs . (27) and (28)
A. = Mena + Ne-”a = te-i’[llfef”-’~- + Ne-(”- ~”].
(30)
Th e tra nsm is s ion coefficien t for the n elem en ts , T%, is d efined by
(31)
From Eq. (28)
M
— g.. + ~-na
T. = ‘T—.
(32)
~+1
If Eq. (30) is s olved for M/N to s ubs titu te in Eq. (32)
T. =
k–i” s inh a
s inh na – te-~e s inh (n – l)a’
or more conven ien tly
1
e e + (m l — tj)e-~~ s inh na
z = Cos h ‘“ +
2t
s inh a “
(33)
(34)
In a s im ila r man ner th e reflection coefficien t
R. = B,/A o
is found to be
[
s inh a —
-$ cos h a s inh (n — l)a
R. = ~e–Zi8
s inh na —
1
(35)
trig s inh (n – l)a “
SEC. 3.4] WAVE EQUILIBRIUM CALCULATIONS 83
If the trans mis s ion and the reflection coefficien ts of the ind ivid a l ele-
m ents are k now n , from Eqs . (33) and (35), the transm is sion and reflec-
tion from the netw ork is k now n .
It is convenien t to w rite the equations
in term s of circu it param eters .
As y et, the elemen ts have not actua lly
been res tricted to a s hunt com ponent; the elem ents m ay s t ll be regard ed
as genera l T-s ections . S ince in th is book , how ever, the general form ulas
w ill be applied only to s hunt s us ceptan ces , Eqs . (34) and (35) are w ritten
in term s of s hunt s us ceptance.
For a s ymmetrica l T-s ection r = r’.
In term s of b, the reflection and transm is s ion coefficien ts m ay be w ritten
2
‘=2+jb”
(37)
quations (35) and (36) becom e
and
where
If the line is
1
(
b
)
s inh na
T. =
cos hna+j s ine +jcos e —
<inh a“’
1 23
l+~ei~
s inh (n + l)CK
——.
En=–b
s inh na ‘
~o~a=co~o_~sino
2“
term in ated in its ch ara cteris tic a dm itta nce,
to k now the abs olu te m agnitude of the trans mis s ion
k!=1+(%3
or
1’
F.
=l+f.
(38)
(39)
(40)
it is s u fficien t
(41b)
The in formation provided in Eqs . (41) mak es it pos s ible to obta in ,
for a given b and 0 , either the los s , he reflected pow er, the trans mitted
pow er, or the voltage s tand ing-w ave ra tio. It is conven ien t to prepare
b
s tan t va lues of j. On th is chart may be s uperimpos ed a curve relating
the frequency epend ence of s us ceptance of the ind ividual elem en t to 0 .
Poin ts of in ters ection of th is la tter curve w ith the cons tan t-f curves give
t!ata on voltage s tand ing-w ave ra tio as a function of the s us ceptance
of th e in divid ua l elem en t.
‘
1
-
—
-
e
d
SEC.35]
MATRIX METHOD
85
As an example of the us e of the fik er chart, cons id er four id en tica l
h igh-Q s hunt elem ents us ually s paced a quarter-w a vele gth apart. The
term high -Q im plies tha t the elem ent s epara tion rem ains es sen tia lly a
quarter w avelength , or tha t 28 / u = 1 over a w id e range of b. Along the
line 20/ m = 1, as b increas es from z ero at m id band , the s tand ing-w a ve
ra tio in crea s es to s ligh tly ove r 2 .5 a nd th en d ecrea s es to u nity for b = 1.41.
As b increas es from 1.41 , the s tand ing-w a ve ra tio increas es rapid ly . If
the frequency depend ence of the s pacing may be neglected , the trans -
m is ion band w ill be s ymmetrica l w ith res pect to b = O. The res ult
of th is procedure lead s ’to the s am e res ult as that d erived by the s im ple
theory and s how n by curve F in Fig. 311 .
If the Q of the elem en ts is s o low that the electrica l-line-length s epa -
ra tion of the elem ents varies cons id erabl over the trans mis s ion band ,
the frequency s ens itivity of the elem en t s us ceptance s hould be given as
b z j(219 / 7r)
Th e ba nd pa s s ch ar-
acteris tic can be traced out by
follow in g th e b = j(219/ 7r) curve
jus t a s , in the preced ing cas e, t e
curve 29/ 3 r= 1 w as follow ed .
For n ega tiv e b, to us e the s am e
ch art, 2 9/ 3 rh as to run in th e d irec-
tion op pos ite to th at for p os itive b.
On the chart is s uperimpos ed a
curve rela ting b to 28/ T for ele-
m ents in s tandard 3-cm gui e,
w h os e Q~ is four and w h os e res o-
nant w avelength is 3 .33 cm .
Figure 3 .16 s how s the voltage
s ta nd in g-w a ve ra tio a s a fu nction
of b from data extracted from the
3.0
2.6
2.2
1.8
1.4
1.0
3.0 3.1
3.2 .3 3.4 3.5
3.6
kin cm
F IG. 3,16.—Fou r -equal-elemen t band-
pass character is tics ext racted from Marcus’
chart.
chart.
It is in teres ting to com pare th is curve w ith curve F of Fig. 3 .1
wh ich n eglects th e frequ en cy d ep en d en ce of th e s epa ra tion of th e elemen ts .
It s hou ld be poin ted out that f is period ic in 20/ r w ith a period
of 2 . Therefore , if a s us ceptance curve runs off the top of the chart,
it m ay be continued at the bottom . The value of 20 / 7 rw hich y ield s
the broades t transm is s ion band is then near one. The read er s hou ld
be in teres ted in s uperimpos ing a fam ily of s us ceptance curves on the
chart w ith 20 ,/ 7 at b = O as parameter.
From th is fam ily of curves
and for the s us ceptance characteris tic chos en , the optimum element
s epa ra tion for m axim iz ing the bandw id th s hould be evid en t.
3 .5 . Mat.rh Method .-The us e of the m atrix nota tion lead s to a fa irly
s im ple form ula for los s . Th is m ethod z m ay be applied s atis factorily to a
m ultiple circu it of nonid en tica l elem en ts , a d ifficu lt ca se to hand le by the
86
BANDPASS TR TUBES
[SEC,35
equilibrium m ethod . How ever, the general expres sions for the los s of
I,
1~
n elem en ts , w h ich a re obta in ed by
-
—-
th e equ ilibr um meth od , ca nn ot be
a ““ D
obta ined eas ily by the matrix
method.
i
4
(a)
If the four-term ina l netw ork
of Fig. 3 .17a is linear and pa ss ive ,
and if reciprocity applies , tw o
11
12 13
linear equations rela te any tw o of
+ 4
+
the quantitie s 11, VI, 12, and Vz
v,
~ to the other tw o. For example,
V, = aV, + bIl,
(41)
(b)
ZI = cV* + d12:
I,
12
In the m atrix nota tion
-
+
m
b~
H=(::)[:))’42)
w here a , b, c, and d are cons tan ts
(c)
d efin ed b y th e electrica l con s ta nts
FIG. 3 .17 .—Sus ceptanceircu its -(a ) a com pos ing the net w o r k . The
four-term ina lnetw ork ; (b)
two success ive
fou r -t erm in a l n etworks; (c) a shun t su scep-
paramete rs mu s t s a tis fy th e follow -
tance.
ing condit ions :
1 . For a los s les s netw ork the d iagonal term s of the matrix are rea l
a nd th e off-d ia gon al term s a re im a gin ary .
2 . If reciprocity a pplies ,
ad+ bc=l.
3 . If the netw ork is s ymmetrica l,
a=d.
If there are tw o s ucces sive netw ork s as in Fig. 3 .17bj for the s econd
netw ork
and by s ubs titu tion of Eq. (43) in Eq. (42), for the tw o netw ork s
(43)
(44)
By m ultiply ing the m atrices of Eq. (44) and by us ing the firs t cond ition
of th e preced ing pa ragra ph, th ere is obta in ed for a los s les s netw ork
(45)
SEC. 3.5]
MA TRZX MET OD
87
where VI and 11 repres en t the input voltage and curren t to a s equence
of netw ork s, and V S and Ii repres en t the outpu t voltage and curren t.
In the pres en t ca lcu la tions , on ly shunt elem en ts and !engths of line
w ithou t los s are of in teres t. For the shunt elem en t of Fig. 3 . 17c
v, = v,,
(46)
1, = jf)v, + 12.
The m atrix repres en ta tion of th e s hunt elem en t is th refore
A line length of t may be repres en ted by
[)(
v , = Cos e
jZO s in 0
I,
jYO s in 8 cos e
)
where
~ = %1.
A,
V2
12
(47)
(48)
Eauation (48) m ay be verified by reducing it to the usual expres sion
for th~ tra ns form ation of im ped ance~hrough a length of ine
~ = ,Z2 + jZO tan e
1
~Z,YO tan 0 + 1’
w here ZI = V1/11 and Z2 = v2/ 1 2 .
(a)
(b)
FIG. 31 S .—Parametersor definitionof ins ertionlos s .
For the m ultip le-elem ent netw ork , it is d es ired to ca lcu la te th e ins er-
tion los s . The ins ertion los s is the logarithm of the ra tio of the pow er
d el vered to a load of unit rela tive im ped ance w ith the netw ork rem oved
fro the line to the pow e r d elivered to the loa d w ith the netw ork in clud ed .
By referen ce to Fig. 3 .18 , it can be s een tha t the ins ertion los s is d efined as
L l
= 10
loglo } 2 .
From Fig. 3 .1 8a ,
[:11 = [: :) (:)”
(49)
88
BANDPASS ’ TR TUBES
[SEC.36
From Fig. 318b,
W ith s ome manipu la tion
L = 10 log,, [1 + *(B – c)’].
(50)
The m ethod outlined w ill be applied to calculate the ins ertion los s
d ue to a particu lar n etw ork includ -
11
12
ing the frequency dependence of
line length . The netw ork of Fig.
lt~
319w illb e con s id e redandnor-
realiz ed admittances w ill be us ed .
The m id dle elem ent m ay be d ivid ed
F1~.3.19.—Athree-elem en tircuit.
in to tw o equal s hunt elem ents .
Th is perm its trans formation th ough the netw ork by means of tw o
ident ical matrices ,
[1’1A[01
where
1
1
j;l”
(51)
(52)
After the ma rices of Eq. (52) are multiplied , it is relatively eas y , by
m eans of Eq. (50), to evaluate the ins ertion los s .
{[ 1}
L= lolog,o 1 +
{(bs in 0–4cos 0)(b s in0–2cos O) .
(53)
3.6 . Num erical Res ults .-The res ults for transmis s ion los s , obta ined
either by the equilibrium method or by the matrix m ethod , s hould be
pres en ted in s uch a w ay that they can be compared eas ily w ith the
experim ental res ults . Experimentally , los s (s tand ing-w ave ratio, or
reflection coe5cient) is m eas red s a function of frequency or of fr~
space w ave length , w hereas th eore tica lly , los s is re la ted imp licitly , th rough
the relation of s us ceptance and of phas e s epara tion betw e en elem ents , to
free-s pace w avelength . It is of in+w es t to rew rite s everal of thes e
implicit formula s for los s .
For th ree id en tica l elem en ts equ ally s pa ced ,
‘=1010g10{1+:[4:sine-cOs’)-lM)
I
I
I
SEC. 36] NUMERICAL RESU.LT8
89
for three equally s paced elemen ts of w hich the end elemen ts have ha lf
th e s us cepta nce of th e centra l elem en t,
([
~(b s in 0 – 4cos O)(b s in O – 2COS t?)
II
L = 10 log,, 1 +
; (55)
and for f u r id en tica l elem en ts equa lly s pa ced ,
L = 10 loglo
{~+4~’(cos@-:s in ey [2 (.os e-:s i~@)2- 1~} (56)
In thes e expres s ions 8 = 2u(l/ &-) w here 1 is the d is tance betw een the
elemen ts and k . is the guide w avelength , The w id e w avelength is in
turn a function of free-s pace w avelength and
the w aveguid e. It is given by the rela tion
w h ere ~ is the cutoff w a velength of the guid e.
w h ich hold w ell over the ~ 6 per
TR-tube s tud ies , w ill be us ed for
the s ueceptance. The experim en ts
s how that b is proportiona l to the
d ifference in w avelen@h from the
re sonan t w ave length .
S ince s om e TR tubes are bu ilt
w ith elem en ts w hich have a loaded
Q., of approxim ately four, s evera l
th eoretica l cu rves a re p reecm ted for
~L, = 4 .0 . Figure 3’20 s how s tw o
theoretica l bandpas s cu rves for
th ree id en tica l elemen ts s p aced on e-
qua rter guid e w a velen gth apart for
a free-s pa ce w a velength of 3 ,33 cm .
Curve B repres en ts th e res ult w h en
the quarter-w a velength s pacing is
as s umed to be ind ependen t of fre-
auencv. Curve A is a dot Of %.
a ls o of the d imens ions of
Th e e xp erimenta l re s ults ,
cen t frequency range important in
.
A =fl?.)
h in cm
FrQ. 3 .20.—Compar ison of two theor ies
for th ree iden t ica l elements for which
QLZ = 4.0,
(54) &ich tak es in to a;count the frequency d epende ce of the s pacing
bet w een elem en ts . The theory tha t as sum es cons tant s pacing pred icts a
broader transm is s ion band and a higher los s in the pas s band . The s ame
gene a l res ult m ay be obs erve in a com pa ris on of the tw o th eoriee a pplied
90
BANDPAfLS TR T BES
[SEC,36
to a three-elem ent circuit in w hich Q Z of the end elem ents is half the
value for the; cent a l elem ent. Th is comparis on is s how n in Fig. 3 .21.
Note that the los s characteris tic is very fla t throughout the pas s band .
S ince 0 depend s on the guid e w avelength , it can be expected that the
percentage bandw id th w ill change if the center of the band is s h ifted
and Q~2 of the elem ents k ept the s am e.
Waveguide of one s iz e is us ed
for three bands of particular in teres t cen tered about w avelengths of
8 .475, 9 .245, and 10.715 cm . In Fig. 3 .22 the los curves for thr e
identical elem ents , Q~z = 4.0 , w ith quarter-w avelength (ce ter of the
band ) s pacings , areplotted as a function of ~/ X, tom ak e the com paris on
A l=f(x)
B 1= ‘0%
1.0
l-l
Ao
3.0 3.1 3,2 3.3 3.4 3.5 3.6
A in cm
~,
FIG.3.21.—Comparisonof twotheories for FIG. 322.E6ect of cen ter ba nd wave-
t h ree elemen t s for wh ich t h e m iddle elemen t
length on inser t ion loss character is t ic.
has QL, = 4.0.
obvious . If the in terval betw een the zeros of los s is us ed as a criterion
of bandw id th , the percentage bandw id ths are 10.0 , 9 .75 , and 8.85 per
cen t res pectively . The band becom es narrow er and the los s in the pas s
band becom es les s as the center w a velength approaches the cu toff w a ve-
length for the guid e. Curve D of Fig. 322 s how s the pas s band w hen
the frequ ency s ens itivity of the line length s is neglected .
All the calcu lations pr s en ted in th is chapter have been bas ed on the
as s umption that the ind ividual res onant circu it is lum ped at a poin t
a long the trans m is s ion line. It is a ls o as sum ed that the coupling betw e en
the res onan t elem ents is
tion may not be va lid .
data is made in Sec. 3 .7 .
negligible. At s hort w a velengths th is as sum p-
The com paris on of theory w ith experim en tal
SEC. 37]
MULTIPLE-ELEMENT CIRCUITS
91
EXPERIMENTAL RESULTS
3.7 . Multiple-elem ent Circuits . -C’on sid era ble d ata h ave been tak en
on los s or, m ore us ually , voltage
w avelength for circuits w ith s ev-
era l elem ents . Qualita tively , the
agreem ent betw een experim en t
and theory is good . No precis ion
m eas urem ents have been tak en
becau s e e xperimen ta l re s ea rch w as
concentrated upon the m ore for-
m idab le gas -d is charge prob lem .
One s et of data is available
for w hich the theoretica l ca lcu-
la tions have been pres en ted . In
the 3-cm region three iden tical
quarter guid e w avelength , have
decibels is plotted as a function
s tand ing-w ave ratio, as a function of
0 .4
G
.E
z 0.2
cj
3 .1 3.2 3.3 3,4
3.5
3.6
1 in cm
FIG.
3. 23-Exper imen ta l resu lt s on
t hr ee-elem e~lt ba ndpa ss 62L2 of ea ch ele-
ment = 4.0.
elem e ts p w ith equal s pacings of a
QL2 = ~.o. h Fig. 323 the los s in
of w avelength to perm it com paris on
w ith t e theoretical curves of Fig. 3 .20, one s id e of the band - is not
4.2
3.8
1
3.4 ~
3.0
~ 2.6
>
2,2
1.8
1,4
1.0
I
3 .0
h in cm
F1~. 3.24.—Exper imen t a l bandpas s cha r act er is tic for one, two, and t h r ee eI emen t e,. All
elements essentially identical.
well defined because of lack of da ta ; never theless it is fa ir ly clea r tha t
the exper imen ta l resu lt lies between the two theor ies. It wou ld be
expected tha t the exper imenta l da ta wou ld agree more closely with t a t
theory which includes the effect of fr equency dependence of line length .
92
BANDPASS TR TUBES
[SEC. 37
The fa ilure of the data to agree w ith this theory m ay be attributed either
to coupling betw een the elem ents or to lack ‘of precis ion in the m eas ure-
ments .
It w ould be interes ting to m ak e m ore precis e m eas urem ents in
ord er to m ak e a m ore reliable com paris on w ith theory .
Another s et of data’ at 3-cm w avelength is s how n in Fig. 3 .24. The
ba nd pas s ch ara cteris tics for on e, tw o, and three elem en ts w e re m eas ured
in term s of the voltage s tand ing-w ave ratios .
Thes e elements have a
FIG. 3.25.—Three-elemen t bandpass cha r -
a ct er ist ic for elemen t s wit h QL~ = 29.
loaded Q.2 of 4 .8 w hich is higher
th an th e va lu e for w h ich th eoretica l
ca lcu la tion s w ere made. Ne verth e-
les s , the three curves s how clearly
that the transm is s ion bandw id th
in crea s es a s th e n umber of elem en ts
increas es . For the three-elem ent
ch ara cteris tic, th ree m in ima occu r
w h ich corres pon d to the three z eros
of los s in the theory of the three-
elem en t circu it. Th e th ree-elem en t
characteris tic is not s ymmetrica l
beeaus e the elem ents are not all
tuned accurately to the s ame fre-
quency . For proper gas -d is charge
characteris tics , the gap in the ele-
m ent has to be made small. A
small gap implies that the ratio of
the res onant-frequency s hift to
change in gap s pacing is large; con -
s equen tly , accuracy of tuning of
the ind ividual elem ents is one of
the d ifficult problem s in the m anu-
facture of the bandpas s TR tube.
An oth er example oi a th ree-elem ent ba nd pas s characteris tic is s how n
in Fig. 3 .25 for the 10 cm band and for elem ents w ith Q~Z = 29. For
s uch large valu es of Q~a ,th e ba nd pa ss w id th agrees clos ely w ith that pre-
d icted by the s im ple theory . Actually there is little departure from the
s im ple theory for QLZ above ten.
F@m e 3.26 s how s the effect of tuning each elem ent of a tw o-elem ent
circu it to s lightly d ifferen t frequencies . q Curve
A
repres ents both
elem ents tuned to AO = 9.692 cm . For curve B one of the elem ents has
been tuned to a d ifferent res onant w avelength , h = 9.592 cm . When
the tw o elements are tuned to the s ame frequency , the bandpas s char-
acteris tic is cen tered about the res onant fre uent y ; w h en they are tuned
to d ifferen t frequencies , the band center is at th e m ean of the frequ encies .
SEC. 3.fl
MULTIPLE-ELEMENT CIRCUITS
93
For elemen ts tuned to d ifferent frequencies , any gain in bandw id th is
ach ieved at the expens e of low los s w ith in the band .
r
FIG. 3.26.—Effeet of s tagger-tuning two elements .
(a)
I&E&k’
A 11=12=LC 9/4
I
* 1,+l~=ko g/ 2
1 ,=0 ,72 12
I
(b)
0.8
0.8
A
0.6
<
0.6
Ill
0.4
0.4
B
0,2 .
0.2
o.
9.4 9.6
9.s 10.0 10.2
9.2 9.4
9.6 9.8
h in cm
1010 10.2
F IG. 327,-E lemen t sp acing a lt er ed fr om >00/4.
From Fig. 3 .15 it has been s een tha t, in order to ach ieve maximum
bandw id th for a circuit w ith four e ual elemen ts , it is bes t to s pace the
elem en ts about a quarter guide w avelength apart. Th is is a ls o true for a
three-elemen t circuit, How ever, it is in teres ting to s ee t e effect on
n
94
BANDPA&S TR TUBES
[SEC.3.7
th e ba nd pa as ch ara cteris tic a s th e s pa cin g betw e en elem en ts is perm itted
to d epart from a quarter gu ide w avelength , Th is ef ect is , in general, a
the curves ’ in Fig. 3 “27 . The elem en ts in thes e circu its w ere tuned
ind ivid ua lly in a piece of w a vegu id e and then rem oved to be incorpora ted
in the m ultipleelemen t circu it. Another examplee of the effect of a lter-
ing the electrica l s pacing from a quarter w a velength is s how n in Fig. 3 .28 .
In both examples in Fig. 3 .28 the elem en ts of the circu it w ere tuned by
the m axim um -transm is sion m ethod . Curve A w as obta ined w hen the
tube w as tuned to a cen ter w avelength of 8 .4 cm , for Cur e B the tube
w as tuned a t 8 .54 cm . F@res 3.27 , and 3.28 ind icate that the band -
w id th is increas ed by spacing the elem en ts more than a quarter w ave-
length apart. For the increas ed spacing there is grea ter los s in the
50 -
\
A l ,=l@og/ 4
4.0 B 1,={2=1 .29 hw/ 4
m
II
ko=8.4cm
.x
$3,0
Qu=5.5
>
2.0B
1 .0
7 .8 8 .0
:;u
8 .2
8 .2
Aincm
8.4 S .6
8.8
I’m .
h in cm
3.28.—E1emen t su acin e a lt er ed
FIG. 3.29.—Phase-shift method of tun in~
fr om kOO/4 t uned by ma ximum - t ransmi~
s ion method .
transm is s ion band . By a d ifferen t tuning procedure, the phas e-s h ift
m ethod , the bandpas s characteris tic can be m ade fla t, Fig, 3 .29 . Th is is
a ccom plis hed , perh aps , by com pen satin g for th e d epa rtu re from qu arter-
w a velength s pacin g by a s ligh t s tagger-tun in g.
It s hou ld be obs erved
that w h en the elem en ts are tuned to giv the fla t band pas s characteris tic,
the bandw id th has been reduced . It s eem s lik ely that little can be
ga ined by a com bina tion of s tagger-tun ing and s pacing of the elem en ts ;
elem en ts w ith quarter-w a velength s pacing and id en tica l tuning s eem to
y ield the optim um bandw id th for eleme ts a ll of w hich have the s am e
QL2.
The four-elemen t bandpas s characteris tic s how n in Fig. 330 is
in tere stin g in th at it con firm s th e th eore tica l re su lt for a mu ltip le -e lemen t
circu it w ith the QL2 of the end elemen ts low er than that of the cen tra l
elem en ts . The cen tra l elem en ts had a Q., of 4 .5 . Both the experim en ta l
SEC. 3-8]
BA DPAS S -TR-TUBE DES IGN 95
curve and curve D of Fig. 3 .11 s how a monoton ic increas e of los s w ith
w avelength ofl the band cen ter. The immed ia te s uppos ition is tha t, if
the Q.z of the elem en t is increas ed gradually , k eeping the netw ork
s ymmetrica l, a fam ily of band -
pa s s ch ara cteris tics is obta in ed a s
curve D of Fig. 3 .1 1 goes over in to
curve F. By accepting a s om e-
3 .0
w h a t in crea sed los s w ith in th e pa s s
band , it m ay be pos s ible to extend
the us ual four-elem ent band in
2 .6
th is fa sh ion .
Th e theoretica l ca lcu la tion s
2 .2
w ith w hich the experim enta l da ta *
h a e een compa red all n eglected
1 .8
th e res is tive los s es in th e res on an t
elemen ts . If thes e los s es w ere
1 .4
tak n in to account, the effect
w ou ld be to in crea se the ins ertion
10
ub
\
.2=;
1= AOg
~
).. =3.33cm
1
u .
los s s ligh tly over the pas s band . ‘“~.l 3 .2
0
3 .3
3 .4 3 .5
This is illus tra ted in Fig. 10 .88 in
~ in cm
vol. 9 of th is s eries .z The band -
FIG. 3.30.—Four-elementbandpasschar-
acteristic.
w id th over w hich the los s is les s
than a given small amount is reduced s omew hat. The effects are , on the
w hole, -ra th er sma ll, a nd th eir n eglect is ju s tifie for mos t ca s es .
3 .8 . Ba nd pas s -TR-tube Des ign .—Th rou ghout th e preced in g s ection s
a tten tion has been d evoted s olely to the cons id era tion of mu ltiple-
res onant elements in w avegu id e and their effect on the transm is s ion
band . N“ow it is appropria te to mention briefly s evera l add itional
factors w h ich in fluence the d es ign of a bandpas s TR tube.
The mos t importan t factor is the fact that the TR tube mus t have
s uch gas -d is charge characteris tics tha t the radar receiver is s hort-
circu ited prom ptly w hen the m agnetron s tarts genera ting r-f pow er. In
other w ord s , the gas d is charge in the gaps of the res onant elem en ts m us t
be formed s o qu ick ly tha t in s u fficien t r-f pow er is transm itted to the
receiver to burn ou t the m ixer cry s ta l. Cry s ta l protection is the prim e
requ is ite of the TR tube. It w ill be s een in Chap. 5 tha t the gas d is -
charge is in itia ted m ore qu ick ly for a s mall gap s p cing than for a large
one, w hich im plies tha t t e res onant elemen t has a high QL2 . The gas -
d is charge phenomena d icta te an upper lim it to gap s pacing and to a
certa in exten t, a low er lim it to Q~z .
S ince cry s ta l protection dem and s high Q.,, and s ince an increas e in
bandw id th m ay be achieved only by reducing QL2 , a com prom is e m us t be
rea hed . To ens ure tha t s uch a comprom is e approach an optimum ,
96
BANDPAS S TR TUBES
[SEC. 3.9
cons id erable data have been accum ula ted on QLZ, a nd on gap s pacing of
the res onant elem en t as a function of its s hape and s iz e.
To build a tube w h ich reta ins the appropria te gas a t low pres sure and
w h ich perm its the trans mis s ion of r-f energy , a w ind ow is need ed at each
end of the tube. It is w ell to k eep in m ind the s chematic d iagram of
the in terna l s tructure of the 3 -cm band and the lo-cm band TR tubes
w hich is s how n in Figs . 3“2 and 31 . The w indow s are made by s ea ling
glas s to a m eta l frame If the proper d im ens ions are chos en , thes e
w indow s can be m ad e to res onate a t a pres cribed frequency .
Abs orption los s has been neglected in the theory , and in the experi-
m enta l res u lts s o far pres en ted it has been negligible. In a TR tube
w h ich requires gla ss w in dow s , h ow e ver, th e a bs orption los s m ay becom e
quite im portan t. In S ec. 3 .10 it w ill be noted that the abs orption los s
and Q~z Q)z of the w indow is cons id erably les s than tha t of the res onant
gaps ) increas e as the w indow is made narrow er. H re aris es another
compromis e w ith ga s -d is cha rge phenomena .
Heating of the w indow and
attenuation of the transm itted radar s ignal, d ue to the gas d is charge,
d ecrea ses as the w ind ow is m ad e n arrow e r.
In the next tw o s ections d eta iled in formation w ill be pres en ted on
both the res onant gap and the res onan t w indow . Such in formation
mus t be obta ined before it can be hoped to des ign a TR tube w hich
a pproa ch es optim um ba ndw id th .
After the data on the res onant gap
and the res onan t w indow have been inves tiga ted it w ill be pos s ible to
d ecid e jus t how the res ults for experim en ta l multiple elements can be
applied in the des ign of a bandpas s TR tube.
3 .9 . Res onant-gap Data .— s a res ult of a gradual m etam orphos is ,
th e res onan t gap u sed ’1’12n the pres en t d es igns of ba nd pa ss TR tubes has
changed in s hape from the rectangu ar res onant s lot of Fig. 3“3a to the
tunable-pos t form s of the res onan t gap s how n in Fig. 3“3 j, g, h . To
ens ure rapid formation of a d is charge in the gap, the gap s pacing mus t
be sma ll. If the d is tance acros s the rectangular res onan t s lot in the
d irection of the electric field is m ad e s mall, it is obvious tha t the capaci-
tance w ill be la rge, w hich implies tha t % w ill be large. TO reta in a
small gap s pacing and at the s ame tim e reduce % only a mall s ection
of the rectangu lar s lot m ay be left small (preferably a cen tra l s ection
w here the electric field is h ighes t) and the rem ainder of the s lot broad -
ened out, a s in the dumbbell s lot of Fig. 3 .3d . Dimens ions other than
the gap s pacing of the cen tra l s ection are us ed to ad jus t the inductance
in th e circu it to ens ure tha t th e elem en t res on ates a t the proper frequ en cy .
His torica lly , the next s tep w as to mak e the cen tra l s ection of the
dum bbell s lot poin ted as in Fig. 3 .3e.
For pra ctica l a pplica tion to the
TR tube, the gap s pacing mus t be les s than 0.010 in . This im pos es s uch
s tringen t tolerances cm the gap s pacing that the res onan t s tructure can-
Sl?c.3.9]
RES ON ANT-GAP DATA
97
not be fabrica ted and tuned ou ts id e of the tube and then ins erted in the
tube w ith he expecta tion that it w ill remain tuned . Th is s ituation can
be a llevia ted m os t conven ien tly
by us ing a pos t fit ed w ith a
screw mechan ism . F@re 3“3j, g,
h s how s s tructures us ed at pres -
ent in TR tubes and in Fig. 3 -32’s
a res onan t elem en t of the ty pe
u s ed in r-f filte rs .
In the 3 -cm region the firs t
d eta iled da ta w ere accum ula ted
for a s tructure of the ty pe s how n
in Fig. 3 .31 . In Fig. 3 .32 are pre-
s en ted datal on gap s pacing and
FIQ. 3 .31—Single resonante lement w ith
~LZ as a function of d iaphragm
posts .
open ing w ith the pos t d iam eter and the angle of the con ica l poin t as
parameters . In genera l, as the open ing of the d iaphragm w increas es ,
;3W
50
400 w
450
d.60
L
I
300 350
400 w 450
FIG. 3.32.—Gap-spacing and QL , dat a on
the tunable-post gap of Fig. 3.31. All
d imens ions a re in roils .
the gap s pacing g increas es to
mainta in the circuit res onant a t
the s ame frequency . Th is means
th at w ith a d ecre as e in ca pa cita nce
in the gap, there is a corres pond -
ing increas in the opening of the
d iaphragm w hich repres en ts an
increas e in ind uctance. Th is is in
th e righ t d irection for qu alita tive
agreem ent w ith the theory of th
FIG. 3 .33.—Single resonant e lement with
t runca ted cones.
in ductiv e d iaph ragm .
As has been m entioned earlier in the text, in the
pres en t s ta te of d evelopm ent of the theory , the s hape of the res onan t gap
of Fig. 3“31 pres en ts too d ifficu lt a problem for theoretica l ana ly s is . It
98
BANDPAS S TR TUBES
[SEC.3.9
is also in teres tin g to n ote tha t QLZ d ecrea ses a sthe capacitan ce of the gap
d ecreas es w h ich agrees qualita tively w ith Eq. (4). S ince the varia tion
of QLZ w ith the angle of the con ica l poin t is les s than the ex erim enta l
error of m eas urem ent, s uch a s et of curves does not appear in the figure.
Ad d tional da ta’z on the 3 -cm band w ere obta ined for a res onan t gap
of the trunca ted -cone ty pe w hich is s how n in Fig. 3 .33 . For this gap,
QL2 and the gap s pacing are tabula ted as a function of d iaphragm open-
ing, of cone angle, and of d iameter of the apex of the trunca ted cone in
Table 3 .2 . From Table 3 .2 it is of in teres t to note tha t ~L2 is a minimum
for an angle of abou t 35° and changes very s low ly w ith o on either s id e
of 35°. The gap s pacing s eem s to be rela tively ind epend ent of angle
over the range of angles pres en ted in Table 3 .2 . Data on Q~* and gap
TABLE 32 ,-TRUNCATED-CONEGAP RESONANT1~T A = 3,33 CM
a. Depend enceof Qr,?on diaphragmopeningw ,cone angle 0,an d coned iam eterd.
d
roils
15
30
45
w
mils
258
284
320
343
398
446
451
467
502
258
284
320
343
398
446
451
467
502
258
284
320
343
398
446
451
467
502
15°
6.6
6,3
4.6
3.6
2.8
2.1
2.1
6,6
6,3
4,3
3.8
2.9
2 .0
2 .0
1 .7
6 .1
5 .3
4 .5
3,.5
2 .6
2 .3
2 .0
1 ,5
30°
4,9
3.2
2.9
1.8
1.3
4.6
4.1
2,9
2.2
1.6
4.5
3,2
2.8
2.2
1.6
cone angle@
35°
4.4
3.8
2.7
2.1
1.6
1.5
4.3
4 .0
2 .9
2 .1
2 ,1
1 .6
1 .5
4 .1
3 ,7
3 .1
2 .4
1 .9
1 .5
40°
4 .5
3 .8
2 .7
2 .0
1 .4
1 .7
1 .2
37
39
2 .6
2 .1
1 .5
1 .4
1 .2
4 .2
3 .0
2..5
1 .9
1 ,5
1 .2
-
45°
4,4
3.9
3.1
2.6
1.9
1,5
4.4
3,6
2.8
2.6
1.6
1.4
4.0
2.8
2.5
1.8
1.4
1.4
50°
41
3.6
2.8
25
1,9
1.5
1,3
1.2
4.0
37
27
2.0
1.5
1.4
1.1
3.9
3.5
2.s
2,2
1.4
1.5
13
1.2
60°
5.0
4.3
3.3
2.8
2,2
2.1
1.7
1.6
4.8
4.2
3.0
2,1
1.6
1.9
1,.5
4.7
4.7
3,1
2.5
1.5
1.6
1,8
SIX!. 39]
RESONANTJ 2i4P DATA
99
TABLE 3t2.—TEUNCATED-CONEGAP RESO~ANT” AT x = 3.33 c~.—(Conlinued)
b. Depen den ce of gap spacing g on diaphr agm open in g w, con e angle 8, and con e
diameterd.
d
mila
15
30
45
w
roils
258
284
320
343
398
446
451
467
502
258
284
320
343
398
446
451
467
502
258
284
320
343
398
446
451
467
502
15”
1,8
2.4
5.0
6.4
14
26
25
31
9
13
18
22
36
.56
65
84
20
27
34
48
62
84
84
30°
3.0
7.5
9.0
31
55
g,~
13
22
39
70
20
34
41
63
85
35°
10
2.5
8.0
17.0
26.5
39.0
9
12
1!9
24
41
61
69
19
24
34
38
60
87
Coneangle@
40°
1,0
3.0
70
20
36
37
64
13
19
23
40
61
67
15
33
40
60
86
45°
1.5
3.0
7.0
10
23
40
8,5
12
18
25
65
79
17
33
40
66
92
50°
1,2
3,0
6
9
23
43
51
74
6
12
19
41
63
76
15
20
31
36
84
86
s u cim z have been extracted from the tables for a cone angle of 35° and
p~otte~ in Fig, 334. Since Q., is ind ependent of the d iam eter of the
apex of the truncated cone, on ly one curve rela ting QL, to w appears .
Such a w id e range of data res ults from the fact that the experim en ts w ere
explora tory . Before th ed ata w e re obta in ed j th e appropria te d im ens ion s
for res onance had to be as certa ined by tria l and error. For applica tion
to the bandpas s TR tube, the curves may be d em ons tra ted for a s pecific
case.
S uppos e m echanical cons id erations d em anded that d be no les s
than 0.030 in ., and the gas -d is charge cons id erations d em and ed that g be
no greater than 0,010 in . Then for the gap to res onate at 3 .3 cm , w
m us t be 0 .266 in ,, and QL* w ill be 4 .1 .
100
BANDPASS TR TUBES
[SEC.
All va lues of Q., a t 3 .33 cm w ere obta ined by eva luating d lr{/ ~
near res on ance from a plot of d ata on Ir I as a function of X u sing Eq. (9”11)
of Chap. 9 . The conductance G of the res onan t gap w as s o small hat
th is m eth od ga ve relia ble res u lts .
The va lues of II’! w e re obta ined from
s ta nd in g-w a ve mea s urements u s in g a ca lib ra ted cry s ta l d etector.
Meas-
urem en ts of length w ere m ad e on a traveling m icros cope to an accuracy
of 0 .000 1 in .
From the s ca ttering of the experim en ta l poin ts , it can be
s een that the data on Q~z are cons is ten t to w ith in 10 per cen t in the
cas e of Fig. 3 .32 and 3 per cen t in the ca s e of Fig. 3“34 .
Direct coupling is another quantity w h os e im portance becom es evi-
d en t d uring the s tud y of th gas -d is charge problem . Y d irect coupling
is m ean t the ins ertion los s of the elem en t w hen it is h igh ly d etuned , that
5[
I
I
150
. ..-.1- .-
4
40
Q3
30 ~
L2
2
1
10
0
.~ o
240 28o 320 360 400440 480520
w
F1~. 3 .34 ,—Ga&spacing and C?LZ ata
on the trunca ted cone gap of Fig. 3 .33
for h = 3 .3 3cm , O = 35°.
40
% 30
c
.-
0
200
300 400 500
w
Fro.3.35.—Direct coupling of
truncated cone gap for A =
3.33C]Il.
is , w hen the gap is s hort-circu ited by the d is charge.
From Fig. 335
it can be s een that for practica l d im ens ions of the res onan t gap, the
d irect coupl ng’ may range from 25 to 35 db.
Not s o broad a pas s band is requ ired for the lo-cm tubes as for the
3 -cm tubes . Th is circum stance m ak es the com prom is e betw een linear
and non linear opera tion of the tube s o eas that manu facture of 10-cm
tubes w as commenced on the bas is of very few meas urem en ts on the
linear characteris tics of the res onant gap. How ever, further m eas ure-
- m en ts have s ince been m ad e w ith the in ten tion of im proving the prod uc-
“ tion d es ign . Table 33 pres en ts da ta on gap s pacing, QL~, and d irect
coupling as functions of d iaphragm open ing, cone angle, and d iam eter
of the apex of the trunca ted cone. Reference s hou ld be m ade to Fig. 3 .33
for the meaning of the s ymbols .
The res u lts obta ined a t 10 cm are
s im ilar to the res ults obta ined in the 3-cm band .
To s ca le by w avelength the d imens ions of a gap, res onan t at one
frequency , to the ppropria te d im ens ions for a gap res onan t a t anothe
:,
-,.
SEC. 3.9] RESONANT-GAP DATA 101
TABLE 3 3 .—TRUNCATED-CONEGAP RESONANTAT x = 10,4 CM
Depen den ce of ga p spacing, ~L 1, an d direct coupling on con e angle, con e diam eter ,
a nd dia ph r agm open ing. ]z
All dimen sion s expr essed in t hou sa ndt hs of a n in ch ,
d
o
20
29
44
w
795
1010
1200
1400
795
1o1o
1200
795
1010
1200
795
1010
d
o
20
29
44
Gap spacing
Cone angle O
25° 35°
—
—
o
2
12
70
155
1
15
60
8
27
94
24
58
w
795
1010
1200
1400
795
1010
1200
795
1010
1200
795
1010
45° 55
. —
o
0
28
38
157
233
364
3
7
22
36
128
183
5 9
38
65
22 29
80 113
QL,
Cone angle 9
25”
2.4
1.75
Direct coupling
35°
3.5
2.4
1.65
4.2
3.3
2.2
5.0
3.2
2,2
4.8
3.1
45° / 55”
—l—
4.3
2.96
2.8
2 04 1.90
1,39
1.40
I
4,6
4,2
2.9 2.8
2.3
2.0
4.6
4.3
2.9 2.7
4,5
4.0
3.1 2.9
Cone angle O
25”
9.2
12.8
35°
19.0
15.4
8,3
26.5
22
19
27.7
22.6
18.8
26.5
23.5
45°
23,9
18.6
15,2
28.3
21
20
27.2
23.6
28.6
23.9
55°
28,5
24.1
21.2
17.9
28
25
21.4
30.0
25,1
29.8
24.5
E G. & G LIBRARY
W VEGAS BRANCH
102
BANDPAS S TR TUBES
[SEC.3.10
frequency can be done on ly very rough ly . Even though the s ca ling is
rough, it s erves as a guide to give the range of d im ens ions to be inves t -
gated . It is pos s ib le to check the res u lts of s uch s ca lings by us ing
Ta bles 3 “2 a nd 3“3 .
3 .10 . Res onant-w ind ow Data .-Before the res onan t glas s w ind ow is
con s id ered , it is a ppropria te to tu rn a tten tion to th e recta ngu la r res on an t
s lot. The res onant w indow has the s ame s hape as the rectangular s lot
except for the corners or end s w hich are rounded in ord er to avoid loca l
s tres s es in the glas s . For the rectangular res onant s lot there is good
exp erim en ta l co%rma tion of th eory .
Thk theory 14 propos es that the characteris tic
ta ngu la r gu id e is
impedance of rec-
(57)
w here p is the permeability , c the d ielectric cons tan t, and a and b are
the w id e and narrow d imens ions of
the gu id e.
It can be s een that as
4.0-
either a or b is changed the other m ay
A=9.80cm
P
be a ltered to reta in the s ame value 3 .o
/
E
2.0 -
/
.0
1.0-
4.0 5.0 6.0 7.0
8.0
a in cm
FIG. 3 .36.—Junct ion of tw o gu ides :
FIG.. 3.37.—Rectangula r slot in
or a dia ph ra gm wit h a r ect an gu la r slot
dia ph ra gm . Compa rison of t h eor y and
in waveguide.
experiment.
of 20. It is in teres ting to as sum e that tw o guides of d ifferen t d im ens ions
but th e s am e cha ra cteris tic im ped ance s hould y ield no reflection at their
junction . Equation (57) may be rew ritten in the orm
“=iz’[a’-
(53)
Equation (58) repres en ts a fam ily of guides all of w hich hav the s ame
characteris tic im ped ance, and all of w h os e corners lie on a hy perbola as
s how n in Fig. 3 .36 . The m inimum w id th of the guid e is jus t equal to
half the free-s pace w avelength; 2a = A.
The d iagram of Fig. 3“36 m ay repres en t not only the junction of tw o
w avegu idea , bu t it m ay a ls o repres en t a w aveguide w ith a rectangular
..’,
,.,
,.,’,. ,.
SEC. 3.10)
RES OATANT-J 1’lNDOW DATA
103
aperture in a trans vers e d iaphragm . S uch a d iaphragm m ay be regarded
as a s hort length of gu ide join ing the tw o guid es on either s id e of the
d iaphragm . Normally the tw o gu id es that are conn cted tvill be of
the s am e s iz e, and for th is ca se Fig. 3 ,37 pres en ts a com paris on of experi-
m ental d ata8 w ith the cons ta nt-im ped an ce th eory .
It m ay be obs erved
that the agreem ent is good for large apertures , bu t for s mall apertures
the length of the s lot a mus t be about 1 .5 per cen t les s than the length
pred icted by the theory .
100
80 -
1
I
1
\ ~
Standard 1~’~ x 3“guide
60
A=1O cm
40 -
\
\
20
t=
1.00“
\
QU 10
8
\ o.50”
6
\ \
w
4 -
\
0.063”
2
\
\
1
10 20
40 60 80100
200 400 600 800x 10-
“3 in.
b
F1~.3.38.—QL*of rectangular dot for three diaphragm thicknesses.
As the frequency of the electromagnetic w ave is changed , the char-
acteris tic impedance of the s hort length of guid e in the d iaphragm
a erture w ill change at a d ifferent ra te from that of the connected gu id es .
This means that on either s id e of a given frequency , a reflection w ill
occur at the d iaphragm . The frequency dependence of the reflection is
importan t for p ra ctica l app lica tion s .
Th is has been m eas ured for three
th ick nes ses of d iaphragm and has been expres sed as QLZ by evaluating
d lI’1 / d l near the res onant w avelength , that is , the w avelength of m in i-
mum re fle ction .
In Fi . 3 .38 extens ive dataa on a thin d iaphragm ,
0 .063 in . th ick , s how that a log-log plot of QL* as a function of b y ield s a
s tra igh t line. S tra ight lines w ere therefor d raw n through the very
104 BANDPASS TR TUBES [SEC.3.10
s pars e d ata on half-inch-and one-inch-th ick d iaphragm s . Even though
thes e data may not be s o reliable, they are importan t in that they ind i-
o.090’fi ~
(b)
F1a 3 .39.—(a) Window
the 3-cm band; (b) window
the 10-cmband .
ca te a trend tow ard higher QLZ as
the join ing s ection of gu id e is m ad e
longer.
The genera l s tructure of the
res onant w indow , a s lotted meta l
fram e filled w ith glas s , is clearly
s how n in Fig. 3 .39. It is d ifficu lt
to obta in ad equate d ata on w ind ow
d im ens ions s ince to d o s o requires
the prepara tion of glas s -to-m eta l
w
in,
0.60
0.56
0.52
M
0’482.9
3.1
3.3
3.5 3.7
Aoin cm
dimension8 for
FIG. 3 .40.—Resonant wavelengths for the
dimensions for
3-cm band indow of F ig. 3.39a .
s ea ls a nd ca refu l grin din g toth e d es ired th ick n es s .
How ever, for a given
2.1
* 1.9
~
:
.-
C
: 1,7
1.5
1
8
10
12
o in cm
F1rJ . 3 .41.—Resonant
wa velen gt hs in t he l(Lcm
region for th e window of
Fig. 3.39b.
w indow height h at 3 cm and at 10 cm , the
length of the w indow as a function of res onant
w a velength is pres en ted ls in Figs . 3 .40 and 3 .41 .
From Eq. (57) it may be obs erved tha t if the
height of the s lot rem ains cons tan t, to m aintain
con s tan t impedance
4a2 – AZ = cons tan t,
w hich gives for the ra te of change of a w ith
res pect to X
da A
= —.
ch 4a
(60)
Applica tion of th is equation to the l~cm w ind ow
w h ich mos t clos e ly re s emb le s th e recta ngu la r s lot
yields
dL A =055
—=— .,
dh 4L
(61)
SEC. 3.10]
RESONANT-WINDOW DATA
105
for h = 10.0 cm and L = 1.8 in . Data tak en from the curve of Fig. 341
give a s lope equal to 0 .37 w h ich is cons iderably below the 0.55 obta ined
from the the ry . The effect of the d ielectric is im med iately ques tioned .
How ever, Eq. (57) s eem s to imply that given a length of s lot, no matter
w hat the d ielectric and its res onan t w avelength , he rate of change of
length w ith res pect to res onan t w a velength s hould be ind epend ent of the
dielectric.
Add itional da ta” on w indow s for the 3-cm band are tabula ted in
Table 3 .4 . The variables are w indow height, th ick nes s of glas s , and
TABLE 3.4.—DATAON WINDOWSRESONANTAT L = 3.33CM
L
, g,
roils
roils
——
2 0 312
2 0 312
125 187
125 187
125 187
62.5 93.2
62.5 93.8
62.5 93.8
t,
mds
33.5
33.5
33.5
33.5
23,0
33.2
33.1
24.2
w ,
roils
5641
580
487
512
551
459
467
487
glass
705
707
705
707
707
705
707
707
I
d&e
w ith respect to
. —
Q
dh,
cm/ mil
. —
1.3 0,0037
1.2 0.0030
2.1 0.0062
2.8 0.0047
2.1 0.0075
4.3 0.0020
6.5 0.0063
4.4 0.0070
dt,
:m/mil
0,039
0,043
0.055
0.042
0.065
0.130
0.037
0.051
dw ,
cm/mil
0.0062
O.oom
0.0120
0.0067
0.0083
0.0050
0.0074
0.0070
One-way
pow erloss
%
3.0
2.1
8.3
5.0
4.3
17.0
13.0
8.5
db
0.13
0.09
0.37
0.22
0.20
0.81
0.61
0.39
k ind of glas s for w hich the appropria te w indow length is pres en ted , for
res onance at XO= 3.33 cm . Note that for t = 0.0335 in . and 705 glas s ,
both Q.z and the ins ertion los s in crea se as the w ind ow height is d ecrea sed .
The va l e of Q.a increas es and the ins ertion los s d ecreas es as the glas s is
changed from 705 to 707, w hich has a low er value of both rea l and
imaginary parts of the d ielectric cons tan t. Furthermore, as the g as s
is m ad e th inner both ~L2 and in s ertion los s d ecrea s e.
The va lues of the
d ielectric cons tant for thes e tw o glas ses are given in Table 2“5 , S ec. 2 .8 .
It w ill be recalled that the narrow -band TR tubes have an ins ertion
los s in the range from 1.0 to 1.5 db at m idband . The bandpas s tubes
are in tended to extend the band w ithout appreciably increas ing the
ins ertion los s and , of cours e, it is d es irable to d ecreas e the los s .
It is
apparent then that w ith tw o w indow s in the bandpas s TR tube, they
s hould have a height grea ter than a s ixteen th of an inch to avoid too
la rg a n in s ertion los s .
The three columns of data in Table 3 .4 on ra te of change of res onant
w avelength w ith res pect to w indow height, length , and th ick nes s are
us efu l in poin ting ou t the m echanical tolerances im pos ed on the w ind ow .
It is not y et k now n how clos ely the ind ividual elemen ts of a multiple-
106
BANDPASS TR TUBES [SEC. 3.11
element circu it mus t be tuned to the s ame frequency in ord er to a tta in
the optimum bandpas s . It w ill be reca lled from Fig. 326 tha t s tagger-
tuning tw o elem en ts by about 1 per cen t res ulted in a very poor bandpas s
characteris tic. Thes e elem en ts had values of Q., low enough to obta in
nearly 10 per cen t bandw id th w hen tuned to the s ame frequency . If it
is arbitrarily requ ired that the ind ivid ual elem en ts m us t be tuned w ith in
0 .5 per cen t of the cen ter frequency of the band , the tolerances on the
d im ens ions m ay be eva lua ted .
For the us e of the w indow in th fifth
line from the top of Table 34 for w hich Q~Z is 2 .1 , a 0 .5 per cen t change
in res onant frequency corres ponds to a w avelength devia tion of i 0 .017
cm and cons equently to
Ah = tO.0027
in.,
At = k 0.00026 in .,
or
Aw = t 0 .0021
in.
Equation (2 . 13) gives a value of s us ceptance tolerance of the w indow
equal to +0.042 , from w hich the voltage s tand ing-w ave ra tio is found
to be 1.05 . In ord er to adhere to the 0 .5 per cen t tolerance on res onant
frequent y a VSWR of 1 .05 at the cen ter-band frequency mus t not be
exceeded.
3 .11 . Pres en t Band Coverage.—The m icrow ave s pectrum has been
d ivid ed in to band s accord ing to the nom inal range of frequen cies of rad ar
transmitters.
The band des ignations and frequency or w avelength
band lim its are given in Table 35.
In order to d es ign a TR tube f r a
TABLE 35.-h”• MINAL TIIANSMITTEI+FREQUENCYANDS
Band
designation
K
X8
XL
Sw,
SW2
SA,
SA,
Ss l
l%
&l
%1
Center
w av elength,cm
1.25
3.23
3.43
8.285
8.640
9.020
9.455
9.s40
10.170
10,515
10.900
Band lim it s
3. 13–3 .33 cm
3.33–3,53cm
}
3550-3700Me/see
340Ck3550Me / s e e
}
325&3400Me/ s ee
3100-3250Me/see
}
300 0-310 0Me/ s ee
2900-3000Mc /see
}
2613w2900Me / s e e
270S2600Me/see
}
Percentage
ba ndwidt h of
ma jor bands, %
12
8.45
9.23
6.67
7.14
given band , it is more importan t to k now the percen tage bandw id th
than to k now the abs olu te bandw id th . The percen tage bandw id th is
SEC. 311]
PRESENT BAND COVERAGE
107
the ratio of the bandw id th in frequency to center frequency m ultiplied
by 100. It is the percen tage of frequency devia tion from the res onant
frequency w hich determ ines the s us ceptance of a res onan t elem en t and
the d evia tion from on e-qu arter guid e w a velen gth of the s epa ra tion s of th e
elemen ts . The percentage bandw id ths have been given for the major
bands ra ther than for each s ubband s ince it has been found pos s ible to
des ign TR tubes that s ucces sfu lly cover the m ajor band s .
N-o attempt has been made to bu ild a bandpas s TR tllhe of the
multiple-elemen t ty pe for the l-cm band .
The s chem e ou tlined in th is
chapter, how e ver, is qu ite applicable and it w ou ld be in teres ting to bu ild
a l-cm tube for com paris on w ith d ata n 3-cm and 10-cm tubes , es pecia lly
L-..”. ,.
F IG.342.-Photograph of 9.2-cm-ha
md I
---
~andpassTR tube showing in t erna l s t ructu re.
w ith rega rd to ga s-d is ch arge ph en omen a.
The w indow w ould be more
d ifficu lt to bu ild bu t the gap shou ld pres en t no unusual problem s . A
s om ew h at d ifferen t approach to a broad band l-cm d uplexer is d es cribed
in Chap. 8 ,
It is d ifficu lt to arrive at the pres en t d es ign of the bandpas s TR tubes
from a logical cons id eration of the data and d is cus sions of th is chapter
and of Chap. 6 . The tubes w e e developed hurried ly and grew in to
their pres en t form s as a res ult of a s eries of s mall changes and neces sary
compromises.
Bandpas s TR tubes have been des igned for the 3-cm band
and for s evera l s ubd ivis ions of the 10-cm band . The manufacture of the
lo-cm tubes w as commenced before the des ign of the 3-cm tube w as
w ork ed ou t. The three lo-cm tubes are cons equen tly qu ite s im ilar in
d es ign and a ls o s om ew h at d ifferen t from the 3-cm tube.
108
BANDPASS TR TUBES
[SEC.311
The 1O-CVZTube s .—All th e 10 -cm tube s have th e s tru ctu re e xemplifie d
by the 9 .2 -cm bandpas s TR tube s how n in Fig. 3 .42 . The internal s truc-
ture of the tube is s how n w ith the gaps and w indow s held together by the
s am e rectangular rod s that fit in to the corners of the tube bod y and s erve
as s pacers for the gaps . Three gaps w ith Q.z equal to about s ix w ere
us ed in thes e tubes and the w indow s w ere des igned w ith a very low Q~z ,
abou t one.
It w as intended that the gaps w ith much higher Q., than
th e w indow s shou ld govern th e bandpa s s cha racte ris tic a lmos t comp le te ly .
In fact it is true that the bandpas s characteris tic of the three gaps is the
s am e w h ether the w ind ow s are s old ered in place or not.
TABLE3.6.—GAFDIMENSIONS,WINDOWDIMENSIONS,ANDELEMENTSPACINGSFOR
THREE TUBES FOR THE 1O-CMBAND
Dimensions
Par t a nd figu re
reference
Gap dim en sion s, r efer t o
F ig. 344
Window d imension s. r efer
to Fig. 339
E lemen t spa cin gs, r efer t o
F ig. 3 .45
Letter
dimen-
sions
a
d
6
h
T
8
w
8
9
QLZ
1
h
t
Q.,
glass
a
d
L
?../4
8.463cm
1B55
O.125in.
0,313
0.182
1.000
0.171
No. 10 -32
0.812
60°
==0.008
5.5
1 .5 60 + .OCE
0,875
0,060
0.8
707
1.02
1.34
4.73
1,03
Cen ter wave length
9.238 cm
PS3S”
0.12.5in.
0.313
0.182
1.000
0.187
No. 1CL32
0.875
60”
=0.008
7.0
1.665 + .00
0.875
0.060
0 .8
705
1.15
1.15
4.61
1.17
10,708 cm
1B58
O. 125 in.
0.375
0.130
1.080
0.250
No, 8-32
1.125
60”
=0.003
5.5
1,905 + .004
0,875
0.060
0.8
705
1.70
1.63
6,66
1.57
* SperryGyrmcow Co. number.
The bandpas s ch racteris tic for each of the lo-cm tubes is s how n in
Fig. 3 .43. Thes e curves are quite s im ilar to both the theoretica l nd
experim en ta l cu rves s how n ea rlier in th is ch apter.
It can be s een that
the voltage s tand ing-w ave ratio fo each of the tubes is les s than 1.5
over the entire bandw id th to be covered .
The 9 .2 -cm tube is not
cen tered properly bu t th is s ituation w ill probably be rectified by the
SEC.3.11]
PRESENT BAND COVERAGE
109
tim e th is book is publis hed . It s hou ld be noted that r equa l to 1 .5 cor-
res pond s to a los s in pow er of on ly 4 per cen t or 0 .2 d b.
In Table 3 .6 are given all the es s en tia l d im ens ions for three tubes
for the lo-cm band . The gap d im ens ions m ay be in terpreted by reference
2:6
2.4
2.2
2.0
~ 1.8
g
1,6
1,4
1.2
1.0
8.0
9,0
10.0 11,6
Wavelength h in cm
FIG. 3 .43.—Bandpass characte ris t ics for the lo-cm tubes.
to Fig. 3 .44 . Thes e d imens ons w ere the res u lt of a rela tively few
experim en ta l a ttempts to obta in a res onan t gap w ith the appropria te
ga p s pa cin g, Q.z, and res onant frequency . There w as no mapping of
gap spacing o of Q.z as functions of various d imens ions for a given
res onan t frequency . The genera l
trends s how n in Figs . 3 .32 and
3 “3 4 and Ta ble 3 .3 a re pertin en t.
Ta ble 3 .6 a nd Fig. 3 .3 9 p rovid e
the w indow d imens ions for res o-
nance at the cen ter w avelength of
each of the band s . Thes e data
of w indow length as a function of
res onan t w a velength in Fi . 3 ,41 .
Th e elem en t s pa cin gs a s given
in Table 3 ,6 w ith reference to Fig.
345 are a ll a quarter of a gu id e
w a velen gth , Xo/ 4 , w ith th e excep-
tion of thos e for the 8 .5 -cm tube.
F1o. 3.44.—Gap dim en sion s of 10-cr n TR
tubes,
When the 8 .5 -cm tube w as des igned it w as though t that incr as ing the
s pacing betw een elemen ts w ou ld increas e the bandw id th . When the
elem en ts are tuned to avoid any large bum ps w ith in the band , the band -
w id th is qu ite com parable to the bandw id th w ith quarter-w avelength
spacings.
It is evid en t from th is fact that the s eparation betw een
1 0
BANDPASS TR TUBES [SEC.3.11
elemen ts is not a t a ll critica l.
This point w as d is cus s ed earlier in
the chapter and data on the 8 .$cm band w ere pres en ted in Figs . 3 -28
and 3.2 9.
Only the reflected los s is includ ed in the bandpas s char cteris tic.
The abs orption los s a t m idband is of the ord er of 0 .5 to 0 .8 db; of th is
Whdow
/ Y
I
[,,,,,,
t - a - t - ’ - + - ’ + +
~L~
F IG. 3.45.—Spacing of elemen t s of 10-cm TR tubes t o a ccompany Table 3.6,
am ount 0 .05 to 0 .1 d b is caus ed by d ielectric los s in each w ind ow , and the
res t is res is tive los s in the tube w a lls and the res onan t gaps .
Doubtless
th is los s w ill d ecrea se a little as prod uction m eth od s a re refin ed .
The 3 -cm Tube.—It is of in teres t to m en tion that a few three-gap
tubes w ere bu ilt for the 3-cm band accord ing to a des ign that w as es sen -
.-
1’1o. :3.46 .—A 3-cm band TR tube , th ree-gap bandpass.
tia lly the s am e as for the 10-cm tubes . A picture of one is s how n in
Fig. 3 .46 . By the tim e a few of the three-gap tubes w ere being bu ilt in
pilot-plant production , a better unders tand ing of the gas -d is charge
ph en omen a wa s bein g a cqu ired .
Th is better und ers tand ing prom pted a
d es ign of a tw o-gap tube. IIhen a s ingle-gap tube is nearly s atis factory ,
Th is w ill be made clear in Chap. 6 . The tw o-gap tube, s how n in Fig.
SEC. 3.11]
PRESENT BAN COVERAGE
111
3.47, repres en ts an improvement over the three-gap tube in that it is
ch aracteriz ed by better gas d is cha rge and ba nd pas s ch ara cteris tics , and
s horter length; it is eas ier to m anufacture, and eas ier to tune.
-i
F IG. 3.47.—A 3-cm ba nd TR t ube, two-ga p ba ndpa ss.
In Fig. 3 .48 is s how n a bandpas s curve for the 3-cm TR tuk . The
pas s band of the tube covers the en tire 3-cm band w hich is 12 ~-r cen t
wide .
The 3-cm band is w ider than any one of the 10-cm bands , and
TABLE 3.7.—GAP DIMENSIONS,WINDOWDIMENSIONS,AND ELEMENTSPACINZFOP.
THE 3-cM TR TUZE (1B63)
Cen ter wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..3.33cm
Ga p dim en sion s (r efer t o F ig. 333)
W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...0275 in .
d . . . . . . . . . . . . . . . . . . . . ...0.025
e.. . . . . . ., ,,. .60”
D . . . . . . . . . . . . . . . . . . . .. L3.0138
QLZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ., ..,4. o
Window dimen sion s (r efer t o F ,g. 339)
2. . . . . . . . . . . . . . . . . . . . . . 0.551” (0,580t )
h . . . . . . . . . . . . . . . . . . . . . . . . . ,, .,. . .0.125(0.250)
t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.0230 (O. 0335)
AL, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 (1.2)
glass . . . . . . . . . . . . . . . . . . . . . . . . . . .707(707)
Tube length L.. . . . . . . . . . . . . . . . . . . . . . . . . . . . ...1555
Elemen t spa ings a= d . . . . . . . . . . 0.489
Quar ter gu ide wavelength x,/4 0.478
* Windowat high-powerend of the tube.
t Windowat mixerend of the tube.
cons id erably m ore care is required in the tube des ign to ens ure cry s ta l
protection an d complete ba nd covera ge s imu lta neou sly ,
112
BANDPASS R TUBES
[SEC.3.12
The tube d im ens ions are given in Table 3.7 . It s hotdd be noted that
~L2 for the gap is much low er than for the 10-cm tubes and that the
gap s pacing g is about the s a e.
Window s of tw o d ifferent s iz es are us ed in the 3-cm tube. One is
ch s en w ith a high QLz s o that the bandpas s characteris tic m ore nearly
s imu la tes th e th ree-elem en t ca s e.
Not s o high a QL~ as is d es irable can
be us ed becaus e the ins ertion los s of the w indow becomes exces s ive.
The h igh-QLZ w indow is smaller and is us ed at the end of the tube w hich
carries th e high-cu rrent r-f d is cha rge.
The s pacing betw een elem ents
is th e us ual quarter w a velen gth .
The abs orption los s at m idband may be as low as 0.4 db for this tube
if it is cons tru cted carefully .
A los s of 0 .2 db in the h igh-QL* w indow ,
2.2
()
2.0
1.8
.
L
h 1.6
JL
1.4
/
1.2
1.
/
1.0.
3.0 3.1 3.2
3.3
3.4 3.5 3.6
A in cm
FIG. 3.48.—Bandpass cha ra ct er ist ic for 3-cm band TR tube
(1B63),
0.1 db in the Iow -QL, w indow , and 0.1 to 0.2 db n the res onant gaps and
tube bod y add up to 0.4 to 0.5 db.
3 .12. S ugges tions for F rther Im provem en ts .—Th e linear problem of
the bandpas s TR tube res olves its elf in to tw o parts . The one part
perta ins to the problem f multiple-res onant circu its ; the other part
involves the s tudy o the ind ividual circu its .
And this problem as a
whole mu st be a tta ck ed w ith its lim ita tion b y th e ga s-d is ch arge properties
alw a ys in m ind .
The m ultiple-res onant-circuit problem is the problem of find ing the
appropriate combina tion of elem enta ry circuits w h ich y ield s a maxim um
frequency range throughout w h ich the ins ertion low never exceed s s om e
arbitrary va lue. The bandpas s-TR-tube problem is rela ted to the filter
problem w hich has been cons idered in s om e detail by Fano and Law s on. z
As the criterion of filter effectivenes s , Fano has tak en the ratio of the
s teepn es s of the s id es of th e ins ertion -los s characteris tic to th e m axim um
SEC. 3.12]
SUGGES T ION S FOR IMPROVEMENTS
113
los s w ithin the pas s band . A s im ilar general ana ly s is s hould be applied
to the bandpas s-TR-tube problem w ith the les s res trictive criterion of
bandw id th required of the TR tube. The bandpas s TR tube is not
in tended to act as a filter and the s teepnes s of the s id es of the ins ertion-
10SScharacte ris t ic is not importan t.
It has b en s how n that the bandpas s characteris tic d epend s on the
.Q.~ of each elem ent, the num ber of elem ents , the s epara tion of the ele-
m ents along the transm is s ion line, and the res onant frequency of each
elem ent. It is d es ired to k now the va lues of thes e four parameters
w hich y ield the m axim um bandw id th cons is ten t w ith the gas -d is charge
requirem ents . A pres ent no m ethod of analy s is y ield s thes e param eters
d irectly . Th eoretically th e problem h as been a pproa ched by calculating
the frequency d epend ence of ins ertion los s for various parti u lar va lues
of the four param eters . Experim entally the gros s effects of each of the
four parameters have been inves tigated . Nfore deta iled s y s tem atic
m eas urem ents are need ed in ord er to provid e a com plete unders tand ing
of the multiple-circu it portion of th e ba nd pa ss -TR-tu be problem .
To obta in m ore information on the bandpas s characteris tics of a
m ultiple-elem ent circu it, the experim enter s hould cons id er us ing the
technique w h ereby a plot of transm itted pow e r as a function of frequency
is pres en ted on an os cillos cope.
Th is technique requires the us e of an
os cilla tor w hos e frequency can be sw ept over the range to be s tud ied .
The method can be made more s ens itive to small values of ins ertion
los s by us ing an r-f bridge in s uch a w ay that the pow er reflected from
the circuit being s tud ied is pres en ted on the os cillos cope. It w ould be
d es ira ble to d es ign th e experim en t s o the pa rameters QL2, the s epa ra tion
of the elem ents , and the res onant frequent y could be var ed continu-
ous ly . How e ver, s uch a d es ign m ight lead to ins urm ountable m echanical
difficulties.
The s econd part of the linear probl m—the s tudy of the ind ividua l
circuits—m ay be d ivid ed further into the cons idera tion of the res onant
gap and of the res onant w indow .
Cons id e rable da ta have been ob ta in ed
in the 3-cm band on the res onant gap fo s hapes that have been thought
proper for th e optim um comprom is e betw een QLZ a nd cry s ta l protection.
As w ill be s een in Chap. 6 the experim enta tion on cry s tal protection has
not been extens ive enough to pred ict the bes t s hape of the res onant gap.
Fu rther res ea rch s hould be con ducted on this problem us ing w a velen gths
near 3 cm at firs t, becaus e a s tart has a lready been m ade there, and then
later us ing other band s becaus e the frequency dependence of the gas -
d is charge phenomena is not y et clearly unders tood . The remaining
linear problem in regard to the abs orptio los s in the res onant gap is not
importan t at pres en t. The abs orption los s due to tw o or three gaps is
us ually les s than 0.1 to 0.2 db if the gaps are carefully s old ered ,
114
BANDPASS TR TUBES [SEC. 3.12
In the res onant w indow , abs orption los s is im portan t. It has been
s een in Sec. 3 .10 that the los s is 0 .20 db or m ore in w indow s w ith QLZ
equal to 2.1 or grea ter. It is d es irable to us e narrow er w indow s than
are us ed at pres en t w ithou t s acrifici g on abs orption los s and w ithou t
increas ing QL, too much . An improvem ent of thew indow in w hich the
abs orption los s is d ecreas ed d em and s new d ielectric m ateria ls that have
low e r in trins ic los s es .
Tw o pos s ib le materia ls are quartz and m ica;
quartz becaus e it has es pecia lly low los s , and m ica becaus e it can be
cleaved s o thin that its los s es a e un im~ortant.
These pos s ib ilitie s
w ill be d is cus s ed further in a la ter s ection d evoted to the fabrica tion
of bandpas s TR tubes and tube parts .
B IBLIOGRAPHY FOR CHAPTER 3
1. H, A. LEITER: “ A Nficrowave Band pass Filter in Waveguide, ” RL Repor t 814,
Nov. 16, 1945.
2. R. M. FANO and A. W. LAWSON:Chaps. 9 a nd 10, Vol. 9, Radia t ion Labora tory
Series.
3. P. M. MARCUS: ‘‘ The Interact ion of Discontinuit ies on a Transmission Line, ”
ILL Repor t 930, Dec. 1, 1945.
4. M. D FISKE: “A Broadband TR Switch , ” GE Resea rch L b. R por t , Oct . 18,
1943.
5. W. R. SMYTHE:St a tic and Dynamic E lect r icit y, McGraw-H ill, New York, 1936, pp.
219, 366.
6. E . A. GU ILLEMIN:Communica tion Networks, Vol. II, Wiley, New York, 1935.
7. M. D, FISKE and ANN D. WARNER:
“ F requ en cy Ch ar act er ist ics of Sin gle a nd
Mult iple Lumped Circuit s in Transmission Lines, ” GE Research Lab. Repor t ,
May 25, 1945.
8. M. D, FISKE: per sona l communica t ion .
9. L. D. SMULLIN:“S-band Bandpass TR Tubes,” RL Repor t 971, Dec. 1, 1945.
10. W. C. CALDWELL:“ X-band Bandpass TR Tube,” RL Repor t 970, J an , 22, 1946,
11. M. D. F ISKE a n d ANN D. WARNER:“ Memor an dum on Design Dat a for Reson an t
Aper tu res in the Broad Band XTR,” GE Research Lab. Repor t , Aug. 6, 1945.
12. C. Y. h fENG: Ra dia tion La bor ator y Da ta .
13. J . C. SLATER: Micr owa oe Tr an sm ission , McGr aw-H ill, h’ew Yorkj 1943, pp.
183-185.
14. M. D. F ISKE : “ Reson an t Wir idows for Vacuum Sea ls in Rect angu la r Wavegu ides, ”
GE Rese rch Lab. Repor t , Feb. 10, 1945.
15. R. N. HALL, “Resonant Slots and Waveguides Having Dumbbell-sh aped Cross
Sect ion ,” GE Resea rch Lab. Repor t, F eb. 18, 1943.
CHAPTER 4
CHARACTERISTICS OF ATR SWITCHES AT LOW POWER LEVELS
BY HAROLD K. I?ARR
This chapter w ill be res tricted to the d is tinctive a s pects of the ATR
s w itch , s ince m uch of the m ateria l a lread y pres en ted in connection w ith
the TR sw itch applies d irectly to the ATR circu it. The d is cus s ion w ill
be further res tricted to the cons id era tion of the ATR sw itch as an
is ola ted circu it com ponen t; the d epend ence of d uplexer perform ance
on the ATR characteris tics w ill be cons id ered in Chap. 5 .
4 .1 . Equiva len t Circu its .—.4n ATR s w itch is a d evice w h ich , p laced
in s eries w ith the trans mitter line, has z ero im peda ce a t h igh level and
in fin ite im ped ance at low level, and w h ich , connected acros s the trans -
J4’
I
I
I
1
$
1
z
-- Antenna ;
1
: Transmitter --
I
A
I
I
;
t
1
M B
c?
0
(a)
(b)
F IG. 4.1.—ATR swit ch a t low level; (a ) ca vit y a nd t ra nsm it ter lin e in cr oss sect ion ; (b)
equivalent circuit .
m is s ion line, gives an in fin ite im ped ance at h igh level and a z ero im ped -
ance at low level. Either the s hunt or the s eries arrangemen t fu lfills
the requ iremen ts of an ATR sw itch . Th is sw itch is requ ired to perm it
the flow of pow er from the trans mitter tow a rd the antenna , bu to is ola te
the trans mitter from the res t of the circu it d uring reception .
More accura tely , a s ection of transm is s ion line w ith an ATR sw itch
m oun ted on one s id e as in Fig. 4 . la s hou ld be cons id ered , a t low level, as
a four-term ina l netw ork . The ATR s w itch is then adequately d es cribed
if its buhavior is k now n in term s of m eas uremen t made at the tw o
pa irs of term ina ls , A and B All th e n eces s a ry electrica l in forma tion
is available if he im pedance at A, for a k now n impedance at 1?, can be
ra lr (Ila ted . Such a circu it can be repres en ted at one frequency as a
T-netw ork s im ilau to that of Fig. 4 .lb .
115
116 CHARACTERIS TICS OF A TR S WITCH S
[SEC.4.1
An ATR sw itch is us ually s ymmetrica l about s om e plane MM’, and
if th e referen ce pla nes A and B are tak en at an equal d is tance on either
s ide, the eq ivalent T-netw ork is a ls o s ymmetrica l, and Z1 = Z8. It is
thus pos s ible to d es cribe an ATR sw itch in term s of tw o complex con-
s tants , Z, and ZZ. The values of thes e cons tants depend on the location
of the reference planes A and B. Thes e planes may be s o chos en as to
s implify th e equ iva len t circu it.
The end B is term inated in a m atched
load , and therefore, it is unneces sary to s pecify the exact location of the
B plane; then the ATR cavity is tuned to r s onance as ind ica ted by a
maximum s ta d in -w ave ratio measured at A. The reference plane A
is located at that poin t clos es t to the cavity w here the im pedance is real.
This poin t is us ually ve y clos e to the center line JVIJM’.
When the ATR cavity is mounted on the broad s id e of the w aveguide
it is s aid to form an -lI-pla ne junction w ith the w a veguid e, s ince the center
lines of cavity and w aveguicle lie in the plane of the electric vector. For
s uch a junction , the real im ped ance w h ich appears at A i h igh compared
w ith th e ch ara cteris tic tra nsm is s ion -lin e impedan ce.
The ATR cavity
its elf us ually pres ents a high impedance at the w indow at res onance,
high voltage acros s the w ind ow wh ich is in terpreted as a high im ped ance.
The high cavity im pedance may be verified by removing the cavity
from its s ide-arm mounting and connecting it to the end of a w aveguide
for impedance measurement. S ince th E-plane mountin leads to a
high impedance oppos ite the ATR cavity , the cavity acts s om ew hat as
though it w ere in s eries w ith the line at that poin t, and that junction is
referred to as a ‘i s eries junction. ”
An ATR cavity w hich is coupled
to a coaxia l line by means of an iris in the outer conductor behaves in a
s im ila r manner.
The reference planes have been chos en in the m anner ind icated , and
the values of the circuit cons tants of the equivalen t T-netw ork m ay now
be found . A cavi y mounted in the E-plane w ith the w indow flus h
w ith the w aveguide w all w ill be cons id ered f rs t. For th is cas e a carefu l
determ ination of thes e quantities has been made w ith a 1ow -Q ATR
cavity of the 11352ty pe for the 8-cm region .
The cavity w as tuned to
res onance at one w a velength , and the circuit cons tants w ere d eterm ined
for various w a~’elengths in th is region w ithout changing the tuning. It
w as found that in all cas es the real part of 22 w as about 300 tim es the
line im pedance, w hich meant that Z~ could , w ithin the lim its of experi-
m ental error, be cons id ered to be an open circuit; that is , the ATR cavity
could be accurately repres en ted as an im pedance in s eries w ith the line
at the reference poin t determ ined accord ing to the above conven tion .
In th is cas e, therefore, the naive conception of the s eries circuit is vind i-
SEC. 41]
EQIJ IVALENT CIRCUITS
117
cated , a cond ition w hich is not at 011an obvious cons equence of the
comp lica ted field s ex is tin g a t th e ju nction .
The verifica tion of the s im ple s eries repres en ta tion of the ,?plane
mou ntin g grea tly s im plifies th e con ception of th e low -level ATR beh avior.
It perm its the defin ition of ZI + 23 as the ATR im pedance and , thr ugh-
ou t th is chapter and Chap. 7 , Z w ill be us ed to des igna te th is quan tity .
The value of Z and the pos ition of the reference plane gives all the im por-
tant in formation. Another im portan t convention w hich w ilf be us ed
throughout th is chapter and Chap. 7 follow s . If any particular im ped -
ance has been d efined by s om e s ubs cript s uch as s , the real and im aginary
com ponen ts w ill be d es ignat d as R, and X,. Thus Zs = R. + jX,.
The corres pond ing adm ittance w ill be Y ., = G, + jBs = 1/ 2 ,. The
reflection coefficient obtained by term inating a line of characteris tic
im pedance 20 in the im pedance Z, w ill be r, = (2s – 20)/ (2 , + 20),
o
L
>:. / .
TO receiver
an tennaline
To transmitter
o
0
0
FIG.4.2.—Equivalent circuit for an ATR
FIG. 43.-Equ iva len t circu it for ser ies
cavity.
mount .
and the voltage s tand ing-w a ve ratio (WSWR) s et up by th is t rm ina tion
w ill be r, = (1 + lr,l)/ (1 — Ir.1). Unles s otherw is e s ta ted , it w ill be
as s um ed tha the im pedances us ed have been norm aliz ed w ith res pect
to the characteris tic line im pedance s o that 20 = 1.
If a matched load is connected at the reference point B , and the
im ped ance is m eas ured look ing in to A, Z is m erely th is im pedance m inus
one. Determ ined as a function of frequency , Z is us ually found to
follow a rather s im ple law . If 1 / 2 = Y = G + jB, it m us t follow from
the choice of reference plane that B = O at res onance. It is a ls o found
that G is cons tant w ith frequent y w hereas B varies a lm os t linearly over
a frequency range of a few per cent near res onance.
This behavior is
characteris tic of a s im ple s hunt- es onant circu it lik e that. of Fig. 4“2 .
On the bas is of the theory of res onan t cavities d eveloped in Chap. 2 ,
th is is jus t the circuit that w ould be expected for high-Q cavities . Even
w ith a cavity for w h ich the frequent y s ens itivity is k ept as low as pos s ible
(load ed Q of 5 or 10), the s im ple s hun t-res onant circu it is a s urpris ingly
good approxim ation . Hence, for an -E-pla ne junction , the four-term ina l
netw ork of Fig. 4 .1 m ay usually be reduced to the circuit of Fig. 4“3.
118 CIIARACTL7RIS T1CS OF ATR SWITCHE.9
[sm . 4.1
The data on the equivalent circuit cons tants of the 1B52 tube, w hich
have been mentioned , illus trate this behavior. For one tube, the con-
d uctance G, m eas w red at s even d ifferent w a velengths over a w a velength
~ (%)---
FIG. 44.-Suweptance of an ATR cavity.
band 6 pe~ cent w id e, r mai~ed
betw een 0.016 and 0.019, or nearly
con s ta nt w ith in expe rimen ta l e rror
The s us ceptance B for the s ame
tube is plotted in Fig, 4 .4 as a
function of the percentage w ave-
length dev ia tion AA/Ao from res o-
nance. The deviation AA is equal
to Al – XO w here Al is the w ave-
length at w hich B is measured and
XOis the w a velength at res onance.
The experim enta l poin ts are ind i-
ca ted as circles and the s olid line
is the bes t s traight line pas s ing
through the origin . It is clear that
B is very nearly linear w ith w avelength, - -
Since B is lin ear, th ree pa ram ters s uffice to d es cribe the ATR circu it
once the reference plane or electrica l cen ter of the tube has been es tab-
lis hed . Thes e quantities are the res onant w avelength xO, the cavity
conductance G, and the loaded Q, QL. This las t parameter may be
thought of as a means of s pecify -
ing the s lope of the curve of Fig.
44 accord ing to the expres s ion
B = –2(1 + G)QL ~ (1)
From thk defin ition it is s een that
QL is a ls o the Q of the circu it of
Fig. 4 .5 , obta ined by connecting
FIG.4 .5.—Load ed -Qf an A1’R cavity .
the ATR circuit of Fig. 4“2 to a matched genera tor. In this circu it the
total load ing is 1 + G and the s us ceptance is given by Eq. (1) w hen
AX/ kOis small.
For ATR measurements , the circuit of Fig. 4 .2 is a proximated if
the cavity is mounted at the end of a transm is s ion line and not on one
s id e. Although the behavior for this m ounting is w ell repres en ted by the
circu it of Fig. 4“5 , the values of the parameters may d iffer from thos e
for a s i e-m ounted tube. It is us ually m ore accurate, therefore, to m ak e
measurements w ith the tube mounted as it w ill e us ed in practice. For
a s eries -m ounted tube, m eas urem ents s hould be m ade us ing the circu it
of Fig. 4%a. The loaded Q of th is circuit is d ifferent from that given by
SEC. 4.1]
EQUIVALENT CIRCUITS
119
Eq. (1) s ince the load ing is now (~ + G). The original definition is
reta ined , how ever, s ince it is d es ired to us e Q~ as a parameter that
characterizes the cavity ra ther
than the circu it in w h ich the cav t y
is us ed . With the circuit of Fig.
4.6a , therefore, ZI is m easured ;
then B, the imaginary part of
Y = 1/ (2 , – 1), is found ; then
Q. is evaluated by means of Eq.
(l). Even if th is is done, it s hould
not be as s umed that the s ame
value of Q~, or for that matter of
XOor G, w ill be found w hen the
cavity is mounted at the end of
a w a veguid e as fo the s id e m oun~
ing. For hi g h -Q cavities t e
agreem ent betw e en the d ifferent
ty pes of mounting may be fa irly
good , but in low -Q devices the
field in th e vicin it y of th e ju nction
mak es a n importa nt con tribu tion
to the cavity parameters w hich ,
ATR
m
a)
E
(b)
ments.
therefore, d e end on the ty pe of junction .
It has been s een that an ATR cavity mounted on the w ide s id e of the
guid e effectively pla ces a high im ped ance in s eries w ith the transm is s ion
To antenna-
receiver line
To transmitter
0
/
—
o
FIG. 4.7.—Eqtiva len t circuit for shun t
mount.
line at res onance. As has already
been p o i n t e d out, how ever, a
cavity is equally effective if it
caus es a short circuit cros s the
line. If a cavity is mounted on
he narrow s id e of the w aveguide
n the s o-ca lled H-plane and the
rea l-im ped an ce poin t is loca ted a t
res onance as w as done for the
re fe rence poin t A, th is poin t w ill
agai be found clos e to the cen ter
line of the cavity , but its m agni-
ude w ill be very s mall com pared
w ith th e w avegu id e characte ris tic
m ped an ce. S ince th cavity its elf
is k now n to h ve a high im ped ance, there m us t be a ph as e revers al betw e en
the 11-plan~mounted cavit and the main w aveguide. Th is is equiv-
a lent to connecting the cavity acros s the main line through a s id e arm
120
CHARACTERIS TICS OF A TR SWITCHES [SEC. 4.1
one-quarter w avelength long, as in Fig. 4“7 . Becaus e nearly all of the
w ork on broadband ATR circuits has been done w ith the E-plane m ount,
3’
a)
FIG.4,8 .—Equivalent circuits for a shunt-
moun ted cavity. (a ) Shunt -resonan t ele-
ment with h/4 line. (b) Ser ies resonan t
the experim enta l veri ica tion f
the circu it f Fig. 4 .7 for the H-
plane mount has not been as com -
plete as that for the E-plane.
Neverth eles s , for th e pres en t, th is
repres enta tion w ill be as s um ed to
b e va lid .
There is an alternative w ay of
repres enting t h e s h u n t mount
~vh ich es ta blis hes an in teres tin g
corres pondence w ith the s eries
mount. I Fig. 4.80 , the imped -
a nce of th e s h un t-res onan t circu it
w ith a quarter-w a velength line is
‘l=~=y=G+’(
In Fig. 4 .8b the im ped ance of the s eries -res onant circu it is
‘2 ‘R’+++
In ord er to have Z, = Zz it is neces s ary only that R’ = G, L’ = C,
C’ = L. If each circuit is conn cted to a m atched generato , the load ed
Q’s w ill be the s am e, for the conductance load ing on the shunt circu it is
then 1 + G and Q~ = C~/ (1 + G). S im ilarly , the loaded Q of the s eries
circu it is L’w / (1 + R’) = Q.. Furthermore,
4=&, =-&=w o>
and the three circuit param eters are th erefore rela ted by
Thus the E-plane m ount can be repres en ted as a s hunt-res onant circu it
in s eries w ith the line, w h ile the H-plan e corres pond s to a s eries -res ona nt
circu it in s hunt w ith the line.
A very us efu l equiva lence betw een the tw o ty pes of mount is illus -
tra ted in Fig. 4 .9 . For the s eries mount, Z, = Z + 21 and for the
s hunt mount, ZI has the s ame alue s ince
z1=&2=Y, =Y’+ Y,=&+& =2+2*.
SEC. 4.1] EQUIVALENT CIRCUITS
121
A ser ies moun t can eviden t ly be made equiva len t to a shunt mount by
shift ing the ATR circuit one- ua r ter wavelength a long the line, provided
the effect ive ATR impedance Z is the s ame in either case. If an actua l
0
\
z, -
Z*- Z3+
z,
- z’
o
z
,
+ A,/2 .-l
1/
Ag
o
7
z,
z, -
0
(a )
(b)
FIG. 4.9.—Equ iva lence of shun t and ser ies moun t ing.
(a ) Ser ies moun t with k/2 line,
(b) Shun t mount wit h A/4 lin e.
cavity were moved from the ser ies posit ion to a shun t posit ion one-
quar ter wavelength down the line, the observed impedance
21 w ould
change s om ew hat becaus e of changes
1
~~ - E L
. J L ’
1! 2
jXC
jXb
in tuning, in QL, and ao forth .
- I : L
jX~
1 ~- 2
‘Yb
1
jXa
o
1
1
0
0
1
0
(a) (b)
Fm .
4.10.—(a) Equiva lent circu it of E-plane junct ion .
(b ) Equ iva lent cir cu it of H-p lane
junction.
Howe ver, the correct pos ition s for locating s eries and s hunt ATR ca vities
relative to the TR junction alw ay s d iffer by one-quarter w avelength
plus the small correction due to the s hift of the reference plane.
Becaus e of th is equiva lence, the parameters for the s huntimounted
cavity can be meas ured in the s ame manner as that d es cribed for the
s eries cas e. For the s hunt mount the impedance m eas ured at the refer-
122
CHARACTERIS T ICS OF A TR SWITCHES [SEC.41
ence poin t A is Z2, and its reciproca l Z I corres pond s to the im ped ance
m eas ured at A w ith a s eries mount.
If a cavity is mounted on a s id e arm at a d is tance from the main
transm is s ion line, the cavity and the junction may be cons id ered s epa-
ra tel y . It has been show n els ew here that a s im ple w aveguid e junction
of th is k ind in w hich the s id e arm m ak es an angle of 90° w ith the tw o arm s
of the main w avegu id e may be repres en ted , a t any given w avelength ,
y the circu its of Figs . 4“10a and b for E- and H-plane junctions res pec-
tively . 1 The term ina ls of the main w avegu id e are referred to the plane
of s y mmetry and thos e of the s id e arm to the w all of the main w avegu id e
as ind icated by the brok en lines in the s k etch . Actually any m eas ure-
m en ts mus t be made in the ~vavegu id e one-ha lf or one w avelength back
from thes e pos itions becaus e the field s are qu ite d ifferent in the region
of th e jun ction .
For a w avegu id e of i terna l im ens ions 0 .4 0 in . by 0 .900 in ., and
for a free-s pace w a velength of 3 .20 cm , the va lues of the circu it elem en ts
of Figs . 4 .10a and b are given in Table 4“1. One of the elem en ts B . is
iven as a s us ceptance and the others as reactance Xc, X6 , . . The
TABLE 4.1 .—EQUIVALENTCIRCUIT ELEMENTSFOR IVAVEGUIDET-JUNCTIOAW
E-plane junct ion
H-plane junct ion
B. = –0.096
x. = 0.17
x, =
0.50
x, =
0.19
x. = –4,85
xc = –1,04
X. = –0.56
x, =
1.00
umbers repres en t va lues w h ch have been norm alized w ith res pect to
the line im ped ance. It s hou ld be rem em bered that s uch a repres en ta ti n
is valid on ly at one frequency and tha t the behavior as a function of
frequency is not neces sarily given by s uch a s im ple circuit.
To find the comple e circu it of the cavity on the s id e arm , it is neces -
s ary on ly to connect to term ina ls (3) a transm is s ion line of the length of
the s id e arm , term inated in Z, w hich is the impedance of the cavity as
m eas ured at the end of a s tra igh t w avegu id e.
Neglecting the rea l part
of Z, jX, can be the im pedance of the s id e arm and cavity as it is seen
look ing back at the cavity from term ina ls (3). The va lue of X. s hou ld
be ad jus ted to caus e an open circu it in the line betw een term ina ls (1)
and (2); that is ,
++ 1
Xd +x,=
o
c
(2)
for an E-pla ne ju nction .
The impedance s een at term ina ls (l), how ever, w ill not be in fin ite
ecaus e of the adm ittance jBa . Hence, in term s of the conven tion
s ta ted above for the reference plane, A w i l not appear at the cen ter of
1RL Serie s ,vol. 10 .
SEC. 4.2]
I) ES IGN AND TESTING
123
the unction to w h ich the term ina ls (1) are referred , bu t w ill be d is placed
to the left an amount 1 w here B . = tan (27rl/ &). For the cons tants
given in Table 4 .1 , 1 = 0.027 in .
Th is s hift of the electrica l cen ter from
the geom etrica l cen ter s eem s to be grea ter f or a s im ple w a veguid e T-ju nc-
tion than for a flus h-m ounted cavity .
4 .2 . Genera l Cons id era tions of Des ign and Tes ting.-In th is d is cus -
s ion of the des ign of an ATR sw it h , it w ill be neces s ary to mak e us e of
s om e of the res ults of Chap. 7 , in regard to the d epend ence of duplexing
los s es on the ATR impedance. It is s how n there that the los s d epend s
on both the conduc ance G and the s us ceptance B of the cavity , s o that
the res u lts obta ined over a band of frequencies d epend on all three
param eters ho, Q., and G.
For a fixed -tuned cavity , k “ is us ua lly s et near the cen ter of the band ;
and for a tunable cavi y , it is s e t a t the opera ting w avelength . As the
los ses a lm os t inevitably increas e \ rith t e s us ceptance, B is k ept as s mall
as pos s ible . For a tunable cavity th is is eas y , but for a fixed -tuned
cavity op ra ting over a band of frequencies , it m eans that QL mus t be
made as low as pos s ible to reduce the los s es at the edge of the band .
For a tunable cavity w hich is a lw ay s opera ted at res onance, the
maximum los s in d ec bels , accord ing to S ec. 7 .5 , is L = 20 loglo a w here
inpu t v oltage
=l+~G.
a = output voltage
For s uch a cavity it is neces sary , therefore, that G be as s mall as pos s ible .
For a fixed -tuned cavity , how ever, there is us ua lly an o tim um value of G
w hich is s omew hat vague s ince it d epend s partly on w hat s ort of los s
d is tribu tion is acceptable. The m axim um pos s ib e los s , for a given ATR
impedance, is us ua lly d eterm ined by the rea l part, R = G/ (G2 + B2),
accord ing to a = 1 + (1 / 2R). If G is made either too small or too large,
the maximum los s es w ill be high . Setting G equal to the va lue of B
at the band ed ge m inim izes the m axim um los s , but a cons id erably s maller
value of G w ill us ually be preferred becaus e of the los s at other poin ts .
The m eas urem ent of R is a rather conven ient m ethod of d eterm ining
the cavity parameters . An ad jus table s hort-circu iting plunger may be
placed as show n in Fig. 4 .6b and the impedance Z1 of the combina tion
obs e ved ; the plunger ad ds a variable reactance X’ to the im ped ance of a
s eries -m oun ted ATR sw itch s o that Z I = R + jX + jX’. The res ulting
voltage s tand ing-w ave ra tio is leas t w hen X + X’ = O and is then equal
to R. Hence, to eva lua te R it is neces s ary on ly to read the s tand ing-
w ave ra tio w hen the plunger is ad jus ted to mak e it (SWR) a m in imum .
Thk is a ls o true for a shunt-mounted cavity .
The res onan t w a velength k , is that w a velength at w h ich R is greates t .
Furthermore, G = l/ R at th is poin t. If G is k now n, B can be found
124 CHAR ACTERS IT ICS OF A TR S W ITCHES
[SEC.4.2
at any w avelength by meas uring R ==G/ (G2 + B2), w hence
If B is k now n as a function of frequency , Q. can be found from Eq. (l).
It is im por an t to notice that the m eas urement of R by the plunger
m ethod (Fig. 4 .6 fJ) is a m uch m ore s en sitiv m eth od of d eterm in ing sm all
va lues of B and , hence, a ls o k Othan that involving the us e of a m atched
load (Fig. 4 .6a). To unders tand th is let r, and rz repres en t the v ltage
s tand ing-w ave ra tios w hich mus t be meas ured in the tw o method s . At
res onance the VS WR m eas ured in the plunger experim ent is rz = R = 1/ G
w hile tha t m eas ured w ith a matched load is rl = 1 + l/ G. S ince G
is us ually qu ite s mall, rl and 72 have about the s am e va lue at res onance.
arther from res onance, how ever, r, fa lls off m uch m ore rapid ly than r,,
for the impedance meas ured in the la tter cas e is Z, = Z + 1 and the
re flec ion coe fficien t is
Z,–1 1
rl=z , +l
.— ,
1+;
+=11+ 2YI=<(I +2G)2+4BZ=(1+2G)
J,+4(&).
If on ly va lues of B and G w hich are small compared w ith one are co -
s ide red , then
1-= 1 + 2 G) [ 1 + 2 ( + d
r,
;
+1
()
B’
l+G+ 1+2G .
TI = —=
1 ._ ~
()
B’
r,
‘+ 1+2G
r~=—
G + B“
G
rz=R=
G2 + B2”
As B increa ses , rz begins to d ecreas e appreciably as s oon as B’ becomes
comparable w ith G2. No appreciable change occurs i rl how e er,
until B2 com pares w ith G. Hence the plunger m ethod for determ in ing
res onance is m ore s ens itive by a factor of I/ G.
Th is comparis on of r, and rt a ls o s how s that a meas urement of the
s tand ing-w ave ra tio look ing pas t an ATR cavity w ith a matched load
bey ond is a very ins ens itive check on its perform ance. The perform ance
is ind icated by R w hich gives the maximum 10SSand R ca n becom e
qu ite sma ll b efore r, d rop s a pprecia bly .
SEC. 4.2]
DESIGN AND TES T ING
125
If G is k now n and R is m eas ured at the tw o end s of the band , a good
check can be made on the perform nce of the ATR sw itch over the band .
It w ill be s een from the res u lts of S ec. 7“10 tha t s etting a low er lim it
on R fixes the maximum los s , and s etting an upper lim it on G ens ures
tha t for mos t transm itter im pedances the los s w ill be sma ll com pared
w ith the maximum . Th is ind ica tes tha t ATR cavities can be tes ted by
m eas uring the SWR at the cen ter of the band us ing a matched load and
at the tw o end s us i g a s hort-circu iting plunger ad jus ted for m in im um
SWR. The us e of the matched load to mak e the SWR as nearly ind e-
penden t of frequency as pos s ible is the bes t m ethod of m eas uring G.
In th is w ay it w ou ld probably be pos s ible to tes t tubes by meas uremen t
a t the nom inal cen ter freq ency w ithout the neces s ity of loca ting the
res onant frequency . The plunger ad jus tm ent in the band -ed ge m eas ure-
m ents w ould be aid ed by a d irection al cou pler to m ea s ure th e reflected
pow er. It mus t be adm itted that thes e tes ts , a lthough s ens itive, m ight
b e ra th er s low for prod uction ch eck in g.
It is convenien t to k now that w ha tever d es ign is us ed for cavity and
junction , it is a lw ay s pos s ible to tune the cavity s o as to get complete
is ola tion betw een the tw o branches of the transm itter line provid ed
on ly tha t the los s es are sma ll enough to be neglected . Th is is read ily
proved if it i a s sum ed that the junction is a perfectly genera l netw ork
w ith three pairs of term ina ls , and tha t the A’17R cavity can be ad jus ted
to prod uce any d es ired reactance at one pa ir.
If the term inals ar labeled (1), (2 ), (3 ), the curren ts and voltages
a t the various term ina ls a e rela ted by the equa tions
3
Ei =
z
.Zi,I~,
(i = 1 , 2 , 3 ).
(2)
)
If an im pedance z repres en ting the ATR cavity is connected to the
number (3) term inals , then E3 = —z ls and the las t of Eqs . (2 ) becom es
23111+ 23212+ (233+ 2)13 = o.
If th is is us ed to elim ina te 1 , from the firs t tw o of Eqs . (2 )
The coefficien ts of II and 12 are the elemen ts z~j of the im pedance
m atrix of the 4-term inal netw ork d erived from the origina l 6-term inal
netw ork by connect ng z to one pair of term inals . The cond ition tha t
12(;
CHARACTERISTICS OF A TR SWITCHES [SEC. 42
there be no coupling betw een term inals (1) and (2) is z~j = O, that is ,
All the elements z ii are purely imaginary s ince there is no los s in the
netw ork and there is , therefore, a s olution z of this equation w hich is
purely imaginary provid ed z13# O and z23# O. The las t tw o con-
d itions m erely s ta te that th re m us t be coupling betw een arm s(1) and (3)
and betw een arm s (2) and (3). Granting th is , there is a reactance w h ich ,
w hen plac d at (3), res ults in no coupling betw een (1) and (2).
Th e d es ign of tunable ATR sw itches us ually pres en ts no particu larly
new problem s compared w ith the corres pond ing TR sw itch . The s ame
electrod es may be uw d and the cavity can be s im ilar except for having
one w indow ins tead of tw o. Where s epara te tubes and cavities are
us ed , the s ame tube can usually be us ed for either a TR or an ATR sw itch
although it is unneces s ary to provid e any k eep-a live curren t for the
ATR tube.
The coupling w indow is us ually made larger in an ATR cavity s ince
the high Q. often us ed for TR cavities is undes irable. As the w indow
opening is increas ed , it becom es neces s ry to m ove the electrod es clos er
to the main w aveguide until finally the electrodes are in the plane of
the w aveguide w all. Further reduction of Q. can be accomplis hed by
in reas ing the electrode gap until, as in mos t low -Q tubes , the only
electrod es are the ed ges of the w ind ow .
.
In any applica tion of a fixed -tuned ATR cavity to a frequency band
about one per cen t w ide or gre ter, the a tta inment of a s u fficien tly
low Q. becomes the paramount problem of the low -level d es ign . The
effectivenes s of an ATR sw itch d epend s on the s ubs titu tion at low
level of a high impedance for the low impedance produced by the arc
a t high level. At m icrow ave frequencies a high impedance can be
obta ined only by s om e s ort of s tub or cavity s ince a s im ple “open circu it”
caus es rad ia tion. Any s uch cavity mus t s tore a certa in amount of r-f
energy w hich mak es a contribu tion to the load ed Q. Further energy
ay be s tored in the electrod es , the glas s w indow , and the w aveguide
junction . The L and C of our equiva le t circuit repres en t all th is
re active en ergy lumped togeth er.
The mos t obvious w ay to mak e an open circu it is by means of a w ave
guid e one-quarter w a velength long, s hort-circu ited at the far end . When
s uch a “quarter-w avelength s tub” is mounted on the s id e of a trans -
m is s ion line, it effectively is ola tes the tw o ends .
Of cours e, the l~gth
of the s tub, m eas ured from the ins id e w a ll of the w a veguid e, is not exactly
one-quarter w avelength becaus e the junction is not an idea l s eries or
s hunt circu it. The s tub length to give an open circu it can be found by
SEC.
4.3]
LOW-Q ATE S WITCHES 127
experim en t, or it can be calculated if the circuit cons tants are k now n
for the equivalent circuit of the junction .
If a w indow is s ea led to the opening of the s tub flus h w ith the w all
of the main w avegu ide and the res ulting tube filled w ith gas at low
res s ure, the arc d is charge acros s the w indow at high level gives con-
tinuity to the m ain w a veguid e.
Mos t of the fixed -tuned tubes have been
built in th is m anner.
If a glas s w indow is added to a quarter-w avelength s tub, the w indow
can ca us e an a pprecia ble change in the a dm ittance.
Compen s ation ca n
be made for th is by changing the length of the s tub, or by proper es ign
the w indow can be made “res onant” s o as to add no s us ceptance to the
s tub. A res onant w indow is one w hich has been des igned to give no
reflections w hen placed acros s a w aveguid e.
The des ign of s uch a
w indow is the s am e as that for a broadband TR tube, and from the low -
level point of view the important problem is to k eep the s us ceptance as
low a s pos s ib le .
S ince the change of ATR im pedance w ith frequency is s uch a s erious
problem , an effort is m ade to effect an im provem ent by us ing m ore than
one res onant elem ent, as is done in the broad -band TR tube. It w ill be
s een in Chap. 5 that good res u lts can be obtained by us ing tw o or m ore
res onant elem ents s paced along the trans m itter line.
As each of thes e
requires a s eparate arc gap or w indow , it is preferable to us e a netw ork
w hich is connected to the transm itter line at on ly a s ingle junction .
Nothing is gained , how ever, by add ing add itional reactive elem ents to a
s ingle junction , for Fos ter’s reactance theorem s tates that the curve of
s us ceptance vers us frequency for any purely re ctive phy s ical netw ork
has a pos itive s lope. It is , therefore, im pos s ible to add
any pure s us -
ceptance w hich w ill reduce the rate of change over the band .
Som ething m ight be accom plis hed by add ing res onant elem ents w ith
appreciable d is s ipation , but there m ay be s om e d ifficu lty in int red ucing
s ufficient los s to obtain the neces s ary negative s ]ope of the s us ceptance
curve w ithout at the s am e tim e increas ing the cavity conductance
unduly . S ince no s uch netw ork is k now n at pres ent, it w ill be as s umed
that the problem is to m inim ize ~. by k eepin g the frequ ency s ens itivity
of each elem ent of the ATR circuit as s mall as pos s ible.
4 .3 . Low -Q ATR Sw itches . -It w as s ugges ted in Sec. 4 ,2 that the
various elem ents of an ATR circu it—the cavity , the w indow , and the
junction—all contribu te to QL . It is not pos s ible to calculate all of
thes e; bu t, by mak ing s om e as s um ptions about the equivalent circuit
and us ing experim ental res ults , the rela tive im portance of the d ifferent
elem ents can be appreciated and it can be s een w hy s uch high values of
Q. are obs erved .
For a w aveguide A’I’R s w itch m a e up of a quarter-w avelength s tub
128
CHARACTERISTICS OF A TR SWITCHES
[SEC.4.3
and a res onant w ind ow , the equivalen t circu it can be d erived by w riting
dow n the circu it for a T-junction and connecting to it the w indow and
the s tub. Th is involves the as s umption that the three components can
be trea ted as d is tinct even though s om e higher-m od e interaction, at leas t
betw een the w indow and the junction, m ight be expected .
For an E-pla ne jun ction the s us cepta nce B. of Fig. 4 .10a is very s mall
(Table 4 .1), and its contribution to Q.t can be neglected . The s tub
reactance X,, w h ich is connected to term inals (3) at res onance, is given
by Eq. (2) w hich becom es X, = – X. – xd = 5.41. S ince th i is in
s eries w ith X~ an is large com pared w ith it, xd w ill be neglected .
The junction s us ceptance w ill be called Bj = – I/ X., the w indow
susceptance Bm, and the s tub s us ceptance B, = —1/ X,. There is s ome
ques tion as to w hether the w indow , w hich is a ls o in s eries w ith arms
(1) and (2), s hould be s how n as connected acros s X= plus X,, or con -
B,
Q
Xb
Bj
Bw
(a)
(b)
Fx~. 4.11.—Circui t for calculat ing QL for a low-Q ATR sw itchfrom the parametersof a
T-junction.
netted on ly to X,. Thes e tw o pos s ibilities are s how n in Fig. 4 .11.
They are equ iva len t, for by neglecting G in Eq. (l), QL can be defined as
()
.=+ ‘~xO=–~B’,
where B k the tota l s us ceptance in s eries betw een arm s (1) and (2),
and
B’ k
the logarithm ic derivative of B. Let Bl = B. + Bj, then in
Fig. 4 .lla
B=–
1
X, –
1“
B, + Bw
If the deriva tive of th is is tak en and it is rem embered that B, + Bw = O
at res onance, B’ = B( + B;. In Fig. 4 .1 lb
SEC.4.3]
LOW-Q ATR S WITCHES
129
If the s tub and w indow are each tuned to res onance s eparately , B , = O,
a nd a ga in B’ = B{ + B:. In either cas e
B’=B:+B; +B;
and the QL of the ATR sw itch is therefore in ependen t of X~ and is the
s um of the ind ividual Q’s of s tub, junction , and w indow .
B:
w indow placed acros s a s tra ight s ection of w avegu id e. The s tub Q is
eas ily calcula ted if the s tub length 1 is k now n .
For, if
*=&l,
A,
(3)
then
B, = – cot 0 .
(4)
If th e familia r w a vegu id e equ ation ,
is d ifferen tia ted w it res pect to A, there res ults
()
ix ~a
Q .
d~~’
(5)
(6)
s ince the cutoff w avelength k . is a cons tan t w hich depend s only on the
s iz e of the w a veguid e. Tak ing the logarithm ic d eriva tive,
()
1=~% _%.
9
dh – h“
therefore
()
2
B;=t?’csc20 =-0 ;
CSC2e,
or
()
. =$0 ~2csc20.
(7)
It is not s o eas y to calcu la te the junction Q s ince the frequency
d epen dence of
Bi
is not k now n. For the sus ceptance Bi of a s im ple
capacitive iris acros s a s tra ight w avegu ide B: = – (&/h) ‘Bi. Since
Bj s hould behave in approxim ately the s am e fas hion , B; can be w ritten
as B; = —a(X~/X) ‘Bj w here a is a factor w hich should be of the ord er of
one. S ince Bi = – B,,
130 CHARACTERIS TICS OF ATR SWITCHES
[SEC.4.3
and , by us ing Eq. (4)
()
Qi=~ ~ ‘Coto.
(8)
By us ing experim ental va lues for the other quantities , a can be
ty pe of s w itch m entioned previous ly . The obs erved values are AO,t?,Q.,
and Qw . Equation (5) is us ed to calculate ~, and Q, is calculated by
Eq. (7). BY s etting Q] = Q. – (Q. + Q,), Qj is found , after w h ich Eq.
TABLE 42.-THE DeCOmpOSit iOn OF QL FOR AN
ATR Sw lm H
Ao (k ,/ A)’ e
Q. Q. Q. Qi a
8.35
1.49 0,82 4.7
2.0 1,2
1,5
2.2
9.10
1.65 1,06
3.85
2.0 1.2
0.7 1.5
10.70
2.22
1,15
4.1 2.0
1,5
0.6
1.2
(8) s uffices to determ ine a. The fact that a is s om ew hat greater than one
can be explai ed if Bj is cons id ered as the s um of tw o s us ceptances of
oppos ite s ign . The e w ould give a greater varia tion w ith frequency
than the s im ple elem ent that w as as s um ed . The data in Table 4 .2
ind icate that all three com ponen ts m ak e a s ignificant contribution to
Q. although the w indow accoun ts for nearly half. The fact that the
ju nction con tribu tes to ~. and tha ~. depend s m ark ed ly on the ty pe of
junction w a s noted by S am uel, Crand ell, and Clark of the Bell Telephone
Laboratories . 1
Their m eas urem ents w ere m ad e on a low -Q, fixed -tuned
ATR tube for us e at w avelengths betw een 3.13 and 3.53 cm . S ince the
electrod es w ere d es igned es pecia ll for better firi g and low er arc los s ,
the Q. w as s omew hat higher than that quoted in Table 4 .2 . Table 43
gives the values of ~. for a tube of the s am e ty pe mounted in d ifferent
fas hions . The tota l change in B o~rer the w avelengt band , w hich is the
T.iBLE43-QL FORJ CNCIIOX. OF J-ARIOCS TYI,E.
1
90° E-plane ; 90° H-plane ~ 120° fI-plaHc
Combin ed TR
IZnd on
junction
~
junction
a nd ATR
junction
~ junction
l—— –-——-
1
average value of B’ over the band rather than its value at the center, w as
us ed to determ ine QL. The 90° junction has the ATR cavity mounted
on one s ide of a s traight s ection of w aveguide. In the 120° vers ion the
1 A. L. Samuel, C. F. (’randell, and J . 13. (la rk, “ Broadband TR and Ant i-TR
t ubes,” NDR , Div. 14, Repor t No. 402, Sept em ber 30, 1944.
SEC. 4.4]
ATR SWITCHES IN USE
191
axes of the cavity and the tw o w aveguid e arm s all m ak e equal angles
w ith one another. T e combined TR-ATR junction cons is ts of a 120°
H-plane junction for the TR branch w ith the ATR cavity mounted on the
axis f the junction as s how n in Fig. 816 in Chap. 8 . It is im portan t
to notice that the 90° E-plane T-junction has the low es t Q. of any
junc ion s how n , a lthough the va lue for the 120° E-plane junction m igh t
be in teres ting if k now n .
It has been cus tom ary to tune the w ind w to the res onant frequency
of th ATR sw itc on the as s umption that th is w ou ld give the low es t QL .
If the w indow s us ceptance d iffers from z ero at the frequency w here
res on an ce is d es ired , it is n eces s ary for th e ca vity to in trod uce an oppos ite
s us ceptance. Although the tw o s us ceptances have oppos ite s igns , their
d eriva tives a lw ay s have the s am e s ign , and th is w ould be expected to
in creas e QL.
Som e data bearing on th is ques tion w ve tak en in an effort to d eter-
m ine the f as ibility of d es ign ing a s w itch to opera te at w a velengths in the
neighborhood of 8 .45 cm w ith w indow s w hich w ere ava ilable on ly a t
res onant w avelengths of 9 .1 cm or 10.7 cm . It w as d es ired to compare
thes e w indow s w ith one tuned to 8 .45 cm , bu t the on ly one ava ilable
for the experim en t w as tuned to 8.3 cm . Table 4“4 gives the va lues of
Q. for each w indow w ith the ATR sw itch tuned to res onance at 8 .45 cm
in each cas e by ad jus ting the s tub length to cance the w indow s us -
TABLE 44.d OF N ATR SWITCH UNED TO 8.45 CM FOE VAZUOUSWINDOWS
Reson an t wa velen gt h of win dow (cm )
Over-all QL
8.3
5.85
9.1 6.5
10.7
6.76
ceptance.
Unfortuna tely , no data w ere tak en for w indow s tuned to
s horter w a velengths , bu t thos e ava ilable con firm the as s um ption that ~L
is leas t w he th w indow is tuned to the res onance poin t of the ATR
switch.
4 .4 . ATR Sw itches in Us e.—In review ing the .4TR sw itches tha t
have been in actua l u s e, it is na tural to d ivid e them in to tw o groups—the
tunable and the fixed tuned . Thes e s ame groups cou ld a ls o be ca lled
h igh-Q and low -Q res pectively s ince there have been no high-Q flxed -
tuned circu its or 1ow -Q tunable circu its . The cavity of the h igh-Q
sw itch is s epara te from the electrod e tube. The tube is the s am e as
tha t u s ed in the corres pond ing TR s w itch , and the cavity is s im ilar to the
TR cavity except for having but one w indow . The low -Q tube com -
pris es cavity and electrodes in one un it. It has a w indow of the s ame
ty pe as the fixed -tuned TR tube but d oes not us e the extra gaps .
The t nable cavities have been us ed at 3 -cm and longer w avelengths
bu t not at 1 .25 cm . The reas ons for th is are partly h is torica l s ince the
132
CHARACTERIS TICS OF A TR SWITCHES
[SEC. 4.4
fixed -tuned cavities and 1.25-cm s y s tem s w ere both d eveloped more
recen tly . S y s tem s developed s ince the fixed -tuned cavities became
a va ila ble h ave u sed th em a lmos t exclu s ively .
Few data are available on the us e of ATR s w itches in coaxia l circu its
although such us e is quite feas ible . One sw itch des cribed in Chap. 8 ,
although id entica l in des ign w ith a coaxia l ATR sw itch , is d ifferent in
function.
14
IG. 4.12.—Cross sect ion of the 3-cm wide-range ATR switch .
In the 10-cm region the 721A and 1B27 tubes have been us ed in
tunable ATR circuits for w avegu ide as have the 724A and B tubes at
3 cm . An experimen tal tube for 3 cm w as bu ilt by the Wes tinghous e
Manufacturing Com pany to tune over a w id er range than tha available
w ith the usual cavities for 724 tubes . It w as s im ilar to the 1B24 TR
tube but had a larger input w indow and no ou put w indow . Another
tube corres pond ing to the 1B26 w as built by the s ame company for 1.25
cm . Neither of thes e tubes w as put in to prod uction b caus e of the ad vent
of the fixed -tuned tubes . It s hou ld be noticed that TR tubes , s uch as
SEC. 4.4]
ATR SWITCH S IN USE
133
the 1B24 and 1B26, s hou ld not be us ed as ATR tubes w ithou t increas ing
the s iz e of the input w indow . The high Q. of thes e tubes lead s to a high
value of the conductance. An ATR tube made by s hort-circuiting the
ou tput w indow of a 1B24 tube, for example, w ould have G = 0.3 w hich
could res ult in a los s as high as 1.2 db. For the s im ilar ATR tube w ith
the larger w indow mentioned above, G = 0.055 w hich w ould k eep the
los s below 0.23 d b.
A 3-cm ATR cavity w hich w as des igned for tuning over a band 12 per
cent w id e is of s om e in teres t here as a lm os t the on ly tunable circu it, that
is much d ifferent from thos e d is cus s ed in Chap. 2 . Such cavities w ere
d eveloped at Ra diation La boratory and at Bell Teleph on e La bora tories
at about the s am e tim e. Previous cavities us ing the 724 tubes w ere tuned
by ind uctive s crew s in the m agnetic plane w h ich perm itted a frequency
range of about 2 per cen t, .i tuning s crew is us ually m uch m ore effective
0
0.050
0.100
0 .
plun gerpeningninches
50
FIG.4.13.—Tuning curve of the 3-cm wide-ran gecavity.
if us ed as a capacitive elem ent.
In an ord inary cavity us ing tubes of
the 724 ty pe, how ever, m os t of the capacitance is in the electrod es w h ich
are fixed . In the pres en t d evice a s econd res onant circu it is form ed
by extend ing th cavity in the d irection of the m agnetic plane and add ing
a capacitive plunger as s how n in the s k etch of the Rad ia tion Labora tory
des ign in Fig. 4 .12. S ince both circu its are in the s am e cavity , they are
tigh tly coupled and only one res onant m od e is obs erved w ithin the tuning
range of 3 .10 to 3.50 cm . The curve of Fig. 4 .13 s how s the res onant
w avelength as a function of the d is tance betw een the end of the plunger
and the bottom of the cavity . The cavity is mounted w ith s hunt
coupling to w aveguide of 0“.400 in . by 0.900 in . ID w ith the w indow
opened to the fu ll heigh t of the guide and w id th of the cavity . Th is
gives G = 0.10 at 3 .5 -cm w avelength and G = 0.05 at 3 . l-cm w avelength .
F@m e 4.14 is an exterior view of the Rad iation Labora tory m od el.
The fixed -tuned cavities w h ich have s o far been put in to m anufacture
cons is t of a quarter w avelength of w aveguide w ith a s hort circu it a t
JAN
t ub e d e s -
ignation
.—
1B36
1B35
1B37
1B52
1B53
1B57
1B56
1B44
Band
designa-
tion
K
xc
XL
S ,
S ,
SA,
SA,
S s l
SS2
SC,
SQ,
Nominal
reconant
wave-
ength,cm
1.25
3.23
3.43
8,285
8,640
9,020
9.455
9.840
10.170
10.515
10.900
TABLE 4.5 .< HAI tAC ,rERISTICSF FIXED-TUNEDATR TUBES
T ra nsmit t er ba n d
3 ,1&3 .33cm
3,3&3 .53cm
3700-3550Me/ see
355&3400Mc/ see
3400-3250Me/ see
325W31OOMe/ se e
3100-3000Me/ see
300W2900Me/ see
2900-2800Mc/ se e
2800-2700Me/ see
Specifiedupperlimit
High
level
VSWR
1.10
1,10
1.10
1.20
1.20
1.20
1.15
1,15
Q.
7.5
6..5
6.5
5.5
5.5
5.5
5.5
5.5
—
G
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.05
Measur ed va lues
Q.
6.0
5.0
5.0
4.0
4.0
4.0
G
0.055
0.035
0.035
0.015
0.015
0.015
Inside
waveguide
d imensions , in.
0.170 X 0. 20
0.400 x 0.900
0.400 x 0.900
1 340 x 2.340
1.340x2.840
1.340 X 2. 40
1.340 x 2.840
1.340X2.840
Manufacturer
GE, Sylvania
GE , Sylvan ia
GE, Sylvan ia
Sylvania
Sylvania
Sperry
Sperry
Sperry
SEC, 44]
A TR SWITCHES IN USE
135
one end and a res onant w indow at the other end . The 3 -cm and l-c
tubes includ e a gas res ervoir m ade by extend ing the w aveguide bey ond
the s hort-circu iting pla te. The la tter has a s mall hole w h ich allow s the
gas to circu la te bu t d oes not a ffect the
electrical properties .
An outline of the characteris tics
The transm itter band denotes the
range of frequencies covered by the
corres pond ing transm itting t u b es ,
Ko defin ite band s can be as s igned to
the ATR tubes s ince the us able band
depend s on the amoun t of los s tha t
can be tolera ted and the number of
ATR tubes us ed . The meas ured
va lu es of G and Q~ refer to repres en ta -
tive va lues of m eas urements m ade at
Rad ia tion Labora tory and at Evans
S i g n a 1 Labora tory . The s pecified
upper lim it of a quantity d enotes the
pres en t JAN s pecifica tion for the 3 -cm !
and l-cm tubes and tha t propos ed for
:.+._. .
the 10 -cm tubes . The w avegu id e
F1~.414 .-The 3.cm-w id e-ran geATR
d im ens ions refer to the trans m is s ion
switch.
line on w hich the tube is mounted .
In a ll thes e tubes , except the 1R36,
the cavity is m ad e of a s ection of rectangular w avegu id e of the s am e s iz e.
For eas e of manu acture and mounting the 1B36 cavity is made from
cylindrica l tub ing.
w .
.- —-7 . ~...
--——
—.= .
1535
NE@ “$
@’
~...
f
‘.
IB36
,:
1
e“”..
,,
-i
.i
,8 .1
#
~ ‘1
-..,..—-——. ... . . . ---- --~.
FIG.4.15.—Fixed-tunedATR tu bes .
Figures 4 .15 and 4 .16 are photographs of s om e of thes e tubes . They
a re a ll d es ign ed for m ounting on the broad s id e of rectangu la r w a veguid e
(s eries circu it) w ith the w indow flu s h w ith the w avegu id e “w a ll. Thos e
made at Genera l Electric and Sperry are held a t the correct res onant
frequency by carefu l control of the w ind ow and cavity d im ens ions .
136
C~ARACTERIS TICS OF ATR SWITCHES
[SEC.44
S ylvania m ak es us e of a tuning ad jus tm ent w h ich is s et at the factory .
On the 1B36 tube th is cons is ts of a tuning s crew in the back of the cavity
which
is acces s ible through the evacuating tabula tion before the
latter
k’
Tuning strut
is sealed off. The 3-cm nd 0-
cm tubes have a d eformable d ia -
phragm in the back of the cavity
w hich can e ad j u~ted by means
of a s tru t tha t pas ses out through
F1~. 4.17.—Sylvan ia met hod of pr eset t in g
ATR tubes.
4 .17. The s tru t is removed b;
fore the tabula tion is s ea ed oE. 1
Fixed -tuned tubes of the vari-
ou s type s a re d is tingu ished la rge ly
by their s iz es and method s of
mounting.
The mounting is an
im portan t problem s ince the tube
mus t be eas ily replaced and y et
mu s t ma k e good electrica l con nec-
tion w ith the w aveguide w aLl a ll
ar?ucd the cren ing. For broad -
bs .d applica tions , the flus h
mounting, the proxim ity of the
‘1 ’R tu be. a nti p os s ibly . a ls o, of a n
.,,
ad ditional ATR tube leave ins ufficien t s pace for a chok e coupling of the
ty pe us ed to connect tw o w aveguides . Hence, aii thes e tubes rely on
actua l contact.
‘ Sy lvan ia Electric Producti, Pub lica tion o. IE&S , “Report on OSRD Tube
DevelopmentS ub-contracton RL PurchaeeOrderDIC 1820 22.”
SEC, 44]
ATR SWITCHES IN USE
137
In the 1B36 tube this con tact is made by means of a beveled edge as
s how n in Fig. 4 .18 . Becaus e of the circular outline, the bevel can be
m ach ined accurately , m ak ing the contact uniform all around the tube.
Care m us t be tak en to ens ure that the beveled s ea t for the tube is n t too
large in d iam eter. If the d iam eter is too large, the face of the tube pro-
F[G. 4.lS,—1B36 tube and moun t
trudes in to the in terior of the w avegu id e, as s how n in Fig. 4“19, and the
s us ceptance of the com bination is a ltered .
The change in s us ceptance
ABis proportiona l to th e in sertion d, and
AB = 0.013d
if d is m eas ured in thous and ths of an inch.
The 10-cm tubes have a fine coiled s pring around the periphery w h ich
is com pres s ed betw een the edges of the tube and avegu id e. For
s ys tem s us ing a pres suriz ed trans mis s ion
line, a fla t rubber gas k et under the flange
ma k es th e a s s emb ly a irtigh t.
The 3-cm ATR tubes w ere too s mall t o us e
the coiled -s prin g con tacts , and the circula r
&
m ounting of the t y pe us ed w ith the B36 tube
FIG-.4.19 .—Effect of too la rge
a sea t for 1B36 t u be.
was too bu lky for cer ta in 3-cm-band applica -
tions . A fla t flange perm itted s ufficiently accurate m achining to ens ure
good contact but d id not provid e a con tact w h ich w a s flus h w ith the ins id e
s urface of the w avegu ide w all. The flange w as , therefore, s et back one
w avelength from the main w aveguide w all as s how n in Fig. 4 .20 and a
little s pace w as left betw een the tube and m ount on all four s id es of the
tube. This s pace form ed a sm all w a vegu id e w h ich, being one w a velength
long, trans form ed the s hort circu it at the flange to one at the m ain w a ve-
guid e w a ll and thus provid ed the neces s ary continuity betw e en the ATR
tube and fibe m ain w avegu id e. A fla t n ick el gas ket a few thous and ths of
138
CHARACTERISTICS OF A TR SWITCHES
[SEC.~i
aninch th ick w as provid edw ith each tube to improve the contact a t the
flange. In principle the little w a veguid e could have been one-ha lf w a ve-
FIG.420.-1B35 tu be a nd m ou nt
len gth in s tea d of on e w a velen gth lon g.
How ever, a h igher-m ode res onance,
w h ich appeared only w h en the s horter
length w as us ed , gave ris e to s om e
reflections on high -level opera tion ,
and for th s reas on the half-w ave
leng h m ount w as ru led out.
The length of the little w aveguide
w a s m ad e s ligh tly grea ter for the 1B37
tube than for the 1B35 tube in order
to k eep the h igh-level reflections as
s mall as pos s ible. To accom plis h th is
the 1B35 tubes w ere des igned w ith a
plane flange and the mount w as made
jus t one w a velength long at the cen ter
of the 3 .23-cm band . The 1B37 tubes
w ere then built w ith a small groove
around the ins id e edge of the flange.
The w id th of the groove is the s ame
as tha t of the little w aveguid e, and
its d epth is s uch’ that it extend s the w aveguide s u fficien tly o mak e it
jus t one w avelength long at the
w ay the s ame mount may be us ed
for either tube. i
An in teres ting 3 -cm ATR tu be,
illus trated in Fig. 4 .21 w a s d evel-
oped but not pu t in to prod uct ion . 2
It made us e of a pair of s harp-
poin ted , clos e ly spaced e le ctrode s
placed a s hort d is tance behind
the w ind ow to red uce the arc los s .
Th is p erm its h igh -le vel op era tion
a t con s id e rably low e r pow e rs th an
is pos s ible w ith the othe low -Q
tubes but s eem s to res u lt in a
s ligh tly h igher QL. For th is tube,
cen ter of the 3 .43-cm band . In th is
. . .
e
A “
“@
,
e,
-
.....
0
! ! ! ’
e
— ,.
FIG. 4.21 .—B1’L des ign of fixed -t u n ed
3-cm ATR t ube,
Q. = 6.3 , w hereas for the 1B35 a d 1B37 tubes , Q. = 5.0 .
I W. C Caldwell and H. K. Farr ,
“ Mount ing for 1B35 aad 1B37 Fixed-tun ed
ATR,” RL Repor t No. 53, Aug. 12. 1944.
z Samuel, Cr a nd ell, C1a rk , op . cd . , Sec. 43.
CHAPTER 5
MICROWAVE GAS DISCHARGES
BY LOUIS D. SMULLIN
5,1 . In troduction . -In the preced ing chapters the d is cus s ion w as
cen tered on the linear properties of TR and ATR tubes . With the excep-
tion of the treatm ent of d irect-coupling attenuation , and the s tand ing-
w a ve ra tios prod uced in the m ain line by the fired TR tube, the d is cus s ion
w as lim ited to the operation of thes e tubes at pow er levels les s than that
requ ired to in itia te a d is charge in the tube. In this chapter s ome of the
ch ara cteris tics of th e h igh -frequ en cy ga s d is ch arges of th e ty pe occu rrin g
in TR and ATR tubes w ill be d is cus s ed .
To und ers tand nonlinear phenom ena is a lw a ys d ifficu lt, and gas -d is -
charge phenom ena are es pecia lly noted for their com plexity . Although
a complete th eoretica l u nd ers ta nd in g of th e qu an tita tive rela tion s h as n ot
been a ch ieved , th e proces s es a re w e ll k now n , and a va st bod y of literature
exis ts d es cribing d -c and low -frequency gas d is charges . The dom ain of
h igh - and u ltrah igh -frequency d is cha rge s has re ce iv ed compara tiv ely little
a tten tion. It is on ly in recen t y ears that s ufficien tly in tens e pow er
s ou rces and a ccura te m eas uring equ ipm en t h ave becom e a vailable w h ich
perm it quantita tive experim ents to be m ade at thes e high frequencies .
B fore 1941 little or no d ata on gas d is charges a frequencies higher than
300 Me/ s ee w e re available.
S ince that ti e, how ever, becaus e of the
rapid development of m icrow ave radar, mos t of the s tud ies of ultra-
h igh -frequ en cy gas d is cha rges h ave been in the 3 000-1 0,000- and 2 4,000 -
Mc/ s ec band s .
Becaus e the goal of the w ork in the y ears from 1941 to 1945 w as the
dev lopment of better TR tubes or new TR tubes to be s ed in new
equipm ents , and becaus e s o little tim e w as ava ilab e, on ly recen tly has
a s ys tem atic s tudy of the d is charge its elf apart from th TR tube begun.
How ever, the properties of the fired TR tube that w ere meas ured w ere
thos e that d irectly a ffect its quality . Thes e quantities are
1. Lea ka ge pow e r.
2 . Arc pow er.
3 . Recovery tim e.
4 . Pow e r range.
5 . Life.
139
140
MICROWAVE GAS DISCHARGES
[SEC. 5.1
The leak age pow er includes all the r-f pow er incid ent on the receiver
during the trans mittli g period . It m ay be s ubd ivid ed into the follow ing
components : sp ike , a rc leakage pow er, d irect-coup led po ver, and harmon ic
—.- .-.
pow er.
The las t tw o are rea lly linear properties of the fired TR cavity ,
ind have been d is cus s ed in Chap. 2 .
Th e spike leakage energy is the
energy trans mitted to the receiver during the tim e in terval betw een the
beginn ing of,th e transm itter pu ls e and the es tablis hm en t of the r-f s tea dy -
s ta te d is charge. During this in terva l the voltage acros s the gap build s
up to s evera l tim es the s us taining voltage of the d is charge.
The tota l
tim e involved is us ually les s than 10–B s econd s ,
h
and the energy is of the order of 0 .1 erg or les s .
Flat
The arc leak age pow er is t e pow er inciden t
on the re~~lver ca us ed by th volta ge d rop a cros s
th e d is cha rge. As is tru e for m any low -frequ en cy
FIQ. 5 .1 .—Enve loPe of
and d -c d is charges , the voltage d rop acros s the
TR-tube leak agepow er.
r-f d is ch arge in the us ual opera tin g range is very
nearly independent of the current w hich it
carries . The envelope of the leak age pow er from a ty pical R tube is
s how n in Fig. 5 .1 . The “ fla t” is the s um of the arc leakage pow er,
d irect-cou pled pow er, a nd h armon ic pow er.
The s pik e energy and fla t leak age pow er of a TR tube are the quanti-
ties w h ich determ ine w h ether or not it is pos s ible to protect the receiver
from d am age by the transm itter pow e r.
In a ll mod ern m icrow a ve ra da rs
s uperheterody ne receivers are us ed w ith s ilicon , or germ anium , firs t-
d etector cry s ta ls . To achieve good s ens itivity it is neces s ary to us e a
rather delicate cen t act betw een the tungs ten (‘ cat w his k er” and the
s ilicon cry s ta l. As a res ult, it is pos s ible to damage the contact w ith
im puls es (d uration 10–s s ee) of 0 .2 to 0.5 erg energy , or w ith s tead y-s ta t
leak age pow ers of the order of 1 w att. To ens ure adequate factors of
s a fety , m os t TR tubes are des igned to have a s pik e leak age energy of
les s than 0.1 erg, and an arc leak age pow er f les s than 100 mw .
The pow er d is s ipa ted in the d is charge is ca lled the arc pow er. Th is
pow e r is im porta nt, firs t, beca us e it m us t be furnis hed by the tran sm itter,
and thus repres en ts a los , and s econd becaus e it is a s ource of heat
that w arms u~ the TR tube, and in extrem e cas es may caus e it to crack
or break . H~at w h ich res ults from arc los s is of par~icu lar im portance
in low -Q ATR tubes , pre-TR, and bandpas s TR tubes . Finally , the
in tens ity of the d is charge ffects the rate at w h ich the gas con ten t of the
tu be is chan ged .
In order for a radar s et to detect echoes from near-by targets , the
attenuation through the cavity mus t d ecreas e rapid ly from its value of
60 to 70 db d ring the transm itting period to its ‘‘ cold” value of about
1 db. Th is m eans that the gap mus t be rapid ly deion iz ed . Deion .iza-
SEC. 51]
IN TRODUCTION 141
tion cannot tak e place ins tan tly , bu t it can be made to proceed at a ra te
fa s t enough to bring the a ttenuati on d ow n below 3 db in les s than 10 y s ec.
The tim e for the a ttenuation to fall to s om e s pecified va lue, $uch as 3 or
6 d b, is ca lled the recovery tim e.
In extrem e cas es , if the recove~ tim e
is too large, the ability of the radar s et to d etect s mall, near-by objects
w ill be lim ited ; or targets d etected at long range w ill be los t w hen they
m ove in to a s horter range ly ing w ith in the recovery period .
The range of pow ers over w hich a TR or an ATR tube w ill opera te
m ay be defined in s evera l w ay s . It may be defined in term s of the ab lity
to prot ct the receiver; in term s of the effect upon the transm itter; or,
fina lly , it m ay be in term s of the pos s ibility of dam aging the tube its elf.
To en s ure s a tis fa ctory cry s ta l p rotection , th e p ow e r in cid en t on th e cry s ta l
mus t be lim ited to a s a fe va lue for any incid en t pow er grea ter than z ero
a d les than the maximum rating of the tube. This is neces s ary to
ens ure protection agains t s tray rad ia tion from nearby rad ar s ets , w h ere
th pow er incid en t upon the TR tube may be many d ecibels below the
transm itter pow er level, bu t is s till large enough to damage a cry s ta l
u nles s it is s uita bly clipped or a ttenuated . S im ilarly , th e pow e r reflected
from large nearby targets m ay be large enough to burn ou t cry s ta ls un les s
it is s u itably a ttenuated If the leak age pow er is lim ited to about 0 .5
watt for inciden t power s between O and 20 wat ts, the protect ion is con-
sidered sa t isfactory, even though a limit of less than 0 1 wat t is requ ired
for normal opera t ion . This larger leakage power is permissible on ly
because it is never applied to the crystal for any considerable length of
tim e. At a repetition ra te of 400 pu ls es per s econd , a pu ls e leak age
pow e r of 50 mw w ill ca us e n o ch an ge in cry s ta l ch ara cteris tics over period s
of 1000 hours or longer. Pu ls e leak age ‘pow ers of 200 to 300 mw w ill
caus e deteriora tion of abou t 1 d b in s igna l-to-nois e ra tio of the cry s ta l
for every hund red hou rs of opera tion .
The m in imum pow er level a t w hich the arc los s becom es small
enough to be neglected is cons id erably h igher than the m in im um fi ing
pow er of the tube. In a multigap tube the input w indow may break
dow n at a pow er level of the ord er of s evera l hundred w atts . Until it
d oes break dow n the s hort circu it in the TR tube is one-quarter gu ide
w a velen gth from th e corre t pos ition to en s ure proper tra nsm itter a ction .
The break dow n pow er of the w indow is the quantity tha t d eterm ines
the m in imum transm itter pow er a t w hich a 1ow -Q tube may be us ed .
The maximum pow er at w hich a tube may be us ed is s pecified in
term s of cry s ta l protection and pos s ible damage of t e tube. The s pik ~
energy and arc leak age pow e r are rem ark ably ind epend en t of line pow e r,
bu t “d -irect-coupled leak age pow e r im pos es a d efin ite lim it to the us e of
h igh-Q TR tubes . In s om e high-Q tubes a s e conda ry glow d is cha rge
is form ed at h igh pow er levels acros s the input w indow or ins id e the glas s
142
MIC OWAVE GAS DIS CHARGES
[SEC.?il
cy lin der a djacen t to it. Th is s econ da ry d is cha rge greatly red uces d irect-
coupled pow er, bu t the heat genera ted often damages the tube. No
d irect-coupled pow er is pas s ed by pre-TR and bandpas s TR tubes and
they protect cry s ta ls at all pow e rs available at pres en t, w ith no evid ence
that they cannot be us ed at s till h igher puls e pow ers . How ever, thes e
tubes have an upper avw a ge pow er lim it d eterm ined by the heating of the
input w indow . Thus , at low duty ra tios , extremely high peak pow ers
may be s afely us ed (10 Mw or more). If the duty ra tio is increas ed
the m aximum allow able transm itter puls e pow er is corres pond ingly
decreased.
The life of a TR or an’ATR tube, if phy sical break age from m is hand -
ling and th e res ults of ex~os ure to exces s ive pow e r a re ign ored , is lim it d
Trwtter
Antenna
TR switch
—
1
Receiver
main t r ansmission line and the r eceiver ,
by th~ rate at w h ich the~s ”’~on -
ten t of the tube is changed by the
r-f d is charge or the d -c d is charge
of the k eep-a live electrode. De-
pend ing upon the ty pe of tube
under cons idera tion , the end of
the us eful life produced “by a
change in gas conten t w ill be
in dica ted b y an exces s ive in crea s e
either in recover~tim e or in leak -
age pow er. A tube o be really
.-.
u s efu l s h ou ld h ave a n opera tion al
-life of at leas t 500 to 1000 hours . 1 Mos t TR tubes j us t m eet th is requirem -
ent. Recent 1ow -Q ATR tubes have lives in exces s of 2000 hours ,
w hile s ome TR tubes have ind ica ted lives of more than 1000 hours.
Befor e present ing deta iled exper imen ta l data and theoret ica l in ter -
preta t ions of the data , a br ief phenomenologica l descr ipt ion of the fired
TR tube will be made. In most respect s the TR and the ATR tubes
behave alike, and therefore u less specifica lly noted to the con t ra ry “ TR”
will include tubes of both types.
F igure 5.2 shows a TR tube mount ed
in a conven t ional manner between the main t ransmission line and the
receiver . The tube is on a T-junct ion , oft en one-ha lf guide wave-
length from the main transm is s ion line. When he TR cavity is detuned
by the d is charge acros s the gap, the high in ut s us ceptance is reflected
as a s hort circu it in the }vall of the main guide, and pow er flow s from the
transm itter to the antenna w ithout reflection . If the transm itter puls e
has a flat top, the envelope of the leakage pow er w ill be as s how n in
Fig. 5 .1 . In mos t h igh-Q TR tubes , the arc leakage pow er is cons tant
d uring the pu ls e-~o”~~~h in ”a -few per cen t and is u sua lly in depen den t of
tlie transm itter pow er over ranges of the order of 10$ or more, In the
——.—-_
721A TR tube this i true for transm itter puls e pow er Icvels from 100 to
SEC.51] INTRODUCTION
143
106 w a tts . It is independent of the cold res onant frequency of the TR
cavity over very w id e lim its .
In a given tube the s pik e energy has been found to be remark ably
cons tan t for a w ide range of variables . With in the experim enta l accu -
racy ; *”1 db, the s pik e en rgy is cons tan t over as w ide a r nge as is the
arc leak age pow er. It is a ls o ind ependen t of the rela tive tuning of the
TR cavity and the transm itter over a range of a t leas t 6 ao/ Q.2 (s ix
ha lf-w id ths of the res onant circu it). It is not k now n how the s hape of
the lead ing ed ge of the trans mitter pu ls e a ffects the s pik e energy . Until
1945 w h en os cillographs w ith very fas t s w eeps and high res olving pow e r
w ere d eveloped , there w as no method of correla ting changes in s pik e
energy w ith changes in the transm itter pu ls e s hape. From meas ure-
m ents of the frequency s pectrum of the energy in the s pik e, the dura tion
of the s pik e has been es tima ted to be betw een 2 and 6 X 10–g sec for m os t
h igh-Q TR tubes .
The energy in the s pik e m ay be red uced con sid era bly f electrons from
an externa l s ource are pres en t in the r-f gap at the beginn ing of the pu ls e.
Th e s ou rce of th es e electrons is th e k eep-a live d is cha rge. Th e k eep-a live
d is ch arge is a d -c d is ch arge mainta in ed betw een th e k eep-a live electrod e
and s ome portion of the tube, s o loca ted as to have a m in imum effect
upon the r-f field s in the cavity .
The s pik e energy is in vers ely propor-
tional to nO, the number of ele trons in the gap at the beginn ing of the
tra nsm itter pu ls e. It is not pos s ible to increas e nO n defin itely , h ow e ver,
becaus e of the effect upon the ow -level properties of the cavity . The
electrons in the gap ave an equ iva len t ad mittance tha t is proportional
to their dens ity . In practice it is us ual to lim it nOto a value s uch that
the electron ic admittance caus es les s than 0.1 d b los s of received s ignal.
By us ing a pu ls ed k eep-a live d is charge,
‘‘ prepu ls ing, ” jus t before the
transm itter pu ls e , a large va lue of no may be us d and the s pik e energy
may be reduced to very low levels . During m s t of the receiving per o
the d is charge w ill be out, and the k eep-a live w ill have no effect upon the
low -level in sertion los s of th e ca vity .
When the transm itter is turned off, the excita tion is removed and
there is no further ion iza tion of the gas in the r-f gap. The electrons
and ions a lread y pres en t in the gap d o not, how ever, d is appear or recom -
bine ins tan tly . If the filling of the tube is a gas w ith a clos ed electron
s y s tem s uch as Hz , Nz , A, Ne, or He, the only proces s w hich can be us ed
for th e remova l of e lectron s is d iffu s ion .
This is an extrem ely s low proc-
es s , and the recovery tim e is hund red s of m icros econd s for s uch fillings .
If, how ever, a gas w ith a large electron -capture cros s s ection is us ed , the
rem oval of electron s w ill be grea tly accelera ted and recovery tim es of the
ord er of a few m icros econd s may be obta ined . S uch gas es are OZ, H@,
the halogens , S O,, and NO.
144
MICROWAVE GAS DISCHARGES
[SEC. 5’1
The gas fillings mos t commonly us ed in TR tubes are H, and H,O
or A and HZO at about equal partial pres s ures and at a tota l pres s ure of
10 to 30 mm Hg. Operated on pu ls ed pow er alone, at a duty ra tio of
about ~, and w ith no k eep-a live d is charge, h i h-Q TR tubes m ay be run
for s evera l thous and hours w ith little or no effect upon their charac-
teristics.
If a d -c k eep-a live d is charge is m ain ta ined , how ever, then the
tube life may be s hortened to as little as 250 hours . Tw o d is tinct proc-
es s es operate to caus e th is s hort life.
The s low er, and herefore les s
im portan t, proces s is the gradual reduction of the gas pres sure by s put-
tering. The other proces s is the reduction and change in “gas conten t by
chem ica l action . The w a ter, und er the action of the d is charge, is d is soci-
a ted accord ing to HZO ~ H+ + OH–.
The OH– rad ical reacts w ith the
copper w alls of the tube to form cuprous oxid e, and free hy d rogen is
relea sed . In th is w a y the partial pres s ure of H1O is rapid ly red uced , w h ile
tha t of HZ is actua lly increas ed .
The res u lt of th is proces s is , firs t, an
increas e in recovery tim e caus ed by the rem oval of HZO; and s econd , an
in cre as e in lea kage pow e r a s th e tota l ga s p re s s ure is re du ced b y s putte rin g.
The ra te of gas cleanup, and therefore the tube life, is lar ely d eter-
m ined by the curren t flow ing in the k eep-a live d ificharge.
In fa t, the
life va ries in vers ely w ith th e k eep-a live cu rren t to a good a pproxim ation .
Us ual opera ting curren ts are from 100 to 200 pa. Low er curren ts w ould
be d es irable but a lthough s atis factory levels of s pik e energy m ay be held
w ith curren ts as low as 50 pa such low -curren t d is charges are lik ely to
be uns table. If the d is charge is uns table nd extinguis hes occas ionally ,
very large levels of s pik e energy may reach the receiver w hile the d is -
ch arge is ou t.
The d is charge in h igh-Q TR tubes tak es place betw een the ends of the
cones and is us ually of a p le blue color.
The peak ligh t in tens ity is
modera tely h igh, bu t a t a duty ratio of ~, the average light flux is
low . If the transm itter pu ls e pow er is too high for the particu lar tube
us ed , a s econd ary d is charge m ay tak e place acros s the glas s ad js cen t to
the input coupling. In the pre-TR tube, 1ow -Q ATR tube, and band -
pa s TR tubes , he main d is charge tak es place acros s the ins ide of the
input w indow , and completely covers it w ith a smooth glow . The
in ternal gaps in a bandpas s TR tube break dow n in a manner s im ilar to
the break dow n in a high-Q tube.
In th e follow in g s ection s of th is ch apter, th e materia l w ill be pres en ted
in the follow ing s equence: (1) A brief view of the more importan t char-
acteris tics of the h igh-frequency d is charge and a com paris on w ith d -c
d is charges . (2) A deta iled d is c s s ion of leak age pow er w ith a pres en ta -
tion of pertinen t data and theoretica l in terpreta tions w here pos sible .
(3) Recovery -tim e data and theory .
(4) Keep-a live and gas -cleanup
problems,
SEC. 52]
HIGH-FREQUENCY GAS DISCHARGES
145
6 .2 . High-frequency Gas Dis charges .-The high-frequency gas d is -
ch arge is d ifferen t in many w a y s from th e low -frequ en cy or d irect-cu rren t
d is charge. (1) Fw s t, its s uperficia l character or s tructure is d ifferen t.
The high-frequency glow d is charge pres en ts a s mooth appearance and
no particular s tructure is apparen t.
Th is is in contras t w ith the d -c
glow d is charge w ith its various bands or b ight and dark s paces . The
a ppea ra nce of th e h igh -frequ en cy d is ch arge is mos t lik e th at of th e p os itive
column in the d -c glow d is charge.
It w ill be s how n la ter tha t th is
res em blance is m ore than s uperficia l. (2 ) The electrod es in the r-f d is -
charge play a very m inor role as compared w ith the major role w hich
they often play in the low -frequency d is charges . An extreme example
of th is is the h igh-frequency electrod eles s d is charge, in w h ich the elec-
trod es a re completely in sula ted from th e d is ch arge. (3) In low -frequ en cy
d is ch arges , both pos itive and n ega tive ion s , a s w e ll a s electron s , a cqu ire
appreciable energy from the applied field , and tak e part in the ioniz ing
process.
At h igh frequ en cies , on ly th e electron s a cqu ire a ny a pp recia ble
energy , and all electron production is by energetic electrons . At 10W
frequ en cies , ion s a cqu ire en ou gh en ergy to ca us e h ea tin g of th e electrod es
and to prod uce s puttering. At high frequencies , th is proces s is of little
cons equence except in d is charges of very h igh pow er.
(4 ) Th e electron
d en sity of th e h igh -frequ en cy d is ch arge may rea ch very h igh levels before
the glow d is charge is trans form ed in to an arc. Electron dens ities have
been es tim a ed to be as high as 101sper cm 3, and current d ens ities have
been es tima ted to be of the order of 15 amp/ cm ’.
Before cons id ering the m uch m ore com plica ted problem of the actua l
gas d is charge, let us con sid er tw o fa irly s im ple problem s . Firs t, cons id er
the motion of a charged particle of mas s m and charge e in a vacuum
und er the in fluence of an electric field E s in d,
m ‘~z = eE s in d
dt’
t
(1 )
w h ere x is the d irection of the applied field , nd VOis the in itia l velocity
of the particle. The particle has a continuous x-d irected motion upon
w hich is s uperimpos ed an os cilla ting motion in tim e phas e w ith the
electric field . The energy of the particle is
W=~mv2=~m
[( )
1
~ ‘(l cos ut)’+2e# (l–cos@t)+ffi (2)
urn
If the in itia l velocity is s mall com pared w ith tha t d erived from the field
146
MICRO WAVE GAS DIS CHARGES
[SEC.5.2
the energy acquired by the particle is invers ely proportional to its m as s
and to the s quare of the frequency .
K. K. Darrow has s ugges ted a s im ple but illum inating method of
accounting for the effect of collis ions upon the m otion of an electron in
a field . 1 This m ethod , a lthough adm itted ly crud e, gives a ins igh t in to
th e gen era l mechan isms in volv ed .
It is as s um ed that the gas m olecu les
are s o m as sive com pared w ith the electron that they are s ta tionary , a d
als o that their d ens ity is great enough to mak e the collis ions of the
electron w ith the molecu les act as a net frictional force oppos ing the
m otion of the electron . Us ing g for the ‘‘ coefficien t of friction ,”
daz dx
rr-+g-=eEsinwt
d t’ dt
‘=%=+b(;sin”’-ucos
‘[+’%)+vo]e-:” ‘3
As before, there is an os cilla tory and a drift velocity . The la tter, how -
ever, is exponen tia lly damped by the
“frictional” force, and is s mall
com pared w ith the os cilla tory s peed .
S in e ne (dx/ d t ) is the curren t dens ity acros s a given plane, w he e n
is the number of charged particles per cubic centim eter, q. (3) a ls o
repres en ts current flow . In-phas e and out-of-phase or quadrature com-
ponents of curren t rela tive to the applied voltage are recogniz d . The
in-phase com pon ent va ries invers ely w ith frequency and has its m axim um
value at w = O. The quadrature component has a maximum value at
~’ = gZ/ m’, and is z ero at ~ = () and ~ .
Increas ing g by increas ing
the gas pres s ure reduces the quadrature rela tive to the in-phas e com -
ponents of the current.
A” con du ctivity ” a nd ‘‘ d ielectric con sta nt” of s uch a clou d of ch arged
particles may be defined . From Eq. (3), the in-phas e curren t is
ne’g
E s in d = SE s in d.
uzm’ + g2
(4)
S im ila rly , th e total quad ra tu re cu rren t a cros s th e ga p, in clu din g d is pla ce-
m ent curren t, is
(5)
1K. K. Darrow , Belt Sy s t . I’edm. J ., 576 (October 1932),
SEC. 52]
HIGH-FREQUENCY GAS DISCHARGES 147
w hich gives the fam iliar res u lt that the d ielectric cons tan t of a s pace-
charge region is les s than tha t of vacuum .
Th is high ly s im plified th eory in dica tes th e follow in g im porta nt fa cts :
1 .
2 .
3 .
It
The in-phas e curren t carried by the electrons d ecreas es w ith
increasing frequency.
At very high frequencies , the quadra ture componen t exceed s the
in-phase component.
The rela tively heavy pos itive and negative ions , m; 2 1847m, ,
get very little energy d irectly from the electric field .
has been s ta ted that the r-f d is charge s trongly res embles the d -c
pos itive colum n. S om e of the s alient fea tu~es of the ‘pos itive colum n are
lis t ed l here :
1 . No net chargeaqual n mbers of pos itive and negative charges .
2 . Low gas tem pera ture, about 100”C.
3 . Low ion tempera tu re; high electron tem pera tu re.
4 . Voltage grad ien t les s for m onatom ic than for d ia tom ic gas es .
The r-f d is charge has no net charge, s ince the en tire ion iza tion tak es
particles is very small. The ins tan taneous gas tempera ture of the r-f
d is charge has never been meas ured . How ever, under puls d , high-
curren t opera tion , the w indow of a low -Q ATR tube may atta in a s teady
tempera ture in exces s of 100”C w ith a transm itter du ty ra tio of ~m .
Thus , the maximum gas tem era ture mus t be muc higher than 100”C.
S ince the r-f d is charge curren t is m eas ured in amperes or tens of m peres ,
w hereas the d -c glow d is charge curren t is us ually m eas ured in m illi-
amperes , the clifference in tempera ture is not s urpris ing. The ion
tem pera tu re in th e r-f d is ch arge is low compa red w ith tha t of th e electron s
s ince the ions , becaus e of their large m as s , get little energy from the field
but get a ll their energy by collis ions w ith electrons . The total voltage
d rop a cros s th e r-f d is ch arge is les s for m on atom ic th an for d ia tom lc ga ses .
The order of the various gas es may be s een in the comparis on in Table
5 .1 . The firs t row of the table is tak n from Cobine2 and gives the
TABLE51 .-C• MFAIUSONOFVOLTAGEDROPACROSSR-F DISCHARGEN VLRIOUS
GASES
Air 0, H,
x, He Nc A
‘i—
E ./ p (pos it ive column)
17 14
8.5 4.3
2.3 0.45 I 0. 2
Arc volt age (r -f d is cha rge)
3.3 2.9 3.1
1,4 1.2
; 0.65
] Cobin e, Ga seou s cm iduct or s, McGr aw-H ill, New York, 1941, p. 233.
2 Cobine, op. al., Chap. VIII .
148
MICROWAVE GAS DISCHARGES
[SEC.%2
electrica l grad ient along the column d ivided by the gas pres s ure for a
given s hape of d is charge tube and at currents of 0 .1 to 0.2 amp. The
s econd row is derived from meas urem ents of the arc leak age pow er of a
1B27 TR tube at a pres s ure of 10 mm Hg, and the numbers are in arbi-
trary units . It is felt that the exact ra tios betw een the va lues for the
various gas es have no s ign ificance becaus e the s hapes of the d is charge
tubes and th d is charge currents are s o d ifferent in the d -c ancl r-f ca s es .
Nevertheles s , the orders in the tw o cas es are about the s am e.
S pectrographic obs erva tions w ere m ad e of the r-f d is charge, and no
particular fea tures w ere noted that d is tingu is hed it from the low -fre-
FIG. 5,3.—Spect ogr ams of r -f d is cha rge in s ever a l IB38 p re-TR tubes .
quency d is charge. Figure 5.3 is a reprod uction of a few ty pica l s pect o-
gram s of the light from 1 0-cm , a rgon -filled , pre-TR tu bes . 1 A“o a ccurate
m eas urements of the efficiency w ith w hich light is produced by the r-f
d is charge have been made. The light from a 10-cm pre-TR tube w as
meas u red w ith a Gen era l Electric photograph ic e xpos u re -me te r.
Ilith a
line pow er of 5 X 10sw atts and a duty ratio of ~~, the ind icated average
s urface brigh tnes s w a s 2.5 X 10–3 lumen/ cm z . This ins trum ent has a
ba rrier-la y er ph otovolta ic cell w ith a n on lin ea r ch ara cteris tic a nd th ere-
fore the m axim um brightnes s w a s probably m uch greater than the ca lcu-
la ted value of 5 lum en/ cm ’.
In a s elf-s u s ta in in g d is ch arge, th e ra tes of p rodu ction and d es tru ction ,
or rem oval of ions , are equa l. Deioniz ation in a low -frequency d is charge
m ay tak e place by tJvo proces ses only : recomb nation, and d iffus ion .
I These were made by R. lI \ ’a lly, J r., of the Spect roscopy Labora tory of M.I. T.
SEC.5.2]
HIGH-FREQUENCY GAS DISCHARGES
149
Recomb in ation of a p os itive ion a nd a n electron is a ela tively imp roba ble
proces s ,l and can us ually be neglected in comparis on w ith the los s of
ch arge b y d iffu s ion to th e w a lls or e lectrod es .
S ince m os t of the negative
ch arge in th ed -c d is ch arge is ca rried by free electron s , th e m ore proba ble
recom bina tion of pos itive ions and negative ions can als o be neglected .
In the r-f d is charge, the en tire alternating curren t is carried by the free
electrons . Th is m eans that capture of electrons by neu tra l a tom s or
m olecu les to form negative ions effectively “deion iz es ” the gap in the
s ens e that its curren t-carry ing capacity is reduced . Thus , in the d -c
pos itive column , ion iz ation mus t ta ke pla ce at a ra te equa l to th e d eion iz a-
tion by d iffus ion w hereas in the r-f d is charge it m us t equa l the com -
bin ed ra tes of d iffus ion an d electron ca ptu re.
Th e proces s es in volved in th e tra ns ition to a s elf-s us ta in in g d is ch arge
are m ark ed ly d ifferen t in the low- and in the h igh -frequency regions .
In both ca ses , thein itia l ioniz ation m us t res ult from s om e ou ts id e s ou rce,
for exam ple, cos mic ray s or photoelectric em is s ion from the cathode.
Th eelectron s prod uced in th is w a y area cce’era ted by the applied fie ld
until they in turn can m ak e ioniz ing collis ions , and thus releas e m ore
electrons.
It is here that the d ifferences becom e importan t. In the
d-c d is ch arge th ere is afa irly ra pid d rift of th e electron s in th e d irection
of the field . They even tua lly reach the a nod e w h ere t hey are lost to the
d is charge. If on ly ion iz ation by en erge tic e le ctron s is con s id ere d, the
number of electron s betw e en the anod e and ca thod e is
n = noe’
(6)
w h ere no is the number of e le ctron s p rodu ce d a t th e ca th od e by an external
s ource, z is the d is tance m eas ured from the ca thode, and a is the num ber
of ion iz ing collis ion s made by an e le ctron per centime te r of path in the
direction of the field . Clea rly , th e a nod e curren t is d irectly proportion al
to no a nd w ill be zero when no is zero. Thus , a se lf -sus ta in ing discharge
cannot be achieved at low frequ en cies if ion iz ation d epen ds en tirely
upon electrons . Recogniz ing th is , J . S . Tow ns end propos ed a s econd
me th od of ion iz a tion , ion iz a tion by pos itive ions . 2 This res ulted in the
equation,
n = no (cl – 6),(”-8)’
(7)
~ _ @t(.–d ). f
in w h ich P r pres en ts the n umber of ioniz ing collis ion s m ad e by a positive
ion per cen tim eter of path in the d irection of the ca thode. If th d enom i-
na tor of Eq {7) can be mad e equal to z ero, n w ill increas e w ithou t lim it,
1Laeb, Fu&m ental Processes bf E lectrical Dischargesn Gas es ,Wiley , New York ,
1939,Chap.2.
s For a ore complete discuss ionof cumulat ive ionizat ion in d-c discharges ,s ee
Loeb, op. cit., Chaps .9 and 10.
150
WA VE GAS DIS CIiA ltGES
[SEC.5“2
and thus becom e independen t of no. Although cons id erable doubt now
exis ts as to the actua l phy s ica l proces s d es cribed by Tow n send ’s s econd
coefficien t / 3 ,t is a greed th at s ome s econ d ary ion iz in g proce s s is n eces s a ry
to produce cumula tive ion iz ation in a d -c field . Deriva tions bas ed on
the s sum ption that the s econd ary proces s cons is ts of releas e of photo-
electrons from the ca thod e by ligh t genera ted in the d is charge have th
s am e form as Eq. (7).1
1,26
1.24
60 Pos. Neg. Pos.
cycle 1.5x40 1.5x40 lx5—
Rodgaps B C D F
7
1.20
1.18
1.16
1,14
1.12
I I
I
I
I
10
& 1.08
85
Above 0.75 in. V.p,
.2 1,06
the data had many - 6 “:
\
inconsistence
:
c D F *O
DE
DE
18
CD
16
14
humidity 0.6085 inches
ry vapor pressure.
12
~ 1.02
I
1
1
I
I I I I Wihl
2#
ot
I
1,00
0.98
-z
0.96
0.94
0.92
0,90
- lC
0.88
0
0.2 0.4 0.6 0,8
0.10 0.12
Inches of mercury - vapor pressure
4-6
F IG. 54.-E ffect of wa ter vapor pr essu r e on br ea kdown pot en tia l (fr om Cobin e, Ga seou s
Conductors,McGraw-Hill, 1939.)
In the h igh-frequency d is charge, the d rift velocity of the electrons
is much les s than in the d -c cas e.
If the extrem e cas e w here the d rift
velocity is z ero is cons id ered then , except for thos e electrons that are
w ith in one m ean free path of the electrod es , there w ill be no los s of e lec-
trons from the d is charge and each electron can m ak e a lim itles s num ber
of ioniz ing collis ions , ‘Once the proces s is
s ource may be rem oved w ithou t a ffecting
1Loeb, 10C.l.
s ta rted , th e in itia l
the fina l curren t.
electron
At the
SEC.5.3]
LEAKAGE POWER AND CRYSTAL BURNOUT
151
extrem e frequencies of 3000to 10,000 Mc/ s ecth e exis ten ce of a s econ da ry
ion iz i g m echanis m of the ty pe pos tu la ted by Tow ns end , ion ization by
pos itive ions , s eem s highly improbable; how ever, the production of
photoelectrons at the electrod es or in the gas by light from the d is charge
cannot be ru led ou t until m eas urem en s of the ionization proces s have
been m ad e in d etail.
The pres ence of a gas s uch as H~O, w hich has a compara tively high
probability of capturing a free lectron to form a negative ion (high
e le ctron -ca ptu re cros s s e ction ), effe ctive ly in crea s es th e b read kow n volt-
age of a gap. Capture of e ectrons effectively removes them from the
d is ch arge s in ce th e proba bility of ion iz ation b y n ega tive ion s is very small,
and energies of the order of 3 to 4 volts are needed to detach an electron
from a negative ion. Figure 5.4 illus tra tes the effect of w ater-vapor
pres sure on the break dow n voltage of rod gaps , s us pens ion ins ula tors ,
pin and apparatus in su la tors , and bus hin gs . 1
A s im ilar res ult w ould be expected in h igh-frequency d is charges . S o
far, a t leas t, n the pres sure region of 5 to 30 mm Hg, the obs erved effect
of HZO on s pik e energy , w h ich is proportiona l to the break dow n voltage,
d oes n ot perm it s u ch a gen era liz ation .
6 .3 . Lea ka ge Pow e r and Cry s ta l Bu rn out.-Th e mos t d ifficu lt requ ire-
ment placed upon the TR tube is that th leak age pow er be lim ited to a
va lue low enough to ens ure the protection of the s ilicon cry s ta l us ed as
the firs t d etector of the receiver. At frequencies below 1000 Me/ s ee
the convers ion of the received s ignal to a low e r, in term ed iate frequency
m ay be perform ed in d iod e or triod e vacuum tubes w ith excellen t s igna l-
to-nois characteris tics . Such tubes are rugged and are not eas ily
m icrow a ve region, h ow e ver, tra ns it-tim e effects m ak e th e cons tru ction
of good therm ionic tu be very d ifficult beca us e of th e d elica te and m in ute
s pacings betw e en electrod es w h ich are neces s ary in ord er to obta in good
performance. Diode converters have been built for us e at 10 cm ; but
their perform ance (s igna l-to-nois e ratio) has a lw a ys been poorer than
that of a s ilicon cry s ta l by about 6 db.
S ilicon cry s ta ls ha ve been brou ght to their pres en t s ta te of excellen ce
by improving the purity , the etching, and the polis hing of the s ilicon ,
and als o by better con trol of the location and s hape of the tungs ten
‘{ca t w h is k e r. ”z
Ty pica l perform ance characteris tics of cry s ta ls for
the 10-cm , 3-cm , and 1 .25-cm band s are given in Table 5.2 .
This excellen t perform ance is the res ult of the extrem ely s mall con-
tact area betw een the tungs ten and the s ilicon , w hich is of the order of
I J oin t Commit t ee on In sula tion Resea rch , EEI-NEMA, “Recommen da tion s for
H igh -volt age Tes ting,” Tr ans . Am er. In st. E lect. E rqrs., 59,598 (1940).
Vol. 5 of th is seri es, Cryst al Rect ifirs.
152
.MfCROWA VE GAS ’ DIS CHARGES [SEC.5’3
TABLE 5. 2.—TYPICAL CRYSTAL PERFORMANCEFIGUEIES
Type
I
Ba nd, cm
1
Conversion
1
A’oise;
loss, clb
factor
1X21B
10
5.5 1.3
11T23B 3.3
6
1.5
1N26
1.25
7 1.5
* Then oisefactorexpresseshenohe poweras a mu ltideoft henoi,e producedat roomt empera tu re
by m idealrenia torof a resistancequalto that of the crystal .
immed ia tely ad jacen t to the contact and , cons equen tly , d es pite the high
melting poin t of tungs ten , the pow er d ens ity is s o grea t tha t on ly a few
w atts are required to fus e the tungs ten poin t and to d es troy the recti-
fy ing con tact.
There are tw o im portan t w a ys in w h ich th leak age pow er can change
or im pa ir the perform ance of a cry s ta l.
One is characteriz ed by a s low ,
con tinuou s degrada tion of th e s igna l-to-
t )
L
nois e ra tio of the cry s ta l a t leak age
V. -
pow ers of the order of 200 mw . The
ra te of d eteriora tion d ep en d s on ly u pon
1 ,
the tota l tim e of applica tion of the
power.
Thus , at a d ty ra tio of ~~,
~ r-- ----- ;
e ,
the cry s ta l changes by about 1 db per
to t,
~ hund red hours w ith 200 mw applied .
F IG. 55.-Wa veform of test volt -
If the s ame pow er is applied as con-
age a plied to silicon crystals in t inuous wave power , the crysta l changes
s imula ted spike burnou t t es ts.
1000 tim es as fas t. Damage of th is
ty pe is not the res u lt of hea t, and is probably as s ocia ted w ith the tota l
ch arge tra ns ported a cros s th e rectify in g la y er.
The other ty pe of cry s ta l fa ilure is therm al “burnou t” in w h ich loca l
hea t ng permanently changes the contact betw een the ca t w his k er
and cry s ta l. Thermal burnout may be d ivid ed in to tw o genera l ty pes
accord ing to the manner in w hich the pow er is applied . In one, the
pow e r is applied for a tim e long com pared w ith the therm al tim e cons tan t
of the cry s ta l con tact. The fina l tem pera ture is d irectly proportional
to th e pow er d is s ipa ted a t th e con ta ct.
In the other, the pow e r is applied
for a tim e s hort compared w ith the thermal tim e cons tan t, and the tem -
pera ture of the con tact is proportional to the total energy d is s ip ated a t
th e contact, tha t is , the hea ting is ba llis tic.
Th eoretica l s tu dies an d th e experim en ts on cry s ta l d etectors in dica te
tha t the s hortes t therm al tim e cons tan t of any cons equence is of the ord er
of I&s s ec.
Cry s ta ls are r qu ired to w iths tand a d -c pu ls e of the ty pe
SEC,54]
THE SPIKE 153
illus tra ted in Fig. 55 and s till have s atis factory s igna l-to-nois e charac-
teris tics . The d ecay tim e cons tan t t, is 5 X 10-’ s ee, and tO<< tI . This
pu ls e is obta in ed by -s u d den ly d is ch argin g a ca pa citor th rou gh th e cry s ta l.
The tota l energy d is s ipa ted in the cry s ta l in thes e tes ts varies from 0.1
erg in the 1N”26 to 2 ergs in the 1N21B. At energies roughly tw ice thes e
tes t levels , a large fraction of the cry s ta ls are d am aged .
When the s tudy of cry s ta l burnout w as firs t begun only “s tead y
s ta te” burnout by the applica tion of long pu ls es (1 ~s ec) w a s con sid ered .
Early cry s ta ls (1943) w ;ere impaired by pow ers of 0 .5 to 1 w att. With
im provem en t in the cry s ta ls th is pow er has been increas ed , and m od ern
cry sta ls w ill w iths tand 3 to 10 w atts w ithout s erious dam age.
It s oon
became apparent that mos t TR tubes had flat leak age pow ers of the
ord er of 100 mw or les s , s o that s tead y-s ta te burnout w a s rea lly no prob-
lem . The energy in the s pik e of the average TR tube, how ever, w as
much clos er to the danger level.
For th is reas on , it w as d ecid ed to
s pecify cry s ta l burnout properties n term s of ballis tic heating as jus t
described.
In S ec. 5 .1 , it w as poin ted out th t the envelope of the TR leak age
pow er could be d ivid ed in to tw o parts , the s pik e and the fla t, as s how n”
in Fig. 5 .1 . This picture can be s een if the leak age pow er is rectified
and pas s ed through an amplifier of 5 - to 10-Me/ s ee bandw id th before
being d is play ed on a cathode-ray -tube s creen . It has been determ ined
by experim en t tha t the dura tion of the s pik e is us ually les s than 10–’ s ec
and , for h igh-Q TR tubes ; is from 3 to 6 X 10–’ s ec.
The energy in the
s pik e is about 0.05 erg for mos t h igh-Q ubes . Bandpas s tubes us uallY
exhibit a s pik e energy tw o or three tim es as grea t.
The arc leak age pow er lies betw een 10 and 50 m w for practica l y a ll
m icrow ave TR tubes , and therefore th is in its elf can hard ly damage a
cry s ta l. The fla t eak age pow e r, h ow e ver, is the s um of the arc, harm onic,
and d irect-coupled leak age pow e rs , and care m us t be tak en to ens ure tha t
harm onic and d ire t-coupled leak age pow ers do not reach dangerous
levels.
5 .4 . The Spik e. -On the bas is of the in troductory des cription , the
s pik e can be defined as follow s : the s pi e energy is that energy trans -
m itted to the receiver during the tim e in terva l betw een the beginning
of the trans mitter puls e and the form ation of the s tead y-s ta te d is charge
acros s the gap of the TR tube. Figure 5”6 s how s , on an expanded s ca le,-
the pres umed envelope of the leak age pow er through the TR tube near
the s tart of the trans mitter pu ls e.
Until recen tly , the exact-s hape of the s pik e had never been obs erved
d irectly . Conventional vid eo-frequency am plifiers and cathod~ray
os cillographs are incapable of res olving trans ien ts w hos e duration is
lb’ s ec or les s .
As a res u lt, the analy s i res en ted in the follow ing
154
MICROWAVE GAs DISCHARGES
[SEC.5.4
s ections w as d eveloped by in ference or deduction from the obs ervable
properties of the s pik e: tota l energy and s pectrum . In April, 1946 ,
C. W . Zabel s ucceeded in obta in ing an os cillogram of the s pik e energy
leak lng through a 1B38 pre-TR tube. Th is w as done in the Ins rd a-
tion Labora tory of the Nlas s achus etts Ins titu te of Technology on the
h igh -s peed os cillograph d eveloped by Lee.’ Th e res ults of thes e m ea sure-
m ents are en tirely cons is ten t w ith previous ly d eveloped theoretica l
analys is .
S tep b s tep , the proces s es in the s pik e are as follow s . At the very
beginning of the trans m itter pu ls e, th ere is an in itia l n um ber of electron s
n , in the gap of the TR tube. As the transm itter voltage increas es , the
voltage cros s the TR gap als o increas es , bu t a t a s low er ra te becaus e of
the compara tively high Q! of the TR cavity . In bandpas s TR tubes ,
the voltage buildup follow s tha t of the trans mitter w ith no appreciable
ti e }ag. Thk w ill be d is cus s ed in
grea ter d eta il in a la ter s ection . The
electron s a re a ccelera ted b y th e v olt-
age acros s the gap until they atta in
~
s ufficien t energy to prod uce further
.%
5
ionization.
The electron d ens ity in
~
the gap then increas es very rapid ly
and begins to s hort-circu it the ga
and to red uce the pow e r trans m itted
FIG. 56.-Presumed shape of spike
th rough the TR cavity to the re-
Iea kage envelop e r ela tive t o magnet r on
buildup.
ceiver. The ra te of ion iz a tion con - ~
tinues to increas e as the pow er
I
increas es un til an equilibrium is reached w ith the incid en t pow e r.
Th e
lea k age p ow e r in th e equ ilibrium con dition is ca lled th e a rc lea lca ge pow e r,
P..
The deta iled s tructure of the s pik e cannot be obs erved eas ily , bu t tw o
s im ifican t m eas urem ents can be m ad e w h ich characteriz e t.
Th es e are
meas urem ents of the tota l energy in the s pik e , and m eas urements of its
frequency s pectrum . The s pik e energy W, can be meas ured in s evera l
d ifferen t w ay s (s ee Chap. 9). From a meas urem ent of the tota l leak age
energy for tw o d ifferen t transm itter-pu ls e w id th s , as s um ing that W,
and Pa are ind epend en t of the pu ls e w id th , W, can be computed . Alter-
na tively , the fact ay be us ed that the a ttenua tion through the TR
cavity , during the s teady -s ta te d is charge, is of the order of 60 db and
is on ly a few db during the s pik e. Th is a llow s the arc leak age pow er to
be canceIed w ith a s mall am ount of pow er obta ined from the main trans -
m itter line through an attenua tor, w ithou t altering the s pik e envelope,
‘ Gordon M Lee, “A Three-beam Oscillographfor Recording at Frequenciesup
to 10,WO MegacycIea,”Pmt. Innt. Radio Enur8,, N. Y., 34, 121a (Ma rch 1946).
SEC.
54]
THE SPIKE
155
Under this cond ition the s pik e energy may be meas ured d irectly . The
tw o m eth od s , if us ed und er the proper cond itions , give equivalent res ults ,
and good TR tubes ave s pik e energies of the order of 0.05 erg per pu ls e.
The meas urem ent of the du ation of the s pik e is much les s certa in
than the m eas urem ent of the energy . The on ly d irect experim ental
m ethod is to m eas ure the frequency s pectrum of the s pik e w hen the flat
leak age pow er is canceled as jus t des cribed . Such meas urem ents are
res tricted to th e amplitudes of the various frequency com ponen ts . S ince
pha se m eas urem ents are im pos s ible w ith pres ent tech niques , the s ha pe of
th e s pik e can not be recon s t ru tted by th e in vers e Fou rier tra ns forma tion .
How ever, on the as s umption that the s pik e is rectangular, and by the
us e of the rela tion betw een puls e w id th r, and the frequency interval
Aj betw een the firs t tw o m inim a in the s pectrum ,
2
‘8 = If’
the duration has been es tim ated to be about 5 x 10–g s ec in a ty pical
high-Q TR tube.
The s pik e energy is of primary inte~es t becaus e of the problem of
cry s ta l burnout. Mos t of the m eas urem ents quoted in the follow ing s ec-
tion s w ill rela te to it, w h erea s m ea s urem en ts of s pik e d ura tion w ill receive
ra th er s can t a tt e nt ion .
A s im plified th eory of the s pik e w ill be pres ented
firs t and then the dependence of s pik e energy upon the follow ing para-
m eters w ill be d is cus s ed :
1 .
2 .
3 .
4 .
5 .
6 .
7 .
Gas con ten t.
In itia l num ber of electrons , no.
Ga p s hape.
Tuning of TR cavity .
Tra nsm itter p ow er le ve l.
Tran sm itte r-puls e s hape .
External circuit.
The varia tion of s pik e energy w ith the gas content of the TR tube
is a s tra ghtforw a rd m eas urem ent and has received m ore attention than
the other m eas urem ents . No abs olu te m eas urem ents of the effect of
no upon W, have been made becaus e of the d ifficulty of meas uring no.
Qualita tive res ults , how ever, have been obta ined . Gap s hape has been
inves tigated on ly by vary ing the gap length of a given tube and by noting
the varia tion in W,. The effect of tuning and transm itter pow er level
have been m eas ured , and coherent res ults obtained . No data are avail-
able on the effect of the transm itter-puls e s hape. Som e data exis t on
the effect of the im pedance and Q of the externa l load upon W,.
156
MICROWAVE GAfl DISCHARGES
[SEC.5 .5
6 .6 . Linear Theory of the Spik e. —There is , a t pres en t, noth ing tha t
can be d ign ified by the title of “theory of the s pik e . ” It is k now n that
a t the s tart f the transm itter pu ls e there are a few electrons in the gap.
Thes e are accelera ted by the h igh-frequency field until their energy is
s ufficien t to ca us e ion iz ation an d prod uce more electron s .
The num ber
of electrons increas es exponen tia lly w ith tim e until the electron ic r-f
adm ittance acros s the gap becom es very large and the d is charge pas ses
in to th e s tea d y -s ta te or fla t con d ition .
It is not pos s ible y et to ca lcu la te
the ra te a t w h ich the ion iza tion proces s tak es place even for s im ple gas es
lik e helium, and for ga ses having m any excita tion levels a t en ergies below
th e ion iz in g p oten tia l s u ch ca lcu la tion s a re e ve n fa rth er from rea liz ation .
Even w ith thes e lim ita tions , it is pos s ible to mak e s om e pertinen t
ca lcu la tions on the bas is of a m u h s im plified m od el.
The jus tif icat ion
for the us e of the s im ple m odel lies in the fact tha t the ca lcu la tions bas ed
on it give res ults tha t agree w ith experim en t.
Th is s im ple m odel of the
TR
Z.
m
L
Magnetron
c
G
Zo= Yy
o
*
F IG. 57.-Lumped- on st an t ir cu it of TR ca vit y loa ded wit h m agn et ron oscilla tor a nd
antenna.
spike assumes that the elect ronic admit tance acros s the gap of the TR
tube is negligible until a critica l voltage is reached , at w hich tim e the
ga p ion iz es in s ta ntly a nd completely .
The linear trans ien t res pons e of
the TR cavity to the transm itter pu ls e is ca lcu la ted up to the tim e i, a t
w hich tim e the gap break s dow n.
It is as s um ed tha t the s p ik e energy
is the energy calcu la ted in th is m anner.
A fu rther s ophis tica tion of the h eory in clud es th e effect of e lectron ic
load ing on the trans ien t res pons e.
The ra te of ion iz ation is ca lcu la ted
bu t it is as s um ed tha t inelas tic collis ions tha t d o not ion ize can be
neglected . This ca lcu la tion involves a k now ledge of the velocity d is -
tribu tion functions of the electrons and the probability of ion iz a tion
corres p on d in g to d ifferen t ele ctron en ergie s .
T. Hols tein of t e Wes t-
in gh ou se Res ea rch La bora tories h as s tu died th is problem in con s id era ble
d eta il, bu t no res ults are y et ava ilable.
In th is s ection the behavior of the s im plified linear m od el d es cribed
above w ill be pres en ted .
The electrica l circu it of the r-f s ection of a
radar s et includ ing the transm itter, TR tube and receiver, and the
antenna , m ay be repres en ted by the equiva len t lum ped -cons tan t circu it
SEC. 55]
LINEAR THEORY OF THE SPIKE 157
of Fig. 57. The TR cavity is as s umed to be connected in s eries w ith the
transm itter line, and the genera tor and antenna are matched to the
characteris tic adm ittance YO of the main line, w hile the receiver has a
conductance G. The d ifferen tia l equation for the voltage V acros s the
res onant TR circuit is then
(8)
If the genera tor voltage V,(t) is k now n, it is pos s ible to s olve for V
and fina lly get an expres s ion for the energy d is s ipa ted in the receiver
load G for any as s umed tim e interva l betw een t = O, the s tart of the
trans mitter pu ls e, and T, the beginning of the d is charge. The firs t prob-
lem , then , is to choos e the proper function for V,(t).
Firs t, it is neces s ary to cons id er on ly s elf-excited os cilla tors s uch as
the magne tron , s ince mas t e r-os ’cilla tor–pow er-amp lifie r comb ina tions are
not y et ava ilable in the m icrow a ve region .
It is k now n that the os cilla -
tions in a s elf-excited therm ion ic os cilla tor build up from zero in the
following manner . As the anode volt age is increased, cu r r en t begins to
flow. At low volt ages the ga in a round the posit ive-feedback loop is not
su fficien t to make the oscilla tor have nega t ive dynamic conductance
equal in m agnitude to the total conductan e load ing the tube, and there
are no s elf-s us ta ined os cilla tions .
There is , how ever, nois e pow er
delivered to the load . As the voltage and gain of the tube increas e,
the nega tive conductance increas es until
fina lly se lf-sus ta ined oscilla tions begin .
In the magnetron , w hile the voltage. is
s till be ow the cu toff level, the rotating
g
s pace charge has tw o effects . Firs t, it acts ~
as a nois e genera tor; and s econd , the nois e
E
voltages induced in the res onant cavities ~
k
~ Exponential
couple back to the s pace charge, lik e pos i-
rise
tive feed back , and tend to bunch it. At
I Noise; linear rise
the critical voltage, the coupling betw een o t ~ tz
the s pace charge and the res onant cavities t
of the magnetron becom es s o tight that
FIG. 5.S .—Enve lope of bu ild -
oscilla tory energy may be delivered to an
up of oscilla t ions in a pu lsed
magnetron.
externa l load with enough volt age left over
to keep the space cha rge proper ly bunched, and thus ma in ta in stable
oscilla tions in the circu it.
The outpu t pow er of the magnetron is s how n in Fig. 5“8 . In the
interva l O < t < h, the tube has an increas ing, pos itive va lue of Q and
is d riven by a cons tan t-curren t nois e s ource.
The output nois e d oes not
h ave th e u s ua l w id e n ois e s pectrum , bu t h as th e frequ en cy ch ara cteris tics
158 MICROWAVE GAS DISCHARGES
[S r%c. 55
determ ined by the effective Q of the tube. The nois e outpu t pow er
tl
tance becom es grea ter in abs olu te m agnitude than the tota l d is s ipa tive
conductance. The Q of the tube becom es nega tive, and the amplitud e
of os cilla tion increas es exponentia lly w ith tim e until it reaches a lim it
im pos ed by the externa l pow er s upply , ca thod e em is s ion , and s pace
charge.
For purpos es of analy s is of the s pik e, it w ill be as s umed tha t the
magnetron has a cons tan t, h igh , pos itive va lue of Q during the nois e
bu ildup. The nois e s ource is the s p ce charge and is as s umed to have
a very h igh impedance. It may be cons id ered as a cons tan~curren t
s ource w hos e s trength increas es linearly w ith tim e. The outpu t pow er
of the m agnetron during th is period , and under thes e as sum ptions , con -
s is ts of a narrow s pectrum of nois e, narrow com pared w ith the TR-cavity
bandw id th , abou t a cen ter frequency u , and w ith am plitud e increas ing
linearly from zero. Becaus e the Q of the magnetron is s o h igh in the
in terva l O < t< t],he outpu t pow er is es s en tia lly a continuous w ave
in term s of the compara tively low -Q TR cavity . During thk nois e-
buildup period
V.(t) = ~ t s in d
O<t <t,. (9 )
For t > t,,he outpu t increas es exponen tia lly and
v,(t) ==
~~a[~-~l)in~~
(lo)
Let us cons id er the res pons e of the TR cavity to thes e tw o fuxictions .
Meas uremen ts on 10-cm magnetrons ind ica te tha t the maximum nois e
pow er is of the ord er of 20 wat ts when the magnet ic field is 1 30 0 ga us s ,
and the r-f pu ls e pow er is about 50 kw . Aty pica l va lue is VO = ~2~,
w h ere YO is th e ch ara cteris tic a dm itta nce of th e tra nsm is s ion lin e cou pled
to the magnetron . The tim e t,d epen ds upon th e s teepn es e of th e a pplied
d -c puls e, and is abou t 10-’ s ec.
To get the res pons e of the cavity to th is linear ris e, Eq. (8) is rew ritten
Th is equation is conven ien tly s olved by the m ethod of the Laplace trans -
formation ,’ The trans forma tion of the d i feren tia l equation in to an
a lgebra ic equa tion giv es
VoYa
[
1
++G ~ ~
—–—–----= V(S ) s ’+.Ts+—
2t 1 (s2 ;sO’)’ LC ;’
(12)
I Gardner and Barnes, Tran.siknts
1942.
in L inear S yaterns, Vol. I, Wiley, brew York,
SEC. 55]
LINEAR THEORY OF THE SPIKE
159
w here V(s ) is the &trans form of V, and s is the Laplace opera tor.
Th e
s olu tion for V(s ) is
82
(13)
‘(s ) = * (s’ + U’)2 (s + ,8 +j@) (s + P –j@)’
w here l/ LC = w 2, @ = (YO/ 2 + G)/ 2C = u/ 2QLl and u >>8 . If the
in vers e, or C–l, tra ns form ation is m a de
– ‘-;(l-e-’’)lsin@’ +[i-i(l-e-;lcOsw’l “4)
~ = VOYO
‘t,cp
{[
Us ual va lues of Q. for a TR cavity are betw een 300 and 400; therefore
B
= 107 s ee–l. With w = 2 X 10’0 s ee-’, @ may be neglected
paris on , and Eq. (14) becom es
VOYO
v—
= 4t,cp
[
1
t– ~ (1 – e–@) s in d.
P
If e-s’ is expand ed in pow ers of Ot,
VOY,
V = ~ t’ s in d.
The pow er d is s ipa ted in the cond uctance G is
v, y2(J
P = IVIZG = *t’s in ’ a t,
1
and the energy d is s ipa ted in the tim e r is
or
by com -
(15)
(16)
(17)
(18)
If it is a s s umed tha t the gap break s dow n ins tan taneous ly a t the
tim e 7 , then Eq. (18) gives the s pik e energy W, d is s ipa ted in the conduc-
tance G. Experim en ta lly , it is k now n that W . is independ ent of trans -
m itter pow er over a range of a t leas t 1000 to 1 . For Eq. (18) to I
correct W mus t be ind ependen t of VO.
If it is a s s umed that the gap
break s dow n at a critica l voltage V’, then , from Eq. (16 ),
If Eq. (19) is s ubs titu ted in to Eq. (18),
(19)
(20)
160
MICROWAVE GAS DISCHARGES
[SEC.55
Thus, W is not independent of Vo and d oes not s atis fy the experim enta l
re su lts , un le s s V’ is a ls o a function of Vo as d efined by Eq. (20). More-
over, if num bers are put in to Eq. (18), then for VO = v’~0, tl = 10–s
s ee, Q = 300, T = 5 X 10–g see, and YO = G, the compu ted energy s too
low by a factor of m ore than 1000.
Thus , it has been demons tra ted that t e va lue of W . ca lcu la ted on
the as s umption of an ins tan taneous break dow n of the gap at a critica l
voltage V’ is much too low if available es tim ates of the ra te of nois e
bu~d up are us ed and the com puta tions are confined to the linearly ris ing
portion of th e magn etron -s ta rtin g ch ara cteris tic. Fu rth er in ves tiga tion
s how s that W. is not independent of the cavity tun ing. That is , for
l/ LC # a’, the energ d elivered to G varies w ith the valu of LC. Let
us now inves tiga te the energy d is s ipa ted in G during the exponentia lly
ris ing voltage output period , tl < t < h.
To s im plify nota tion , let us s h ift the tim e s ca le s o tha t t, is z ero tim e.
Then V,(t) = Voe”’. S ince the energy contribu ted by the linear ris e is
s o small, it w ill be neglected here, and it w ill be as s umed that a t t = O,
V,(t) is s uddenly applied to the netw ork . If the s olu tion for V is found
in the s am e w ay as before, the ~-trans form equation is
(21 )
‘(s ) = %&a+ju) (s –a –jti)s (s +-B+j@)(s+d -j@)’
(22)
The energy d is s ipa ted in G is
(23)
The quantities YO, B, C, and G are d efined as before. The tim e cons tan t
of the magnetron is a = 0:’2Q~, w here the buildup Q has a ty pica l va lue
of Q~ = – 25. In the 10-cm band a = 4 X 108s ee–l. S ince the va lues
of 7 are betw een 5 X 10–g and 10–g s ee, Eq. (23) cannot be expanded
in to a s hort s eries of one or tw o term s as w as done for Eq. (15). A
graphical s olu tion of Eq. (22) and Eq. (23) s how s that for ~ > 2 X 10–g
s ee, the energy is ind ependent of VO over a w ide range.
Furthermore,
if VO = {20, YO,G = 1’0 ,a = 4 X 108,/ 3= 2.5 X 107,C = 3 X 10–8Y0,
and 7 = 9 X 10–g s ee, then it is found from Eq. (23 tha t U- = 0.07 erg,
w h ich is in good a greem en t w ith experim en t.
S ince th is s im ple theory agrees w ith experim en t w h en the m agnetron
and TR cavity are tuned to the s ame frequency , Uz = 1 lL~, it is inter-
SEC. 55]
LINEAR THEORY OF THE SPIKE
161
es ting to s ee w hat happens w hen the tw o are tuned d ifferen tly , and
& = (u + Au)’.
If th is rela tions hip is s ubs titu ted into the initia l d ifferen tia l equation,
then the ~-trans form ed equation is
vO@Yo ~
v(s ) = ~
(s –a+ju) (s –a–@) [s+ L!&w +Au)][s+B-j(u+Au )]” ’24)
Th e invers e tra ns form ation of th is equatio gives
w here w is large compared w ith a, f?, a d Au.
This expres s ion m ay be
rew ritten a s
v=
VOYO
4C / (Aw )2 + (a + @)’
[(e”’ – e-~’ cos Ad ) sin (d + ~)
– e-~~ .OS (t it + ~)
s in Ad], (26)
w here @ = tan–l [(a + @)/ Ao]. The abs olute value is
Iv] =
VOYO
_ <e,d - Ze(.-d )f + 1,
4C / (Au)’ + (a + / 3)2
(27)
This equation is s im ilar in form to Eq. (22) and for t greater than 5 or
6 X 10–9 s ee, a change of Au has the s ame effect as changing V,, and
therefore has no effect upon the s pik e energy . This agree w ith experi-
m ent w hich has s how n that W, is independen t of Aw over a range of at
least
Thus , an extremely s imple empirical theory of the s pik e has been
formulated . Its claim to valid ity res ts upon the fact that if ty pica l
data for m agnetron s tarting, TR-cav ty Q, and s pik e duration are us ed ,
the calculated value of s pik e energy W, agrees w ith experim ent and als o
upon the fact that it pred icts the independence of W upon VO and Au,
w h ich is cons is tent w ith experim ent.
The tw o as sum ptions involved
concern the s tarting of the m agnetr n and the ins tantaneous break dow n
of the gap.
162 MIC OWAVE GAS DIS CHARGES
[SEC.56
5.6 . Nonfinear Theory of the Spik e.-If a cloud of lectrons in a gas
s ubject to an accelerating field is cons idered , the ra te of increas e of
electrons m ay be w ritten as
(28)
w here n is the electron dens ity , S is the average electron s peed , L t he
mean free pa th , a nd p is th e proba bilityy of ion iz ation per collis ion .
This
m ay be w ritten
(29)
where V k the voltage acros s the gap.
It w ill be s how n in S ec. 5 .13
that the r-f adm ittance of a cloud of elec-
V
m
n,
1 dg.
~e
~ dt
— = I#l(v),
(30)
.
w here the electron ic adm ittance is as -
(a)
s umed to be a pure conductance g,,
Th e
%
equ iva len t circu it is s h ow n s ch ema tica lly
v
in Fig. 5 .9 a.
Th e s olu tion of th e non lin ea r
d ifferentia l equatio of this circuit for V
- ~ (t)
is a ted ious tas k . Numerica l s olu tions
‘e
1 have been carried out by T. Hols tein of
the Wes tinghous e Res earch Laboratory
but reports of th is w ork have not y et
(b)
been published .
~IG. 5.9,—Circuitfor analys isof
Fh-s t, let u s con sid er th e circu it of Fig.
spikeenergy.
5.9b. This circu it repres en ts a nonres o-
nant (or very -low -Q) TR tube s uch as a pre-TR or bandpas s tube. In
th is circuit the voltage acros s the gap is given by
v=
.& ‘g(t)”
(31)
For s im plicity , let it be as sum ed that @(V) in Eq. (30) is a linear function
k V, That is , the probabilityy of ion ization increas es linearly w ith the
applied voltage. Now , if Eqs , (30) and (31) are com bined ,
kV=~d*=
g, d t
$2G ‘g(’)”
In tegration of Eq. (32) gives
(32)
(33)
SEC.5’6]
NONLINEAR THEORY OF THE SPIKE
163
w h ere go is the electron ic cond uctance corres pond ing to no, the in itia l
electron d ens ity in the gap, furnis hed by the k eep-a live d is charge. S in e
the circuit is as s um ed to be no res onant, the period ic genera tor voltage
V,(t) may be replaced by its envelope Vo(ta ’ – 1), w here VO and a are
the quantities d efined in Sec. 5 .5 . The numerical s olu tions of thes e
equa tions are pres en t e d in Fig. 5 .10, w here all the cons tan ts have been
normaliz ed . Thes e res u lts ind ica te that the s pik e energy is rela~ively
ins ens itive to rz~ (or g~), in view of the fact that a range of 100/ 1 in go
is repres en ted y the extrem e curves .
The area under the squares of
3.2
2.8
2.4
~ 2.0
.1
u
w
- 1.6
$
-+
Ilm 1.2
b
0.8
0.4
0
0
1
2
3 4 5
6
7
LYT
FIG. 5.10.—Calculated spik e t ra n sien t of low-Q TR t ube.
thes e curves is proportiona l to the energy d elivered to the load . For
the three va lues of go as s umed , the energies lie in the ra tio 1, 1 .4 , and
2.6 for go = 0.1 , 0 .01 and 0.001 es pectively .
S im ilar res u lts have been obta ined by Hols tein for the h igh-Q cas e.
It is in teres ting to note that th is theory pred icts the exis tence of a
“pseudo-flat.”
This is the fla t portion a fter the initia l s pik e trans ien t;
it is a t a cons id rably higher level than the arc leak age pow er of the
s teady s ta te d is charge. The ps eudo-fla t las ts until the transm itter
pow e r has reached its peak and leveled off, a t w h ich tim e the s tead y -s ta te
d is charg is es tablis hed . Until recen tly it w a s im pos s ible to prove or to
d is prove the exis tence of the ps eudo-fla t. Figure 511 is a retouched
164
MICROWAVE GAS DISCHARGES “ [SEC.56
0s (
0s (
:illogram
:illogram
of the leak age pow er through a 1B38 pre-TR
w as tak en by C. W. Zabel of the Rad ia tion L~
tube.
~borat
This
:ory on
the
Ins
ps e
:high-spt
:ulation
,udo-flat,
FIG. 5.11,—Oscillogram of spike from 1B3s pre-TR tube.
:ed os cillogra ph a t th e Ma ss ach us etts In s titu te of
Labora tory . The picture s how s quite clearly
and the trans ition to the true fla t. The d eflectio
Tech
the
‘n sem
nology
spike ,
;itivity
SEC.5.6]
RONLINEAR THEORY OF THE SPIKE 165
of th is os cillogr ph is very low and therefore it is im pos s ible, unfort -
nately , to record the break dow n trans ient in a high-Q TR tube, w h ere the
s pik e leak age energy is about 10–4 that in the 1B38 pre-TR tube.
The calculated curves of Fig. 5“10 s how a com para tively s low drop
in voltage after the peak of the s pik e.
This is in s trong contras t w ith
the as sum ption m ade in Sec. 5“5 that the break dow n is ins tantaneous .
This s am e contras t is furnis hed by the os cillogram show n in Fig. 5“11
w h ere the break dow n tim e is as long as the bu ildup tim e or longer.
Th e
num erical calcula tions for t e high-Q circu it m ad e by Hols tein s how the
rela tively s hort break dow n tim e as sum ed in S ec. 5 .5 Thus , there appears
to be a d ifference betw een the s pik es i low - a d high-Q TR tubes . Th is
is probably bes t expla ined if, in Eq. (22), it is noted that the voltage
V
is independent of the load conductance G in the tim e interval unde
consid~ra t ion . This is equiva len t to saying tha t th e s urge a dm itta nce
of the cavit is very large compared w ith Yo.
S ince go is about 0 .01 YO,
g./ g0 m ~ls t reach very m uch larger values than are required in the non-
res onant TR tube in order to produce a given reduction in oltage.
S ince n , or g., grow s exponen tia lly , Ivhen the voltage is red uced by elec-
tronic load ing, it fa lls very rapid ly , and gives a s harp break dow n
characteristic.
One of the larger void s in the unders tand ing of TR phenom ena con-
cerns the rela tions hip betw een s pik e leak age energy and the Q of the
TR cavity . Quantita tive experim en ts to d eterm ine this rela tions hip
have been few , and the res ults are conflicting. It is k now n, how ever,
that although W, is rela tively independent of the input coupling (Qm ),
it is a s tro g functi n of the ou tput coupling (Q~”,). Thes e rela tions hips
hold for a given TR tube in the region 100< Q,., <400.
The jump from high-Q TR tubes to bandpas s tubes , how ever, w here
Q.,
= 5 is d ifficult to unders tand , s ince W, in the bandpas s tubes is
abou t 0 .1 erg as com pared w ith 0 .03 erg in the h igh-Q tubes .
Moreover,
w here 0,1 to 0.3 erg of s pik e leak age energy from a high-Q tube dam ages
m any cry s ta ls , the s am e total energy from a bandpas s tube, if a llow ed
to fall upon a cry s ta l for hundreds of hours , does not damage it. The
d ifference is believed to res ult from the d ifference in s hape of the s pik e
in the tw o tubes . In a h igh-Q tube, the energy is confined to a tim e
interval s hort com pared w ith the thermal tim e cons tant of the cry st l.
In the bandpas s tub , the s low er break dow n, it is believed , caus es t e
s pik e energy to be dk tribu ted over a longer tim e interval.
If th is tim e
is longer than the cry s ta l tim e cons tant, then burnout is caus ed by a
com bination of ballis tic heating and s t ad y-s ta te heating.
Estimated
tim e cons tants are of the order of 10-’ s ee, w hereas the duration of the
s pik e is about 5 X 10-9 s ec for the high-Q tubes , and 10–6 s ec for the
bandpas s tubes . Thus , the bandpas s tube is jus t in the borderline
166
MICROWAVE GAS DISCHARGES
[SEC.57
region , and the explanation given above is a t leas t plaus ible. Further
too d ifficu lt a nd s hou ld y ie ld in teres tin g res u lts .
6 .7 . Effect of no upon S pik e Leak age Energy .—The curves of Fig. 5“10
ind ica te the d epen den ce of W, upon nO, th e n umb er of electron s in itia lly
in the TR-tube gap. It has been obs erved from experim en t tha t the
s pik e eak age en ergy varies invers ely w ith n o; h ow e ver, no quantita tive
d ata w h ich give the exa ct re a tions hip exis t.
The nature of the TR tube is res pons ible for th is gap in the bas ic
u nd ers tand ing of th e brea kd ow n .
The in itia l, or prim ing, electrons a re
furn is hed by t e d -c k eep-a live d is charge. The dens ity no of thes e
electron s can be con trolled by va ry ing th e d is ch arge cu rren t, or by chang-
ing the pos ition of the d is charge rela tive to the gap, bu t neither of thes e
parameters bears a s im ple rela tion to rLO.Furtherm ore, in norm al
engineering practice, it is us ual s o to arrange the k eep-a live electrod e
tha t w ith a normal curren t ( =
100 pa) the k eep-a live in teraction , the
reduction in low -level trans mis s ion d ue to go, is about 1 per cen t.
Th e
res t of the tub~gas , s hape, and coupling—is then ad jus ted to mak e
the s pik e leak age energy low enough for s afety . Thus , the d es ired res ults
are meas ured d irectly ra ther than by me ns of the ra ther academ ic
quantity n o.
How ever, it w ould be of va lue to have experim en ta res u lts of the
effect of no on Ws . In principle , a t leas t, o can be meas ured d irectly
by means of d -c probes in the gap.
In cell TR tubes , it is pos s ib e to
m eas ure the curren t collected on the cone acros s the gap from the k eep-
a live, w hen it is a t a small pos itive poten tia l. Thus , a ca libra tion of no
agains t k eep-a live curren t can be obta ined , and can then be us ed to
in terpret a curve of W, as a function of k eep-a live curren t.
Th e in tera ction of n o upon th e low -level tra nsm is s ion ma y be m ea s ured .
A cloud of electrons in a gas may be repres en ted (s ee S ec. 5“13) by an
adm ittance YO = go + jbo referred to the input term ina ls of the TR
cavity , the cavity los s es may be repres en ted by g:, and the gem rator
and load conductance by unity .
‘The rela tive trans mis s ion of pow e r
to the load in s uch a circu it is
“’(’++i’+(v
(34)
Meas urem en ts on a s pecia l tube ind ica te tha t the electron ic admittance
is main ly rea l (g. > bo).l Then , if b. is n eglected , th e s olu tion for go is
1Ting-Sui K&and L. D. Smullin ,
“A IQw Power X-Band R-f Gas Sw itch ,”RL
Report No. S41 ,Oct. 19 ,1945 .
SEC.5.8]
EFFECT OF GAS FILLING L’PO.V SPIKE E.VERGY
where
()
,—2
T= l+% .
ince go c no,
()
l–a
‘ E9”=;F a ‘
167
(35)
(36)
where
a = 4Te/T.
Thus , Eq. (36) is a means of d eterm ining “the
rela tive va iues of n“ in a given TR
tube for various cond itions of the ~,
keep-a live circu i ~.
& 0.6
“ L
Keep-alive off
Figure 5.12 s how s the s pik e a
leak age energy through a 724A TR ~ 0.5
tu be, opera ted w ith ou t a k eep-a live
a l 0 .4
d is charge, as a function of trans - $10.3
m itter repetition rate. In th is ex- ~ 0,2
perim ent the electrons in the gap S
~ 0.1
at the s tart of a pu ls e w ere thos e
left over from the- p revious r-f d is -
oo~
charge. T us the higher the repeti-
Transmitter repetition rate- pulses/see
tion ra te (s horter ti e betw een
FIG. 5.12 .—Effectof t ra nsm it ter r ep e-
puls es ), the grea ter is nO, and the
t it ion ra te on sp,ke leakage energy for a
724A t ube a t a lin e power of 20 kw,
smaller is IV,. An exper m ent of
this type, cou pled w ith th e recovery -tim e a na ly s is d is cu ss ed in S ec. 5 .13,
m ight give s om e in teres tin g quantita tive res ults regard in g n o.
5 .8 . Effect of Gas Filling upon Spik e Energy .-In the preced ing s ec-
tions an a ttem pt w a s m ad e to pres en t a m ore or les s rational explana tion
f the gros s as pects of the s pik e, and o the proces s of break dow n. No
a ttem pt, h ow e ver, w a s m ad e to explain th e d eta iled proces s of ioniz ation .
Th is involves accura te k now led ge of the excita tion and ioniz ation levels
and cros s s ection s of the particu lar gas un der con sid eration , and a m ean s
f ca lculating the actual electron energy d is tribution function at every
ins tan d uring the brea kd ow n proces s .
Thk has not y et been done and
is certa in ly bey ond the s cope of th is book .
From the engineering poin t of view , how ever, w hat is d es ired is a
k now ledge of the effect of pres sure and of the particular gas or m iz ture
of ga ses u pon W,.
Thes e data have been obta ined from m eas urem ents
pon particular TR tubes . Becaus e the w ork at the tim e w as urgent,
em phas is w a s alw a ys placed upon the d evelopm ent of a particular tube.
As a res u lt, com plete s ets of m eas urem ents on a particular tube, us ing
ifferen t gas es and pres sures , are a lm os t nonexis tent. N attem pt has
168
MICROWAVE GAs DISC’HA RGES
[SEC.5.8
been made to correlate the optimum pres s ure (m inimum W,) w ith gap
s pacin g and frequ en cy .
It is doubtfu l w hether the data now available
w ould be am enable to s uch analy s is .
The variation of W, w i h the k ind of gas us ed s eem s to be cons is ten t
for tubes of d ifferen t ty pes and of d ifferen t frequency band s . The TR
tubes have been filled w ith m ixtures of either H and H,O or A and HuO.
Th e w a ter va por is u sed o ens ure s hort recovery tim e, w h ile the h yd rogen
or argon is us ed to ens ure adequate cry s ta l protection at s ub-z ero tem -
pera tures and als o to in crea se tu be life .
Figure 5.13 is a plot of the s pik e leak age energy W, through a 1B27
TR tube opera ting at 9 .1 cm w ith ~L2 = 300. The data w ere obtained
FT~.5.13.–
0.2
G
:
‘ 0 .1
s
~ o,06
al
:
&0 .04
~
;
& 0 .0 2
‘z
Ln
0.01
0.008
3
6810 20
40 60 100
Gaspressure-mm Hg
-Spike leakage energy TV, through a 1B27 TR t ube for va riou s ga ses.
by meas uring the leak age pow er through the TR tube at tw o puls e
w id th s and a ss um in g that the a rc leak age pow e r w a s fla t and ind epen dent
of pu ls e length . No attempt w as made to view the leak age puls e on an
oscilloscope during the se experimen ts .
Th es e p re caution ary s ta tements
are made principa lly becaus e of the curve for Oz . The other gas es
behaved as expected ; but the very low s pik e energy obta ined w ith oxy gen
w as s omew hat s tartling. Becaus e thas e particu lar tes ts w ere made at
the end of 1945, there has been no opportun ity to check them . It
m ight be concluded that m onatom ic gas es w ould ion iz e m ore eas ily than
d iatom ic ga ses , s in ce d iatom ic gas es can a bs orb electron energy in m ole-
cqlar vibra tion thus red ucing the probability and the rate of ioniz ation.
The curves of Fig. 5 . 3 do not s upport th is conclus ion . On the other
hand , Fig. 5 .14 repres en ts data tak en on a 1B26 TR tube at 1 .25 cm in
w hich the m in imum s pik e energy for argon is about one-eighth that for
hy drogen . In th is cas e W. w as meas ured by canceling the fla t leak age
pow e r w ith pow e r through a linear attenu ator w h ich d id not pa ss through
SEC.5.8]
EFFECT OF GAS FILLING UPON SPIKE ENERGY
169
the TR tube. Meas urem ents on the 3-cm bandpas s TR tubei give the
s am e relative s pik e leak age ener ies for the noble gas es , argon, neon,
and helium as thos e s how n in Fig. 5“13.
Many m eas urem ents of s pik e leak age energy w h ich are not pres ented
here had to be om itted becaus e of the ques tionable purity of the gas es
us ed . The effect of im purities is apparently m os t s erious in the cas e of
the noble gas es .2 Ord inary TR tubes do not eas ily lend them s elves to
1,0
0.8
0.6
0.4
0!2
0.02
\
!
0.01
0.008
I I
0.006 -
I
o 10
100
partialressure of A or Hz- (mm - Hg)
FI~, 5,14.—Spike-pressure character ist ic for a 1B26 T R tube at 1,25 cm.
h igh -tempera tu re ou tga s s ing becau s e of s oft-s old e red join ts , or compara -
tively w eak copper-glas s butt s eals .
Thus , thes e data m us t be trea ted
aa repre s en ta tiv e of lea kage ene rgie s that can be e xpected from commerica l
tubes rather than as an ind ication of the in trins ic properties of the par-
ticu lar pu re ga s.
Figures 5.14 and 5.15 s how the ffect of the add ition of w ater vapor
to an H#illed TR tube upon W8.
In both the 1.25-cm and the 10-cm
tubes , the us e of H*O m ak es the s pik e energy s urpris ingly independent
1M. D. F~ke, (‘F ina l Technica l Repor t on OSRD Cont ract OEMsr-1306,” GE
I&sea rch La bor at or y, N ov. 7, 1945.
z Loeb, “F un damen ta l P rocesses of E lect rica l Disch ar ges in Ga ses, ” Wiley, N ew
Yor k, 1939, Ch ap. 2.
170
MICROWAVE GAS DISCHARGES [SEC.
5.8
of the partia l pres sure of H2 or H20.
Thus , the choice of the proper gas
fillin g mu s t be d icta ted by con s id era tion s oth er th an s pik e lea k age en ergy .
Thes e factors , arc pow er, recovery tim e, and life, w ill be d is cus sed in
succeeding sections .
Although Fig. 5 .14 ind icates that the us e of pure argon res u lts in
exceptiona lly low values of W,, th is is of little im portance in a TR tube
d es ign ed for r d ar u se beca us e of the extrem ely long recovery tim e of s uch
I
s O,*
I WI
ck
0.1
10-3
I I
1 1
., ,4,,,, ,,~u,
13.06k~ 10mm H~of
0.02I
I I I
I
1 1
I I
I
I
1
2
4 6 810 20
40 60 80100
Partial pressure of H2- mm of Hg
F IG. 5.15,—Effect o a ddit ion of wa t er va por t o H~filled 1B27 TR tube.
a tube. The add ition of s ufficient w a ter apor to ens ure s hort recovery
tim e and reas onably long tube life , mak es the A and H20 s pik e energy
about the s ame as that for the Ha and HZO m ixture.
Eflect oj Gap Length upon W,.—In the TR tube, s pik e leak age energy
increas es w ith increas ing gap length , if other factors (except tuning)
remain cons tant. Figure 5.16 s how s the characteris tics of the 1B24
(3-cm ) and lB27(10-cm ) TR tubes ; W, is plotted agains t revolutions of
the tuning s crew , w h ich produce a linear m otion of the cone. Thes e data
w ere obta ined With the exciting pow er com ing from a fixed -frequency
m agnetron and , therefo e, the TR cavity w as detuned from the m agrw
tron by alxw t f 6 per cen t at the extrem es of the tuning range. Other
SEC,5.9]
ARC LEAKAGE POWER
171
tests in w hich the magnetron frequency w as varied over a com parable
range w h ile the TR cavity w a s k ept tuned to a cons tan t frequency s how ed
varia t ons of W , of 1 db or les s . The curves of Fig. 5 .16 obvious ly obey
d ifferen t law s . How m uch of th is res ults from d ifferences in frequency
and how much from electrod e s hape is not k now n .
Som e ind ica tions of a m inimum spacing, below w hich W. s tarts to
ris e again , hav been found . Th is occurs in the 1B27 at a s pacing of
,
abou t 0 .005 in . No quan tita tive
exis t, and no data exis t for other
frequencies.
Accura te m eas ure-
men ts of th is m inimum as a func-
tion of frequency and pres s ure
s h ou ld p rove va lu able in a fford in g
a clearer ins ight in to the fund -
men ta l p roces s e s .
It is believed
that th is m inimum has the s ame
s ign ifica nce a s th at of th e Pa s ch en
curve for low frequencies . When
the gap becom es s hort enough , a
large fraction of the electrons in
the gap may be los t to the elec-
0.1–
008
3006
–
~ 0.05–
“s 0 .04–
~.
0.03
$
~ 0.02—
g
(R
0.01–
0.008
[ [
I [ [
I
0123456789
Turns of tuning screw- decreasing gap length
F IG. 516.-Va r ia t ion of sp ik e leakage ener gy
wit h ga p len gt h in 1B27 a nd 1B24 TR t ubes.
trod & ‘before they can con tribu te to the further ion iza tion of the gas .
5 .9 . Arc Leak age Pow er.—The arc leak age pow er is the pow er d is s i-
pa ted in the receiver load and res ults from the s tead y-s ta te voltage d rop
acros s the h igh-frequency d is charge in the TR tube. In the normal
pres sure and current range encoun tered in TR tubes , the voltage d rop
acros s the d is charge is v ry nearly ind epend en t of the current carried by
it, and for m os t cas es the d is charge can be treated as a zero-im ped ance,
cons tan t-voltage source .
S om e of th e s im ila rities betw e en th e h igh -frequ en cy d is ch arge a nd th e
pos itive colum n of the d -c d is charge have been ind icated earlier in th is
chapter. In th is and the follow ing s ection s , the s elf-s us ta in ing r-f d is -
charge in TR tubes w ill be d is cus sed , in w h ich the quantities of in teres t
are the arc leak age pow er and the arc loss, the pow er d is s ipa ted in the
d is charge. S om e of the independ en t variables that a ffect the d is charge
are:
1 . Ga s con ten t.
2 . Tran sm itter pow e r level.
3 . Extern al circu it (ca vity cou plin gs , etc.).
4 . Gap s hape.
The on ly quan tities w h ich can be m eas ured conven ien tly are the arc
172
MICROWAVE GAS DISCHARGES
[SEC.~g
leak age pow er, arc los s , and the trans fo m ed d is charge im pedance. No
m eas urem ents have been m ad e of the electron d ens ity or of tem perature
in the d is charge, although es timates of the former have been made. It
s hou ld be pos s ible to m ea su re th e electron tempera tu re by m ea ns of probes
s im ilar to thos e us ed in the s tudy of d -c d is charges . 1
Before pres enting the experim enta l da ta , or d is cus s ing s om e of the
theoretical as pects of th is pr blem , let us s ee how the m eas ured leak age
pow er varies w ith the des ign of the TR cav ty . Figure 5. 17a is a
s chem atic d iagram of a TR tube connected in s eries w ith a trans mis sion
line w hich is energized by a matched genera tor and term inated in a
matched load . The TR cavity is loaded by an arbitrary , rea l conduct-
ance G/ YO = g. The equiva lent lumped -cons tan t circu it is s how n in
Fig. 5 .17b, w h ere the reference plane has been chos en at the center of the
Z.
T
E
Z. +
-- Reference
i
plane
G
2b2Z.
m“
(a)
(b)
F IG. 517.-Equ iva len t cir cu it for a r c lea kage power .
TR tube. The equiva lent genera tor s een at the center of the TR tube is
obtained by the us e of Th6venin’s theorem .
The in ternal im ped ance is
2 b2Z0and th e open -circu it volta ge is bE , w here B/ YO = b is the suscept -
ance of the TR-cavity coupling iris es .
If b = 10, then the genera tor
im ped ance s een from the gap is 200Z0.
If a line pow er of l-k w peak s , and
a 50-ohm coaxia l trans mis s ion line are as sum ed , then E = 1400 volts rm s ,
and the trans form ed generator voltage bE = 14,000 volts . Meas ure-
ments made on the 721A TR tube ind icate that the voltage d rop acros s
the d is charge, ea , is about 100 volts z w hen an H*-H,O gas filling is us ed ,
and is 200 to 300 volts in the argon-filled 10-cm pre-TR tubes . This
large ratio betw een emand bE allow s the d is charge to be trea ted as if it
w e re energiz ed from a con stan t-cu rm z t sou rce.
The magnitude of the d is -
charge curren t d epen ds upon the transmitter pow e r, upon the am plitud e
and phas e of s tand ing w aves in the m ain trans mis s ion line, and upon the
coupling to the TR cavity .
1Cobine, Gaseous Coraducfw-s, McGr aw-H ill, N ew Yor k, 1941, Ch ap. 6.
2 Bethe, Marshak, Sclfa inger , “Theoret ica l Results on the TR-Box, ” NDRC
Repor t D1-1 16, J a n. 20, 1943.
SEC.59]
ARC LEAKAGE POWER 173
Itis an experim en ta l fa ct that w ith in the a ccu ra cy of th e experim en ts ,
the arc leak age pow er of a TR tube in to a given loa is ind ependen t of
transm itter pow er over a range of s evera l thous and to one. Th is m eans
that th e a rc- volta ge rem ain s-con sta nt w h ile the
curren t is varied by a factor of fifty or m ore, and
a llow s the d is ch rge to be trea ted as if it had a
zero d y nam ic im pedance and cons tant voltage
drop.
The pow er d elivered by a cons tan t-voltage
genera tor to a load is P = E2g, w here g is the
conduct ante of the load . The load s us cept ante
has o effect upon the tota l pow er abs orbed by
the load . Meas urements of arc leak age pow er
as a function of load adm ittance give con tours
of cons tant pow er w hich fa ll upon lines of con -
s tan t con du cta nce on tran sm is s ion -lin e ch arts ,
12
k
~8
a
%
~
M4
~
o
0
0.4
0.8 1.0
T
FIG. 5 .18.—Var ia t ion
of a rc r ea ka ge power wit h
t ra nsm ission t hr ou gh t he
TR swit ch .
and w h ich s how lit tle or no d epen den ce on th e s us cepta nce.
The rece iver
g/ b~ ,
pow r is
pa = ~:~.
(37)
2
The externa l Q of the ou tpu t circu it is
Q,., = I+
.
and there fore
‘“ ‘&”
(38)
For con ven ien ce in ca lcu la tin g, th is s im ple rela tion s hip ma y b e exp res s ed
in term s of s om e other param eters .’
1 , For a cavity coupled for m atched inpu t cond uctance,
2 . For equal inpu t and ou tpu t coupling (1 / b~ = g/ b~),
(39)
(40)
w here T is the s gna l t ransmission ra t io, the ra t io of t ransmit ted power to
the ava ilable power , and gc is the cavity conductance. F igure 5.18 is a
I S~muel, McChea , and Mumford,
“The Gas Discharge TR Switch ,” BTL MM-
42-140-26, April 17, 1942.
174
MICROWAVE GAS DIS CHARGES [SEC.59
plot of Pa for t es e tw o cas es as a function of T . Note that Pm is directly
proportion al to th e ca vity con du cta nce g., a nd th erefore, for a given in s er-
tion los s , the arc leak age pow er varies invers ely w ith the unloaded Q of
th e ca vity .
The pow er d is s ipa ted in the d is charge m ay be calcu lated in a s im ilar
manne r, 1
The curren t in the d is charge is
and the pow er is
P, = iae== e.
4P1%
b
(41)
(42)
As before, the pow er d is s ipa ted in the gap may be rew ritten for tw o
specia l case s .
1 . Matched input coupling,
(43)
2 . Equa l cou plin gs ,
P, = dP,Pa .
(44)
Thus , the d is s ipa ted pow er is proportiona l to the geom etric m ean of the
line pow er Pl, and of the arc leak age pow er P.,
Thes e rela tions ind icate that in order to d es cribe the leak age ow er
of a TR tube, either the ou tpu t coupling, or the cavity transm is s ion ,
02 4 6 8
Turns of tuning screw
Decreasing gap ~
FIG. 5.19,—Variation of arc leakage power
with gap length.
ing the TR cavity by vary ing the
s hunt onductance, and ratio of
input to ou tpu t coupling corre-
s pond ing to any given value of P.,
mu s t b e s pecified .
Detuning the TR cavity from
the transm itter frequency by
means of tuning plugs in the TR
cavity (or detuning the trans -
m itter) has practica lly no effect
upon the arc leak age pow er.
Once the gap has brok en dow n,
the cond uctance of the d is charge
is very large compared w ith the
s us ceptance in troduced by the
detuning of the cavity . Detun-
gap s pacing has a mark ed effect
upon Pa. Figure 5.19 s how s th e varia tion of Pa w ith ga p s pa cin g (a dju st-
1Ibid,
SEC.510]
DEPENDENCE ON TRANSMITTER POWER
175
ment of the tuning s crew ) in the 1B24 and 1B27 TR tubes . Thes e data
Thes e curves have the form Pa = Cekr, w here C and k are cons tan ts and 1
is the gap length . On a linear plot of the data m ight be fitted by a
square -law curve , Pa = A 12,w here A is a cons tant.
A s im ple picture of
the d is charge pos tu la tes a cons tan t gradient, the voltage d rop varies
linearly w ith s pacing, and the leak age pow er therefore varies w ith the
s quare of the s pacing. As an engineering approxim ation , it is probably
s a fe to as sume that the arc leak age pow er is proportiona l to the square
of the gap length .
5 .10 . Depend ence of Arc Leak age Pow e r u pon Transm ittin g Pow e r.—
The arc voltage e. is ind epend ent of the d is charge current in rad ar equ ip-
ments opera tin g under norma l cond ition s .
At line pow ers jus t above the
m inimum break dow n level, the d is charge exh ibits a d ecid ed nega-
tive characteristic.
Figu re 5 .2 0 illu s tra tes th e lin ea r va ria tion of lea k age
FIQ,
v
I
Line power
S.20.—Leakage power at ver y low
levels a s a funct ion of lin e power .
I.&L
(E )
/
d(E)
i E’ E
FIG. 5.21.—Product ion and des t ruct ion of
elect r on s a s a funct ion of field st r engt h .
pow er w ith line p w er up to the poin t of break dow n , bey ond w hich it fa lls
off w ith in crea sin g pow e r a nd fin ally rea ch es a con sta nt level.
A th eory
to expla in th is behavior has been advanced by Margenau. 1
Let us cons id e the follow ing d ifferentia l equation , w h ich i s im ply a
s ta tement of equ ilib rium ,
dn
x
= p(,!l)n – d (E)n = O,
(’!5 )
w h ere n is the num ber of electrons per cubic cen tim eter in the d is charge,
and p(E) and d (E) are the voltage-d ep ndent ra tes of production and
des truction (d iffu s ion ) of e le ctrons .
Th is equation has on ly on e equilib-
rium voltage E; at w hich p(n) = cZ(E), Fig. 5 .21 . The number of elec-
trons n does not affect the res ult, and cons equently , if th is equation
d es cribed an r-f d is ch arge, its volta ge wou ld be a con sta nt, in depen den t of
current dens ity . How ever, a correct theory s hou ld pred ict the experi-
m ental curve of Fig. 5 .20 .
1H. Margen au , “Th eor y of Alt er na tin g Cu rr en t Disch ar ges in Gases, ” RL Report
No. 967, J an. 10, 1946.
176
MICROWAVE GAS DISCHARGES
[SEC.~10
Equation (45) may be mod ified by add ing to it a cons tant term c.
Then , a t equ ilib rium ,
dn
at = [P(E) – d(E)]n – c = O,
(46)
and
n=p(~) : d(n)”
(47)
Figure 5.22 is a plot f Eq. (47).
The left portion n(l?) is negative and
h as n o ph ys ica l s ign ifica nce; h ow e ver, th e right portion , if replotted w ith
the axis s uitably rota ted , gives a curve of the s am e form as Fig. 5“20.
This cons tan t c is phy s ica lly s ignificant for it im plies a m echanis m for
the des truction of electrons at a ra te
I
K
ind epend ent of n .
It can be s how n that
/
/
L
th e ca ptu re of electron s by n eutra l a tom s
/
I ,’TL
or m olecules to form negative ions obey s
o \
1,
s uc a law . Some gas es s uch as the
,~ E’
E noble gas es , hy d rogen , and nitrogen ,
. . .
p-d
have zero e lectron -cap ture cross section ;
A
7/
others , how ever, lik e oxy gen , the halo-
gen , and w ater vapor, have compara-
F1~.5.2 2.—S tabilityond itionsfor a
tively large electron-capture cros s s ec-
steady-stateischarge.
tions . Let us cons id er a TR tube w hich
has an atmosphere, part of w hich has a finite electron-capture cros s
section.
The analy s is w ill u se the follow ing s ym bols :
n = electron dens ity .
Y = number of neutral captors .
Y’ = number of negative ions .
M= Y+ Y’.
Q = collis ion cros s s ection of electron s and ga s molecu les .
h
= p robab ility of ele ctron captu re p er collis ion .
h~~= probab ility of ele ctron rele as e p er collis ion .
v = electron velocity .
C = Quh .,p = probability of elect on capture per s ec.
R = Qvh,,l = proba bility of electron relea s e per s ec.
Then,
d Y’
dt
— = C’n(M – Y’) – RnY’.
(48)
S ince onl the s teady -s ta te d is charge is cons idered , n m ay be as s um ed
cons tant. Then by s olving for Y’, the follow ing equation is obta ined ,
Cluf
— [1 - e-’’+’)”].
“=R+C
(49)
SEC. 510]
DEPENDENCE ON TRANSMITTER POWER 177
In the d is charge, the electron tem pera ture is high, probably about 10
electron volts , and the probability of releas e is m uch grea ter than that
of cap tu re , R >> C. Then at t = m ,
yl=#=hmD
~; M.
,0
(50)
Thus for a given concentration M of captor molecu les , the number of
nega tive ions form ed is a function only of the ratio of the probability of
electron capture to that of releas e w hen the electron energy is high.
There w ill be a continual d iffus ion of Y’ out of the d is charge to the w a lls
or to the electrodes . This rate w ill be independen t of n and independent
of E. Th erefore, on ce s tea dy -s ta te con dition s ha ve been reached , elec-
trons w ill be captured at a rate jus t rapid enough to m ak e up f or the num -
ber of negative ions los t by d iffus ion , and thus a phy s ica l proces s
corres pond ing to the cons tant c of Eq. (46) res ults .
If th is theory is cor ect, it w ould be expected that a TR tube filled
w ith gas s uch as argon w ould not have a nega tive s lope in the leak age-
pow e r characteris tic, w h ereas a tube containing HzO w ould be expected
to have a large negative s lope.
Before d eterm ining w h ether th is con-
clus ion is jus tified by experim enta l data , the ~ctual m eas urem ents
involved s hould be cons id ered . The meas ura i-,le quantities are arc
leak age pow e r, w h ich is proportiona l to e:, input admittance of the fired
ca vity , in cid ent pow e r, and pow e r
d is s ipa ted in the d is charge. The
ea sies t com bin ation to m ea su re is
incid ent pow er as a function of
arc leak age pow e r, as in Fig. 5 .20.
~~
Although this curve con ta ins all ‘- -
of th e in forma tion wh ich is n eed ed
1
from the view poin t of practical
FIC. 5.2. .—Diagram to illu s tr a t e admit t ance
duplexer design , it r ea lly tells very
r ela t ion s in a cavit y.
lit{le a bout {h e d is cha rge its elf.
Th is is ‘)ecaus e the abs cis sa , or line
pow e r, is an unk now n function of the actual d is charge current.
Con s id er th e circu it of Fig. 5 .2 3.
The cavity is load ed at its cen ter by
the d is charge adm ittance Y.. With Y= = O, the cavity is pres umed to be
res onant and the adm ittance at the cen ter M Y. + (Yo/ b~) = Y. The
input admittance is
Y,
Y – jb,
Y ,
= ll + ~ _ ~ybl’
(51)
If th is equation is s epara ted into its real and its im aginary parts , and if
b? >>1 is a s s umed ,
Y,
~ = (1 + bf$ + g’b:
1
+ ~ ~, + (b’ – bb, + g’ – l)b, ~52)
(1 + bbJ 2 + g’b~
178 MICROWAVE GAS DISCHARGES
[SEC.5.10
Exam ination of Eq. (52) ind ica tes that w hen ga and ba are of the ord er of
m agnitude l/ b~, the input s us ceptance w ill be a s trong function of Y.. As
th e a rc a dm itta nce in crea ses , h ow e ver, th e in put a dm itta nce a pproa ch es
a limit,
lim Y, = $ + jb,,
(53)
y ,,+.
and it becom es d ifficult to mak e accu ra te m ea su rem en ts of the im agina ry
30
Relative current
Fm. 5.24.—Rela t ive r -f cu r r en t and volt age of d is cha rge a t low levels.
80
e
g 70
0
o— o
i
>
n
.
0
600
, I
1
[ 1
,
‘d.
1
2
3
4
IIIin ma
FIG. 5,25,—Magn it ude of r -f cu r r en t vs. volt age in helium ,
compon en t of Y., a lthou gh the cond uctan ce w ill be d irectly proportion al
to the input s tand ing-w a ve ratio.
1 + Irl
2b1+ l+;
~’=l–lrl=
2
= gabl.
(54)
z
Th us a mea s uremen t of th e leu el an d th e .s ta nd in g-wau era tio a re s ufficien t
to give n umbers proportional to the oltage and current in the d is charge.
SEC.511]
EFFECT OF GAS FI LING UPON Pa 179
If the s hape of the cavity is accura tely k now n, the absolute volta ge a nd
curren t in the d is charge an be com puted .
2
-4
-3
-2
-1
0
lma~inary part of current in ma
FIG. 5,26.—Rea l vs . imagina ry par t s of r -f cu r r en t in helium discharge.
Figure 5.24 is a curve of the rela tive curren t vs . voltage in the d is
charge of a 1B24 TR tube filled w ith 15 mm Hg each of Hz and HZ().
Figure 5 .25 is a s im ilar curvel
meas ured in a s pecia l cavity filled 11
w ith helium at 3.2 mm pres s ure
and A = 9.8 cm . By s tand ing- lo
L
w ave m eas urements it w as pos s i-
:
ble to find the phas e angle of the .
current w ith res pect to the volt- ~d~
age. Figure 5.26 s how s the rea l ~
\
Partialressure
part of the curren t p o ted agains t s 1
of H2=10 mm Hg
th e im agin ary pa rt.
58
Fig re 5 .27 is a s im ilar plot for ~
a number of d ifferen t gas fillings ~
in a 1B24 TR tube. The tw o 7 -
figures do not neces sarily agree
Omm’
Hg. H20
s ince they w ere tak en w ith d iffer-
en t tubes , tuned to clifferen t $00
0
200 300
400
frequencies.
500
Incident power, P,nc in mw
5 .11 . Effect of Gas Filling
FIG. 5.27.—Leaka geow eras a func-
upon Pm .—As in the cas e of the
t ion of inciden t power in a 1B24 tube with
spike, it is difficu lt to predict
various fill ings.
theoret ica lly not on ly how gases will cliff er in a rc 1eakage power , bu t a lso
how they will va ry with pressu re.
It has been s een , how ever, tha t the
1M, A. Her lin a nd S. C. Br own , Bu ll. Am er. Phys. S ot. 21, 28 (1946).
180
MICROWAVE GAS DISCHARGES
[SEC. 5’11
order of the voltage d rop for various gas es in the r-f d is charge is the
s am e as that for the pos itive colum n in the d -c d is charge.
The characteris tics of a gas w hich affect the r-f voltage d rop can be
is ted . Firs t to be cons id ered , referrin to Eq. (45), are the rates of
production and des truction of electrons as functions of gap voltage.
Des truction can be lim ited to d iffus ion, s ince the recom bina tion of an
electron and a pos itive ion is an extrem ely improbable event.
Th e
d iffus ion is of the s o-ca lled am bipolar ty pe w hich tak es place at about
tw ice the rate of d iffus ion of gas m ol cu les . Thus , it w ould be expected
that the lighter gas es w ould d iffu se m ore rapid ly , and the s us taining volt-
age w ould be increas ed . The rate of prod uction of electrons , or of ioniz a-
40
20
: 10
8
5
~6
R4
&
lJ
;2
2
a
;::
0 ,6
0.4
12 4 6 810 20 40 60 100
Ga spressure n mm hg.
FTC;,52S.-.4w le:IkiIw ~mn-r t fronl~ 1B?7 TR tuh as a funct ion of pressure .
t ion , is dctcrmillet l ill p:~r t I)y t l~e ioniza t ion potent ia l, the number of
excita t ion levels belolv the ioniza t ion level, and the number of molecu la r
resonances which can al)sorb elect ron energy withou t result ing in fur ther
ioniza t ion of the gas.
Figure 528 is a plot of the arc leak age po~ver in a 1B27 TR tube as a
unction of the pres s ure of the vario s gas es tes ted . Thes e curves w ere
obtained from the s am e experim ent as thos e of Fig. 5“13, and the s am e
comments apply , The rmblc gas es lie w ell be]o~v the other g s es . In
hes e curves , the m inimu vd IIc of Pa for argon is about 0 .05 that for
hydrogen.
( )t Iler itlvrs t igat ors report m -err low er va lues for argon.
l;xtw rne purity apparen tly res ults in the lm vcs t ~:llues of P. for argon,
NTOre lia l)le da ta exis t F(J [,thos e m i~tu rrs of nob le ga s es \ vhich i~,e a very
low breakdolvn voltage in d -u LIis (lla rge s .
SEC.512]
THE RECOVERY PERIOD
181
Margenau, in a theoretical s tud y of the r-f d is charge,’ has propos ed a
s im ilarity principle for s uch d is ch arges .
On the as s umption that the
s ources of ioniz ation rem ain in pla y over th e range con sid ered , h e d erives
an expres s ion for the m inim um of the voltage-pres sure curve for a given
gas , w hich s tates that at the m in im um ,
w
=a
i
E
.-
=b
I
(55)
P
w here a and b are cons tan ts , p is the
angular frequency and am plitud e
of the im pres s ed field . Th is s ta te;
that the pres s ure for m inim um volt-
age d rop, and the actual value of
the m inim um drop, are proportiona l ,
I
gas p essure, and u and E are the
I
to OJ. Figure 529 illus trates this n
rela tions hip. This theory has not
been check ed w ith data tak en w ith
m l
a s ingle tube of fixed s hape. The ,.”” ~ , ~
experiment is not d ifficult, and it
1’1 P2 P3
s hou ld prove va lu able in exten din g
F1~.5.fKl—Diagramto illus trates imilarity
the u ders tand ing of the r-f
principlefor r-f d is charges ,
discharge.
5012. The Recovery Period .-The recovery period is the time after
the trans mitter pow er has fallen to zero. During th is im e he gap in the
TR tube deioniz es , and the attenuation through the TR tube d rops from
the value of 60 or 70 db during the transm itting period to 1 or 2 db. In
Sec. 52 a crude form ulation of the adm ittance of a s pace-charge region
w as pres en ted . If the electrons are in a vacuum they los e no energy by
collis ion w ith heavy a tom s , and the current repres en ted by their m otion
is in quadrature w ith the applied field , and therefore the s pace-charge
region appears as a pure adm ittance w ith a d ielectric cons tant les s than
unity . If the electrons are not in a vacuum and therefor m ak e collis ions
w ith atoms or m olecu les , s om e of the os cilla tory energy the electrons
obta in from the applied field is changed into thermal energy by the
collis ion s , a nd cannot b e retu rn ed to th e extern al circu it.
Th ere is th ere-
fore a net input pow er to the d is charge, and the gap adm ittance has a
real component.
The electron energy in the r-f d is charge is com para tively high, and
it is m uch greater than that f the gas . Becaus e of their random m otion
I H. Margenau , “Theory of Alterna t ing Curren t Discharges ia Gases, ” RL
Repor t No. 967, J an . 0, 1946.
182
MICROWAVE GAS DISCHARGES
[SEC.5.13
there is a cons tant d iffus ion of electrons out of the gap. The rate of th is
proces s is retarded by the pos itive ions in the d is charge Irh ich exert a
field oppos ing the rapid outw ard m otion of the electrons . The net d rift
of electrons and pos itive ions is referred to as am bipolar d iffus ion , and
tak es place at a rate corres pond ing to tw ice the mobility of the ions ,
When the excita tion is removed , the electron temperature is quick ly
red uced , by collis ions , to the tem perature of the gas .
It reaches a value
of tw ice the gas temperature in about 1 ps ec.
It w ill be s how n that the
d iffus ion proces s es much toos low to bereliedupo for the recovery of
TR tubes .
To m ak e the recovery tim e s ufficien tly s hort, it is neces s ary to rem ove
electrons by s om e other m eans .
Electron recom bination by m eans of a
three-bod y collis ion has little probability , and therefore cannot caus e a
s ufficien tly rapid recovery . Capture of electrons by neutral a tom s or
molecules has a com paratively high probability . The us e of a gas s uch
as HZO w ith a large electron-capture cros s s ection gives tubes w ith a
recovery tim e of only a few m icros econds . .
In the follow ing s ections the theory of the recovery period w ill be
pres ented firs t. This w ill be follow ed by a d is cus s ion of the properties
of various gas es and a pres enta tion of experim enta l data .
6013. Theory of the Recovery Period .-The follow ing analy s is is due
to Margenau. 1 In S ec. 5 .12, three pos sible m echanis ms for reducing the
electron d ens ity in the d is charge w e re m entioned : d iffus ion, recom bina-
tion , a nd captu re.
Thes e Ii-ill be exam ined in th is ord er.
Diflus ion .-In ord er to calcu late the rate of d iffus ion , it is neces sary
to k now the electron and ion temperatures . During the d is charge the
electron temperature is very high , many thousand degrees . In the
recovery period th is energy is red uced by collis ions w ith gas m olecu les .
The rate at w hich th is reduction tak es place may be determ ined as fol-
low s . Let u be the average electron velocity , L the m ean free path , 2’the
electron tempera tu re, and TO th e gas tempera tu re.
Then the mean los s
of energy by the electron per collis ion is
AE = ~mk (T – TO),
The rate at w hich the mean energy decreas es is
() ()
1cT ‘i 4m
—
;L ~lcT =k (T– TO) —
m m“
(56)
(57)
‘ H. Ma rgen au , “ Th eoret ica l In terpret at ion of t he Recover y Time of TR Boxes;’
RL Repor t No. 929, J an . 9, 1946.
SEC. 513]
THEORY OF THE RECOVERY PERIOD
183
The s olution of th is is
(58)
w here the s ubs cripts 1 and O refer to initia l and final cond itions , and
8
)
km g
9=7ZZ “3- “
The tim e requ ired for the average s peed to d rop to a tim es its final value
is given by
t. =
+0 in S
(59)
a—l
w here TI >> TQ.
For argon at a pres s ure of 10 mm Hg and a = 2, the relaxa tion period
is about 1 .5 ps ec.
Thus , for time s
longer than 5 or 10 ps ec, the elec-
Pre-TR tube
trons may be cons id ered to be at
th e ga s tempe ra tu re TO.
The calcula tion of the rate of
d iffus ion f eIectrons out of the
‘0=’0
gap of a h igh-Q TR tube involves
s ome ve ry d ifficu lt computa tion s ,
and has not been carried out.
How e ver, as a pertinen t exam ple,
-1
let us cons id er the recovery of a
FKG.5.30.—Dischargen pre-TR tube and
pre-TR tu be, w h ere the d is charge
equivalentcircuit.
is as s umed to be in the form of a thin s lab of th ick nes s d ad jacent to, and
covering, the low -Q input w ind ow , Fig. 5 .30.
The d iffus ion equation is
(60)
w here n is the electron dens ity and D is the mobility or coefficien t f
d iffus ion. For the s hape under cons ideration , if the electron dens ity nO
is uniform at the end of the transm itter puls e,
‘“”OI’(%)-:[(%9 -4%)1) ‘“)
/
r)(u) = ~ =e-z ’ dx.
*O
In Eq. (61) the as s umption is made that the d iffus ion tak es place only
to the input w indow , and that s ince d is sm all, the los s of electrons from
184 .lIICROJ\ ’.4YE GAS DISCH.4 RGES
[SEC.513
the edges of the d is charge is negligible. The d iffus ion coefficien t D is
not that predicted by kinet ic theory for a cloud of elect rons.
The difiu-
sion tha t takes place is ca ll d ambipolar . 1
It takes place at a reduced
ra te because the massive, slow-moving posit ive ions act as a broke on
the electrons. Thus, as soon as a few elect rons hare left the discharge,
a posit ive space cha rge is set up that inhibit s the loss of any more elec-
t rons until an equal number of posit ive ions have diffused out of the dis-
charge. The net ra te is about tmice that of the gas molecules a lone.
In the 1B38 pre-TR tube filled with 10 mm Hg of a rgon, the ambipolar
diffusion coefficien t is about 5 cm’~sec, and if the thickness of the dis-
charge d is 1 mm , the recovery tim e w ould be s evera l thous and m icro-
s econd s . S ince it is neces sary to have recovery tim es of the or er of 1 to
10 ~s ec, d iffus ion a lon e ca n con tribu te very little .
A ca lculation of the effect of the recom bina tion of electrons and pos i-
tive ions on recovery tim e ind ica tes tha t abou t 1 s ec w ould be requ ired
to deion iz e the gap s u fficien tly . S ince d iffus ion and recom bina tion as
m echanis ms for obta in ing s hort recovery tim es have been d is cus sed , let
us next cons id er the capture of electrons by ne~tra l a tom s .
In the ca lcu la tion of the effect of capture upon arc leak age pow er
(S ec. 510), the electron dens ity n w as cons id ered cons tan t. In the
recovery period there is no prod uction of electrons and the constant term
is the total negative charge,
N = cons t = n + l“.
As b efore ,
M = cons t = 1’ + 1“{.
The ra te of chs mge of e ectron dens ity is
In th e recovery period , a fter th e firs t m icros econ d, the elec ron en ergy
is low and h,.1
= O. During the firs t few m icros econd s , the electron s ar
los in g en ergy ra pid ly a nd n eith er ha. nor h,el a e cons tan ts , nd the s olu -
tion f Eq. (62) becom es extrem ely d ifficu lt. La ter, how ever,
dn
x=
— vQh_P (M — N)n = —vQh_PMn,
(63)
w here the in itia l num ber of ne tral a tom s Y“O= >> no.
This is an expres s ion for the ra te of change of electron d ens ity . Let
us now s ee how th is caus es the a ttenuatiori through the TR tube to vary
w ith tim e. The transm is s ion through an attenuating med ium betw een
1Cobine, Gaseous Conductor s, McGraw-H ill, New York, 1941.
SEC.5.13]
THEORY OF THE RECOVERY PERIOD
185
tw o uniform , nond is s ipative m ed ia m ay be w rittenl as
E. =
cos yld + jsin T ld
z
co’’~-$(2+2)sin@’
(64)
w here E. and Ei are the output and input field s : T1 and YZ are the propa-
ga tion con s ta nts in th e n on los s y a nd 10SSYmedia ,
Z2 , T2
res pectively ; Z 1a nd 22 a re th e res pective ch ara c-
teris tic im ped ances ; and d is the th ick nes s of the
z , -r,
Zj, -f,
attenuatin m ed ium , Fig. 5.31. The character-
is tic im ped ance of a w aveguide is
-Ei
t
t
EO
z=:= ~:,
u
’65) @
Q
“= - (;)+@)+u66) , ~ , , : - T ,
ogy for tranamisaion
where E. = E.eird , a is the w id e d im ens ion of the
t h rough at tenua t ing
guide, and u is the conductivity of the m ed ium .
medium.
If
y d is as sum ed s mall, Eqs . (65) and (66) are s ubs titu ted into Eq. (64),
and u = u, + jai, then
(68)
This equation is of the s am e form as the expres s ion for the attenuation
due to a lum ped -cons tan t s hunt adm ittance replacing the d is charge,
s ee Fig. 5 .30, w here the transm is s ion is [(1 + g/ 2)2 + (b/ 2) 2]-l, and g
and b are the norm aliz ed componen ts of the d is charge admittance.
Conductivdy oj the Ionized
Gas .- argenau2 has s how n that if the
electron mean free path , and the frequency and the amplitude of the
impres s ed h igh -frequ en cy volta ge a re a dju sted s o th at th e electron s ma k e
rela tively few collis ions per cy cle and the electron energy is below the
ion iz in g level, th en th e d is tribu tion of electron velocities w ill be ~Ma xw e l-
] J . A . S tra tton , Ekdroma#ndti !/ VwW,McGraw -Hill, New York , 1941,p . 511 .
*H. Margenau, “Dispersion of High Frequency Radio Waves in Ionized Gas es,”
RL Report No. S36,Oct. 2 6, 1945.
186
MICROWAVE GAS DISCHARGE.q
[SEC. 513
lian . At the opera ting pres s ures encoun tered in TR tubes (10 to 30 mm
Hg) thes e cond itions are s a tis fied in the recovery period w here the
im pres s ed voltage (received s igna l) is rela tively w eak , Under thes e
cond itions the conductivity of the gas is
4
‘2Ln , [Kz (x ,) – j.rl}’K;2 (x ,)],
u = 3 (27rm k7)~~
(69)
w here e , m , and n are the electron charge, mas s , and d ens ity ; L is the
electron mean free pa t ; k is the Roltzmann cons tan t; T is the abs o]u t e
tem pe ature; X1 = m (&) 2/ 21i; and the functions KS and K44 are’
In TR tubes w it u = 2 X 1010 and L = 0.005 cm , Z1 > 100 and
the follow ing lim iting form s m ay be us ed ,
If thes e lim iting form s are s ubs titu ted in Eq. (69),
(71)
(72)
At a frequency of 2800 Me/ s ee and a gas pres s ure of 5 mm Hg the
nume rica l re s ults a re
u , = 1 .9 x 1O–%,
(in k s un its )
Ui = 1 .6 X 10–’2n .
The im aginary term of Eq. (72) w ill be recogn iz ed as the res ult w h ich
w ou ld be obta ined for electron s in a vacuum .
Th is term va ries in vers e ly
w ith frequ en cy , and is ind epend en t of pres s ure.
The rea l com ponen t of
u , how ever, has a maximum value w hen the m ean free tim e betw een
collis ions is abou t equal to the period of the im pres s ed r-f voltage,
t = %r/ co. Specifica lly , the maxim um occurs for a va lue of
muLZ
“ = 2’1 = 2kT
For a given s e of cond itions , frequency and pres sure, the dens ity of
electrons n that w ill res ult in a certa in va lue of a ttenua tion m ay be ca lcu-
I The exponen tia lin tegra lE; (—ZJ and the error function Erf (&) are de fied in
JahnkeandErode, Table oj Fund iorw , St ech er t, N ew Yor k, 1938.
SEC. 5.14]
ELECTRON-CAPTURE PROPERTIES
187
la ted , if the s hape is k now n and is amenable to compu ta tion . In the
pres en t example of the pre-TR tube, w ith the d is charge confined to a
thin s lab of th ick nes s d, Eqs . (68) and (72) can be us ed to mak e th is
convers ion . By th is m ethod , m eas ured recovery -tim e curves have been
converted to n -vs .-tim e curves , and from a k now ledge of the partia l
pres sures of the gas es pres en t, electron -capture cros s s ections m ay be
computed.
The attenuation va ries w ith the s quare of the s hunt a dm ittance; there-
fo e, for the gas d is charge, it varies w ith nz .
6 .1 4. Electron -ca ptu re Prop erties of Va riou s Ga s es .—Th e mech an ism
by w h ich electrons are captured by a tom s or m olecu les is not s im ple, nor
is it u niqu e.1 f2 3
The electronega tive character of the gas is one of the
m ore im portan t factors w h ich in fluence capture
The k inetic energy
of the electrons is im portan t. Depend ing upon the particu lar gas under
con sid era tion , th e proba bility of ca ptu re may eith er in crea se or d ecrea s e
w ith increas ing electron energy .
As in os t d is charge phenomena ,
im purities play a role tha t is not very w ell und ers tood .
In the recovery period of a TR tube, in teres t is primarily in fa irly
w eak s ignals of the order of 10–6 to 10–12w att in tens ity .
The e le ctric
field s p oduced by s uch s ignals acros s the gap of a ty pica l h igh -Q TR
tube, w ill be s maller than the break dow n poten tia l by a factor ly ing in the
range betw een 10 and 10 ,000 . Cons equently , it is a s s umed that the
energy im pa rted to the electrons by th e received s ignal is negligible com -
pa red w ith th eir th erm al en ergy .
Th is therm al en ergy w ill be a function
of the gas tempera ture and the tim e tha t has elaps ed s ince the end of the
tra nsm itter puls e .
The electron affin ity of an atom may be des cribed in term s of the
w ork done on an electron by the field betw een it and the a tom . Atom ic
oxy gen and the halogens have electron a ffin ities of 3 or m ore electron
volts . Hy d rogen , on the other hand , has a value of 0 .76 ev, and the
noble gas es have nega tive va lues w h ich ind ica te that they form uns table
ions . A more us efu l w ay , for our purpos es , of comparing gas es is in
term s of their electron attac m ent coefficien t 8 , w here d is the average
number of collis ions an electron mus t mak e w ith the a tom s of the gas
before it is captured . In Table 53 , there are tabula ted for s evera l gas es
va lues of 6 , of N, the num ber of electron collis ions w ith gas m olecu les per
s econd at one atmos phere and room tempera ture, and of t= = 6/ N, the
average tim e required for an electron to be captured . 4
The capture of electrons by molecu lar gas es may tak e place by a
1Loeb, op . cit., Chap. 6.
2 Ma ssey, N egoliu e Ion s, Cambr idge Tr act s, Ma cMilla n, N ew Yor k, 1938.
8Cobine, op , cit., Ch ap. 4.
4K. T. Compt on and I. Le.agmuir , Rev. Mod. Phgs. 2, 193 (1930).
188
MICRO WAVE GAS DISCHARGES [SEC.514
TABLE 5+L-ELECWFKON*TTACHMENTOEFFICIENT,OLLISIONSISRSECONb, AND
TIME FORCAPTUREFORVARIOUSGASES
Ga s
16
,\ -Ohlegases , >-j, and
H,
m
co
1 .6 X 10E
NH,
9 .9 x 107
h-,o
6.1 X 10’
Air 2.0 x 10’
0,
4.0 x 104
H,O 4.0 x 10’
cl, 2.1X103
2.22 x 1011
2.95 X 10’1
3.36 X 10”
3.17 x 10’1
2.06 X 10’1
2.83 X 1011
1 .5 X 10L1
0 .72 X 10-3sec
3.35 x 10-4
1.82 X 10-0
0.63 X 10-’
1,94 x 10-7
1.41 x 10-7
0.467 X 10-’
n umber of d ifferen t proces s e s .
On the bas is of a s eries of m eas urem ents
made by Bradbury , 1 and Bradbury and Tatel, 2 Loebt has pos tu la ted a
num ber of d ifferen t reactions w h ich are pres en ted in Table 5-4 .
TABLE5.4 .—MINIMUMELECTEONENERCYANDMEcHANISMOFELECTRONAPTURE
IN VARIOUSGASES
Ga s
Cl,, Br ,, I,
HC1, HBr ,
HI
NH,
N,O
co,
H,S
0 ,
0
s o,
NO
H,O
H,O
Ground
state
A’eg. ions
of ga s
formed
No
No
No
No
No
No
Yes
Yea
Yes
Yes
No
No
l~in.
electron
mergy for
ttachmenl
o
0 .4 ev
in HC1
3 v
1.7ev
3.7ev
o
0
0
0
0
5,4ev
Reaction
Cl, +e ~C1- + Cl + (4 .1 – 1.5 )ev
HC1 + e + (4.5 –4,1)ev+H + Cl-
NH8+e+3ev-NH-+H,
N~O+e+l,7ev~0-+iY2
H,S+e+3.7ev-+HS-+H
O,+e+O~
o+e+o-
So, + + so;
2N0 ~ (NO), + e ~ N’O-
+ No
2(H,0) + e - 2(H,0)-
H,0+e+5.4ev-HO-+H
Gaaes s uch as OZ and SO, form negative mo ecu lar ions d irectly
by the capture of electrons . Mo ecu lar i&s are form ed by NO; but the
probability of electron capture is d epend en t upon pres s ure and it is
xBradbury,J . C?wm. Phya,, ‘2,827 (1934); 2, 840 (1934).
2Bradbury and Tatel, J . Chem. Phy8., 2, S35 (1934).
8 Loeb, “F un damen ta l P rocem ea of E lectr ica l Diech ar gea in Gawa ,” Wiley, New
York, 1939, Ch ap. 2.
SEc. .Y14] ELECTRON -CAP2’URE PROPERT IES
189
as s umed that a complex, (NO)%, mus t be form ed . Th is complex is then
as s umed to capture an electron and form NO-, the exces s energ of the
6
HzO
II
,;m~~
O 2 4 6 8101214161820
24681012141618
~
P
100~
,,
s o -
0
02+Ar 0 + He
.0060
:
40 -
20 -
0
I ,
1 {
! !
o
24 68
.
3
2
‘0
:
1
1P
C12+ A
0
a
0
0
0
Q~
02468101214
3
z
2.4
- ;1
s o~
2 .0
% 1.6
~ 1.2
\
i
0.8-
\
(J,4.’4,
J
04
8 12 16 20, 24 28 32
z
FIG.5 .32.—Probabilit ies of e lect ron capture for var ious gases .
elect ron being carr ied away by the neut ra l N’(l. Alone, l&O shou ld not
capture elect rons , s ince it has a clos ed electron s y s tem .
With su fficient
190
MICROWAVE GAS DIS CHARGES [SEC.515
energy , z 5 .4 ev, an electron w ill d is s ocia te the w ater in to HO– and H.
How ever, it is true that w a ter has a large electron-capture cros s s ection
for the s low -m oving electrons .
Bradbury and Tatel report that the
probability of capture of s low electrons in H 0 is s trongly pres s ure-
d ependent. At a pres s ure of 2 .5 mm Hg of H20 no capture of s low elec-
trons w a s obs erved . At h igher pres sures , the probability of capture ros e
rapid ly . Th is w as tak en as evid ence that a com plex, 2(H20), w as
form ed , w hich cou ld then be ion ized d irectly . Figure 5“32 gives the
probability of electron capture h as a function of the param eter z / p for
various gas es , as m eas ured by Bradbury and Ta tel. In th is cas e z is
the voltage grad ien t, ‘and p the pres s ure in m m Hg. Figure 5 .32a s how s
the values of h for 02 . As z / p increas es from very low values , h d rops
rapid ly . At x/ p
= 5, the curve ris es s harply . At th is poin t the electron
energy is abou t 1 .6 ev, corres pond ing to a m et as table excita tion level in
02 . Electrons w hich m ak e thes e inelas tic collis ions have their energy
reduced to a level a t w hich the probability of capture is again high.
Figure 5 .32b s how s the eilect of m ixing argon , helium , or nitrogen , w ith
02 , in equal volum es .
Figure 5 .32c s how s the pres s ure dependence of electron capture in
NO w hich has been d is cus s ed . Figure 5 .32d s how s the probability of
capture in a m ixture of argon w ith Clz .
The gas Cl~ is a chemically
inert gas w hich has a clos ed electron ic s y s tem , and therefore Cl; ions
cannot be form ed . Ins t cad , it is believed that the ioniz ing proces s is
the one ind ica ted in Table 5 .4 . Figure 5 .32e is for electron capture in
SO,, and SO, plus A.
Figure 5 .32f s how s the pres sure d ependence of electron capture in
HZO. Th is is expla ined by as sum ing the form ation of nuclei of cond ens a-
tion , w h ich th en ma k es th es e comp lexes ca pa ble of ca ptu rin g low -velocity
elect rons .
Im purities s uch as C02 or OJ are pres um ed to aid th is effect,
w hereas A or N2 do not. In the next s ection (S ec. 5“15) the available data
on recovery tim e in TR tubes w ill be exam ined to s ee w hat can be learned
abou t effective p robabilities of electron captu re.
5 .15 . Recovery -tim e Data .-The recovery characteris tic of a TR
tube is a curve in w hich attenuation through the tube as a function of the
tim e after the transm itter puls e is plotted . The attenuation plotted is
the d ifference in decibels betw een the ins tantaneous va lue and the
attenuation through the “cold” or un fired tube. Tim e is m easured from
the end of the transm itter pu ls e.
Figure 5 ,33 s how s ty pica l recovery curves of a 1B27 TR tubel m eas -
ured at s evera l d ifferent levels of trans m itter pow e r.
The tube is filled
w ith a m ixture of 10 mm Hg, each , of Hz and HZO. Figure 534 s how s
‘ Smullin and Leiter , “Th IB27 TR Tube,” RL Repor t No. 594, Oct . 4, 1944
SEC.5“15]
RECOVERY-TIME DATA
Time in~sec
191
0° 1
2345678 910
86 kw
2
176kw
+3
/
.E
%
/
54
f
5
)
6
(
7
/
8
, Y
/
/
10
FI~, 5.33.—Recovery cu rves of 1B27 TR tube for t h r ee in cid en t power levels .
t he effect of the wa ter -vapor con ten t upon the recovery t ime of a 1B27
TR tube, when the par t ia l pressu re of HZ is held const an t .
Recovery cu rves for 3 -cm an d l-cm
TR tubes are s im ilar in s hape to thos e
s how n here; bu t the tim e s ca le is con -
s id erably s horter. N’o quantita tive
exp la na tion of th is d ifferen ce has b ee n
propos ed . It is thought, how ever, to
be the res ult of the sm aller volum e of
the d is charge in the high-frequency
tu bes , w h ich a llow s d iffu sion to play
a rela tively more i m p o rt a n t role.
M. D. Fis k e has propos ed a “s w eep-
ing” ty pe of d iffus ion . In th is , right
at the end of the transm itter pu ls e,
s om e of th e h igh -en ergy electron s n ea r
th e electrod es a ctu ally rea ch th e elec-
trod es and are los t. This produces ‘a
pos itive s pace charge near the elec-
trod es w h ich attracts electrons from
the cen ter of the d is charge. Some of
th es e electron s go righ t th rou gh to th e
Partial pressure of H20 in mm Hg
FIG. 5.34.—Recovery char acteristics
of 1B27 TR tube as a funct ion of pres.
su re of wa ter vapor . The t r ansmit ter
power wa s 100 kw, a nd t he pa rt ia l pr es-
su re of Hz was 10 mm Hg.
No quantita tive analy sis of th is
m echan ism has been made; bu t it s eem s a plaus ible proces s , s ince the
effect s hould be larger for the sm aller tubes .
192 MICRO WAVE GAS DISCHARGES [SEC.515
The life of mos t TR tubes is lim ited by the ra te at w hich the w ater
vapor is cleaned up or d ecom pos ed , thus increas ing the recovery tim e.
Becaus e of the rela tively s hort life of pre-TR tubes operating at high
Time in p sec
10°
50 100 150 200 250 300 350 400 450 500
/
n
u
.=20
/ N
%
r-
5mm
~
Argon
30
40
50
FIG. 535.-Recovery characteristic of well-baked 1B38 tube filled with pu re ar gon.
Time in Nsec
oO-
2 —
3 —
4 —
~5
c
“Z 6
~7
8 —
10 —
20 —
30 —
6
/
I
/ /
I 7
[ /
,
—
i
I
I mm
I*O ,
lm A
L
L
f
?
mrr
HZO
Im A
Fx~ .5 .36.—Recovery of mixtu r es of a rgon and wa t er vapor .
lin e pow ers , a s tu dy of va riou s ga s es w a s u nd erta k en to d eterm in e wh eth er
a s ubs titu te for HzO m ight be found .
The m eas urem ents w ere all m ad e
in 1B38 pre-TR tubes at a line pow er of about 700 kw .
The gas es us ed
SEC. 15]
RECOVERY -T IME DATA
193
inthes e m eas urem ents w e re the pures t obta inable comm ercia lly , and the
tubes w e re care u lly cle ned and pumped before filling.1 The follow ing
cu rves are ta ken from th es e exp rim en ts .
Figure 5.35 is the recovery characteris tic of a carefu lly cleaned and
bak ed tube filled w ith comm ercia l “s pectros copica lly pure” argon; th is
tu be has an extrem ely lon g recovery tim e. Figure 5.36 s how s th e recovery
Time x in sec
.~ KI 20 30 40 50 60 70 8(3 9iJ
100
c
10 mm
of 02
2
7m m of 02
f
/ ‘
/
5 mm
of 02
3
y
4
I
A
/
g5 -
-6
,E
/ ! / /
>‘
8
_17
8.
10
20-
30-
FIG. 5 .37.—Recove ry cha ract er is t ic of oxygen a t va r ious p res su res .
tim e for various m ixtures of HZO and A.; Fig. 5 .37 is for various pres s ures
of pure OZ; Figs . 5 .38 and 5.39 are for m ixtures of argon and ch lorine,
and argon and pen tene. Other gas es tes ted , bu t not s how n here, w ere
H2S , CH,, C,H2, CZH1, benz ene, iodoform , and methy liod id e. All of
th es e exh ibited s hort recovery tim es .
The urity of the organic gas es
w a s more or les s u ncerta n, s in ce th e ch em ica l rea ction s in volved u sua lly
prod uce a num ber of d ifferent gas es bes id es the in teres ting gas .
The importance of a high degree of purity is bes t illus tra ted by the
experience w ith CO. Commercia l 1B38 tub s are filled w ith 10 mm Hg
1 F . L. Mc Milla n, 1. H. Dea rn ley, C. H. Pearsa ll,
“ Recover y Time Mea su r emen t s
in Ba ndpa ss TR’s for Va riou s Ga ses, ”
RL Repor t N’o. 895, Dec. 18, 1945.
194
MICROWAVE GA DISCHARGES [S EC.5.15
of com mercia l argon. The tube its elf is as sem bled w ith s oft s old er, and
therefore it cannot be outgas s eci by bak ing. As a res ult, even though
no w ater is put in to the tube, the recovery time of mos t of the tubes is
s hort. Spectros copic m eas urements made on a la ge number of thes e
tubes s how ed , among the other things , that CO w as alm os t invariably
. . . . .
Tirhe u in sec
Fm. 5.3S .—Recovery of a rgon -
chlorine mixtur e.
pres en t m tubes bavmg a short recovery
tim e. Although it has been reported to ha e
zero electron-capture probability , 1 it w as
decid ed to tes t a CO-A m ixt re. Independ -
ent m eas urements by Fis k e at the General
Electric. Research Laboratories and McMillan
at Rad iation Laboratory s how ed very s hort
recovery times for s uch m ixtures .
Subse-
qu en t tes ts , h ow ever, w ith pu re CO, prepa red
chem ically in the vacuum s y s tem , s how ed
that CO really had no effect upon the re-
covery tim e, and the initial res ults m us t have
been caus ed by s om e other gas pres en t as
an impurity .
Let us now cons id er s om e of thes e curves
in detail. The variation in recovery time
w ith line pow er, illus rated in Fig. 5 .33,
s how s the expected phenomenon of longer
recovery tim es for higher pow ers .
This , of
cou rs e, can be in terpreted as corres pond ing
t larger values of na, the electron dens ity
in the d is charge, s ince the rate of capture
of e lectrons dn / n dt is con sta nt, rega rd les s of lin e pow er.
Figure 5.34 s how s clearly that the rate of capture of electrons is
d e endent upon the amount of w ater pres ent, and that HZ has a small,
p erhaps z e ro, e le ctron -captu re cros s s e ction .
Figure 535 s how s the expected long recovery tim e for pure argon.
If the data are recalculated to give a curve of n vs . t, it can be s how nz
th t the function – td (ln N )/ d t is about 3 , w here N = nd , d being the
th ick nes s of the d is charge. If only d iffus ion is opera tive, th is quantity
cannot have a value greater than ~.
Thus j the recovery tim e is s horter
th n expected . Under the cond itions of th is particular experim ent, no
im purities w ere pres en t at a pres sure grea ter than 0.01 per cent of that of
the argon. If the impurity had a capture efficiency equal to th t of H20,
1Loeb, “F un damen ta l P rocesses of IH ect rica l Disch ar ges in Ga ses)” Wiley, A-ew
York, 1939, Ch ap, 2.
~H. Ma rgen a u,
‘‘ Th eor et ica l In ter pr et at ion of t he Recover y Tim e of TR Boxes, ”
RL Repor t No. 929, J an . 9, 1946.
SEC.515]
RECOVERY -T IME DATA
195
it w ou ld ave had to be ‘pres en t a t a pres s ure of 0 .18 mm Hg, w hich is
ou t of the ques tion . There are thus tw o pos s ibil ties—the pres ence of
an extrem ely efficien t electron-captu re agen t, or the form ation of s om e
u nk now n ion , a s A;.
Ne ga tive a rgon ion s s e em more lik e ly ; th e a na logou s
ion He; is k now n to exis t.
Time in u sec
1
0 30 60 90 120 ’15~ ’180 210 240 270 300
1 mm of Pe tene ,
I I
11“1mr1 of PImtsne
5 mr lof A gon
2
1
1
10-2r hm of ?ente+e
5 ~m of f$rgon
I
I
1/
L“‘
.“ ,, ,,, , .,! Penter e
q
5n $m of Mgan
20
30 .
PI
40
F IG. 539--- Rerove ry of m ixt u res 0[ a r gon and pen t ene.
of F ig. 5.36 may be used to determine the captu re crosshe data
s ection of HZO, by repotting in term s of in n and t, and us ing Eq. (63)
w h ich m ay be rew ritten
(73)
va lues for h ,..
If th es e ca lcu la tions are m ad e w ith Q = 15 X 10–’8 cm ’, v corres pond ing
to 300° K as (3kT)~5 / m = 1.2 X 107 cm / s ee, then the
are
1.0 x
10–4
from the 2 mm curve.
0 .93 x 10-’
from the 3 mm curve.
(), ~ x 10–4
from the 5 mm curve.
Th es e ca ptu re proba bilities a re for th erm al velocities , w h ich h ave n ot
been obta ined by any other m eans .
They agree in ord er of m agnitud e
196
ZCROWA VE GAS DIS CHARGES
[SEC.615
w ith the res u lts of Brad bury and Ta tel, 1 w ho lis t va lues as high aa
4 x 10–4 at s omew hat grea ter energies . The important d ifference lies
in he fact that no pres s ure d ependence is ind icated by thes e res u lts .
Th is m igh be in terpreted as meaning that s ingle H,O molecu les can
Capture thermal electron s . On the bas is of pres en t k now led ge, th is
s eem s im proba ble, and fu rther s tu dy is requ ired .
Figure 5 .37 s how s an in teres ting anom aly , w h ich is that the recovery
tim e is not a monoton ic function of the oxy gen pres s ure. Margenau2
has expla ined th is on the bas is of the fact tha t both 02 and O are pres en t
(a),
(b)
(c)
(d )
FIG. 540.-Decay of light intensity from discha rge. Curve (a ) is for 7 mm HzO;
curve (b) is for 10 mm argon and 1.5 mm HzO; cu rve (c) is for 20 mm Hg of lamp argon
(0.5’% N,); cu rve (d) is for 20 mm of dr y t an k N,.
in the discharge. The da ta can then be in terpreted as an indica t ion
of differen t elect ron affin it ies for the molecu le and for the a tom.
If it is
assumed tha t most of the oxygen is in a t mic form at the end of the dis-
charge, then the a toms recombine in to OZ by way of a th ree-body col-
lision , and the ra te w-ill be propor t iona l to the square of the pressu re.
Thus, O will last longer a t low pressures. According to the da ta , then ,
above 5 mm pressure 02 is the more act ive captu re agent ; and below
5 mm O is the more act ive. On this in terpreta t ion , 2 mm pressure, wh ich
cor responds to 4 mm of a tomic oxygen , is as effect ive as 10 mm of OZ.
The numerica l resu lts based on th is a rgumen t a re h ,~~ s 3.2 X 10-4 for
O, and h .,.
= 1.5 X 10-4 for 02.
LBradbury a nd Tatel, J . Chem . Phys., 2, 835 (1934).
2 Margenau, 10C.cit .
SEC.5’16] EFFECT OF KEEP ALIVE DISCHARGE ON RECO ERY 197
Figure 539 s how s the trans ition from cond itions in w hich there are
enough captors to elim inate all electrons to thos e in w h ich there are not
enough. The corres pond ing In n-vs .-t curves s how s traigh t term ina l
s lopes forpres sures of lm m Hgand O.1 mm Hgofpentan , bu t d efin itely
curved characteris tics for the 10–Z and 10-a mm Hg pres s ures .
Th e
latter tw o are probably tend ing tow ard s a d iffus ion as oppos ed to a
capture characterist ic.
If the trans ition is as s umed to lie betw een 0.1
and 0.01 mm Hg partia l pres sure, th is ind ica tes that the initia l electron
dens ity in the d is charge is betw een 3.5 X 10’4 and 3.5 X 10” per em s .
This va lue is in agreement w ith es timates obtained by extrapola ting
the curves of lnnto zero tim e.
In on e attem pt, w h ich w a s u ns ucces s fu l, to d evis e a s im ple prod uction
recovery -tim e tes t, m eas urem ents w ere m ad e of the d ecay of light in ten-
s ity w ith tim e after the trans mitter puls e.
Figure 5.40 s how s the d ecay
of light in tens ity from the d is charge af er the excita tion , trans mitter
pow e r, is rem oved . Th es e cha ra cteris tics w e reobtained b y rneas uring
the light of a 1B38 pre-TR tube w ith a photom ultiplier tube connected
to a vid eo am plifier and cathod e-ray os cillograph . The tubes filled w ith
argon and w ith n itrogen exh ibit long recovery tim es , w h ile in thos e con-
taining HzO, the light is very quick ly quenched . No particular s tudy
has been made of th is phenomenon , but it is believed that the (‘ fter-
glow “
is caus ed by the pres ence of m etas table atom s w hich may have
fa irly long iv es .
6 .16. Effect of Keep-a live Dis charge on Recovery Tim e.—In S ec. 57
it w as s how n that in order to mak e the s pik e energy small, and to mak e
the variations in energy from puls e to puls e
low , it is n eces s a ry - to in trod uce electron s in to
~
O.c discharge
the gap from an externa l s ource. This s ource
is a d -c glow d is charge s o loca ted that the
<L
J
des ired no electrons are furnis hed to the gap
, /
by d iffus ion, Fig. 541. If the k eep-a live elec-
trode is negative w ith res pect to the TR tube,
r’=& \
electrons are accelerated tow ard the gap. If ~ee~.a tive
the k eep-a live is pos itive, h ow e ver, electron s electrode
r
I
move away from the gap. Under thes e con-
FXG. 5.41.—Keep-alive
dit ions, the spike energy is m any tim es larger ~~~~~~ ‘thin ‘he cone’ ‘f
than w hen the k eep-a live is negative, and it is
us ua lly im pos s ible to protect cry s ta ls . For the moment the leak age-
p ow e r con s id era tion s w ill b e n eglected and th e efle ct of k e ep -a live pola rity
on recovery tim e w ill be d is cus s ed .
The recovery ~haracteris tics of an argon-fille 721A TR tube for
pos itive and egative k eep-a live polarities are illus tra ed in Fig. 5 .42.
The effect of the pos itive k eep-a live is m ark ed . The d ifference betw een
198
MICROWAVE GAS DISCHARGES
[s~c. 5.16
the tw o curves can be expla ined if the s tructure of the d is charge is
cons idered , s ee Fig. 5 .43 . With the k eep-alive pos itive, there w ill be
a pos itive column extend ing tow ard the TR tube gap, as s how n .
Since
m os t of the voltage drop in the d -c d is charge occurs near the cathode,
o 5 10 15 20
Time after transmitter pu ls e in A sec
F IG. 542.-Recover y of a 721A TR t ube
filled wit h 10mm Hg a rgon , at 50kw pu lse
power with posit ive and negat ive keep-
alive discharge.
tlls w ill h ave th e effect of prod ucin g
a new “virtual anode” at the cath .
od e end of the pos itive column .
As a resu lt, the penetra tion of the
d -c field in to the gap is enhanced .
The d ifference in pos ition betw e en
the virtual anode and the k eep-
alive electrod e m ay be es tim ated
from the fact that the length of the
cathod e fa ll w ith a copper cathod e
is 0 .3 to 0 .8 mm at a pres s ure of 10
mm Hg.l
The d is tance of the
k eep-a live electrod e from the cone
is about 5 mm . Thus the virtual
anode is abou t 0.15 as far from the
gap as is d le k eep-a live, w ith the
res ulting increas e of the d -c field
in the gap. The d irection of the field s erves to sw eep electrons out
of the gap, and thus overcom es the retar ing force of the pos itive ions .
Th is phenomenon has been k now n for s om e tim e, and s ugges tions
have been made for the us e of an argon-filled TR tube that w ou ld have
Glass Transmitter
+
// pulse
*
/ -,
n.
Approx.
(
I
I
)
extent of
\
)
pos column
+11
.--—=
Position of
Gap
virtual anode
:ti~
F IG. 5.43.—Ext en t of pos it ive column and
FIG. 5.44,—Pulsed keep-alive voltage,
vir t ua l a node in keep -a live disch a rge.
very low leakage po er with a nega t ive keep-a live, and cou ld be made to
have a shor t r ecovery t ime by making the keep-a live posit ive just a fter
the t ransmit ter pulse. The keep-a iive pola r ity wou ld vary with t ime
somewhat as shown in Fig. 5.44. This type of opera t ion is en t irely
feasible, and was, in fact , used by the Brit ish in one radar insta lla t ion.
it has the advan tage of longer tube life, since ther e is no chemica lly act ive
1Cobin e, Gbmua Condu ct or s, McGr aw-H ill, N ew Yor k, 1941, pp. 215-218.
SEC, 517]
THE KEEP-ALIVE
199
gas s uch as HzO to react w ith the metal part of the tube. Th is , it w ill be
s how n later, is the m os t s erious factor lim iting tube life in conventiona l
TR tubes . The d is advantage of a t be of th is ty pe is that the circuit
neces sary to prod uce the alternately negative and pos itive k eep-a live
is m ore com plica ted than the s im ple h igh-voltage rectifier needed for
conven tional tubes . Although the actual com plica tion is not exces s ive,
des igners have usua lly avoid ed it on the bas is that fa ilure or pa tia l
fa ilure of th is circuit w ould res ult in cry stal burnout and failure of the
entire radar s et. Th is is certa in ly moot ques tion and s hould , in he
auth or’s opin ion , re ce iv e fu rth er s tu d y .
The application of d -c sw eep ng field s to aid recovery tim e has not
been extended to bandpa s TR tubes , w here th recovery tim e of the
tube is lim ited by that of the 1ow -Q input w indow . To sw eep the elec-
trons aw ay from the w indow w ould require a grid -lik e electrode a ros s
the w aveguide and jus t behind the w indow . The cons truction of the
tube w ould be s erious ly com plicated by the add ition f s uch a s tructure.
5 .17. The Keep -a live.-The k eep-a live circuit is of equal im portance
w ith the gas filling and the s hape of a TR tube in determ ining the s pik e
leak age energy . The k eep-a live d is charge is generally a low -curren t,
d -c glow m aintained betw e en he k eep-a live electrod e and s om e portion
of the TR tube, and is s o loca ted that the res ultant d ens ity of electrons
in the r-f gap is s ufficient to k eep the s pik e leak age energy W. to a s afe
level. S ince the k eep-a live is an auxiliary device w hich is concerned
only w ith the h~gh-level opera tion of the tube, it mus t be des igned to
have little or no effect upon the low -level pe formance of the TR tube.
This means , firs t of a ll, that the k eep-alive electrode mus t either be
s h ielded from the r-f field in the cavity or, if it is w ithin the cavity
proper, it m us t be s o d is pos ed that r-f currents flow ing along it w ill be
m in im ized . S im ilarly , the glow d is charge m us t not caus e any apprecia-
ble d ecrea se in low -level transm is s ion through the cavity , either beca us e
of its ow n conductance or becaus e of the conductance caus ed by the
electron s it fu rn is hes to th e ga p.
This las t requ irem ent m us t of n eces s ity
be a comprom is e w ith the need for having no large enough to give ade-
quate leakage-pow er protect ion .
To ens ure m inim um in terference w ith
the reception of w e ak s igna ls , r-f nois e cou pled d irectly to the firs t d etec-
tor, or low er-frequency nois e coupled to the i-f am plifier from the d is -
charge, m us t be small.
It w as pointed out in Sec. 5.16 that the k eep-a live polarity mus t be
negative if electrons are to be furnis hed to the r-f gap. In the d is cus s ion
w hich follow s , a negative k eep-a live polarity w ill a lw ay s be aas umed
un le s s oth erw is e s ta ted .
In practica l TR tubes it has been pos s ible to m aintain s ufficiently low
valu es of W , w ith a k eep-a live d is charge that cau ses a change of low -level
200
MI CROWA J ’E GAS T)ISGHA RGES
[SEC.5.17
transm is sion of les s than one per cen t.
Th e reflection a nd d is s ipa tion
los s e s ca us ed b y r-f cu rren ts flow in g in th e k e ep-a live electrod e a re n ea rly
z ero in one ty pe to be des cribed , and of the order of 1 per cen t in another
ty pe. The glow d is charge produces r-f nois e s o low that it mak es the
m eas ured values unreliable beca us e of experim enta l errors ; how e ver, it
(a)
(b)
(c)
FIQ. 545.-– Types of keep-a l ive e lect rodes .
certa in ly caus es l s s than 0.1 d b change in s ignal-to-nois e ra tio of the
receiver. Un der certa in circum s tances , i-f nois e can be appreciable; bu t
it is not d ifficult to k eep it ou t of the receiver circu its .
A cla s s ifica tion of k e ep -a liv e e le ctrod es bas e d upon shape or con s tru c-
tion recogniz es three major ty pes .
Thes e are the coaxia l electrod e,
Fig. 5 .45a , and tw o m od ifica tions of the s id e-arm ty pe, Fig. 5 .45b and c.
FIG. 6.46.—Keep-alive elect rode in t ube in ser ted in ca vit y.
Ws torica lly , the coaxia l k eep-a live electrod e is the old es t. AS s ho~
in the s ketch , it is mounted w ithin one of the hollow electrodes or cones
fofing the r-f s park gap. A d -c dk charge is main tained betw een the
k eep-a live electrod e and the ins id e of the cone. This ty pe of electrod e is
particu larly s u itable for us e in the ell-ty pe TR tube. For th is tube it
SEC.$17]
THE KEEP-ALIVE
201
is d es ired to have cons truction tha t is axia lly s ym metric in ord er to be
able to clam p the tube in to a s plit annular cavity , Fig. 5“46 . The k eep-
a ive electrod e and d is charges are both com pletely s hield ed from the r-f
field w ith in the TR cavity , and thus have no effect upon low -level trans -
m is s ion . The Vos ition of the electrod e w ithin the cone, how ever, m us t
be m ain tained %th in ra ther clos e lim its s ince the electron d ens it y in the
gap is a s ens itive function of th e d is tance of the k eep-a live electrod e from
the gap; and therefore, the low -level los s or “k eep-a live in teraction”
ca us ed by no change s ra pid ly w ith pos ition .
Keep-a live electrod es of the ty pes s how n in Fig. 545a and b are us ed
in in tegra l-cavit TR tubes . The 1B24 tube us es a coaxia l k e p-a live ,
w hile the 1B26 and lB50 us e the s id e-arm ty pe. In bandpas s TR tubes ,
e lectrod es s im ilar to th os e of Fig. 5“45a and c have been u sed .
The s id e-
arm electrode in c actua lly extend s in to the r-f field w ith in the tube;
how ever, s ince it is perpend icu lar to the electric field no longitud ina l
curren ts are induced on it. S ince the electrod e rad ius is small. the
capacitance in trod u ed by it is s mall, and the res ulting reflections are
negligible.
In common w ith m any other techn ica l problem s , the des ign of a k eep-
a live s y s tem involves a num ber of com prom is es .
To reduce the s pik e
leak age energy to a s afe level, the num ber of electron s no in the gap s hould
be large. How ever, no m us t not be s o large tha t the low -level trans mis -
s ion is s erious ly a ffected . A further res triction on the k eep-a live aris es
from the fact tha t the d -c d is charge cha ges the gas con ten t of the tube
either by chem ica l d ecom pos ition of the gas , or by s pu ttering w hereby
gas m olecu les are d riven in to the w a lls and captu red . Th is proces s tak es
place a t a ra te tha t increas es w ith the curren t carried by the d is charge.
Therefore , to obta in maximum
R
tu be life , th e k eep-a live d is ch arge
s hould be run at a curren t leve l as
t
low as pos s ib le , cons is ten t w ith
v
~
c
I?fl
s a fe va lues of W .. Th is lim it is
o
s et by tw o res trictions .
A lim it
is d ete m ined by the curren t leve3
a t w hich , for a given electrode
s hape, no becom es too s ma ll. Be-
fore th is lim it is rea ch ed , h ow eve r,
J -
t—
the d is charge m ay becom e un-
F I@. 5,47.—Rela xa tion oscih tion s of a ga a
stable or break in to a relaxa t ion
discharge.
oscilla t ion . With the discharge in termit ten t , there is a f inite probability
that it w ill be ou t jus t before and during a transm itter pu ls e. When
th is happens no w ill be s maU and the s pik e leak age energy w ill be very
large, and cry s ta l burnout m ay res ult.
202
MICh’Oli’A t’E GAS DIS CHARGES
[SEC.517
l’hc rela xa tion os cilla tion en cou ntered h ere is s im i!a r to a ga s-filled -
tu be s aw tooth os cilla tor, Fig. 54 7.
If th e res is ta nce of th e d is ch arge
is s m all com pa red w ith the res is tance of the pow e r s upply , and the voltage
V is grea ter than the break dow n ~oltage of the gap V~, then os cilla tions
of the ty pe s how n w ill tak e place.
Th e ca pa citor volta ge V, w ill ris e
at a rate d eterm in d by the tim e cons tan t l?C, until the break dow n volt-
age Vb is reached . At th is poin t the gap w ill break dow n and d is charge
the capacitor un til the extinction voltage V. is reached . The d is charge
w ill go ou t, the voltage w ill bu ild up as before, and the cy cle w ill be
repea ted period ica lly . It is en tirely feas ible to m ak e a circu it that
os cilla tes w ith a period cons id erably in exces s of one s econd . The m axi-
m um frequency of os cilla tion a tta inable is lim ited by the deion iza tion
tim e of the gap and m ay be of the ord er of s evera l hund red k ilocy cles per
second.
In the k eep-a live d is charge, s uch os cilla tion m us t either be en tirely
s uppres s ed , or be made to have s uch a h igh frequency that even though
the d is ch arge is period ica ll extin gu is hed , th e d en s ity of electron s in th e
-f gap will exper ience only small fluctua t ions.
If the discha rge cur ren t
is to be ma inta ined with in a rela t ively nar row fixed range, then the fr e-
quency of oscilla t ions cannot be ser iously a ffect ed by a change of the
pow er-s upply voltage V, s ince the s eries res is tance R, and hence the
charging tim e cons tan t, m us t be changed to m ain ta in the gi en curren t
d es pite the change in V. If the characteris tics of the gap are as s um ed
fixed , then the on ly w ay to increas e the frequency is to reduce C. The
capacitance of in teres t here inclu des all lum ped and s tray capacita nces
to ground , from th e k e ep -a live e le ctrod e to th e firs t la rge cu rren t-lim itin g
resistor.
B placing th is res is t ante righ t a t the TR tube, the tota l
capacitance becom es jus t that of the k eep-a live ele trode, and is of the
order of 1 p~f. If R is 4 m egohm s , a ty pica l va lue, the os cilla tion fre-
quency w ill be of the ord er of 200 k c/ s ee.
If there are s evera l inches of
uns hzk ld ed w ire betw een the res is tance and the tube, the frequency w ill
be red uced by a fact or of five , a pproxim ateely , and if shielded w ire is u sed ,
the red uction in frequency w ill be m uch grea ter.
Let us exam ine in grea ter d eta il the factors affecting the os cilla tion .
If R, <<R, at the ins tant of break dow n nearly all of the d is charge curren t
w ill flow from the capacitor C. In Fig. 5 .48 w hen V. reaches Vb the gap
break s dow n and the opera ting poin t m oves ou t to s om e poin t s uch as
A on the V-I curve of the d is charge.
As the charge on C is d ra ined off,
the opera ting poin t m oves aw ay from A to the left until it reaches the
con s ta nt-volta ge portion of th e cUNe beginn in g a t B. If the equ ilibrium
voltage v = VRr/ (Ro + R) < VB, the d is charge w ill go ou t a t th is
poin t and v., s ince there is go curren t d rain , w ill now preced e to bu ild
up tow ard s vb again .
If, how ever, v = V R,/ (R. + R) > V, there
SEC.517]
THE KEEP-ALIVE
203
will be a s table operating poin t,, and a continuous d is charge w ill be
main ta ined . Thus , increm ing V or decreas ing Ii is in the right d irec-
tion to s top os cilla tions . S im ilarly , red es igning the el ctrod e or chang-
ing the gas filling of the T’R tube m ay change the gap res is tance I?q e ither
up or dow n.
TO change the gas conten t in order to get s table operation of the k eep-
a live discharge is usuaKy not pos s ible s in ce the gas filling m us t be ch os en
for m inim um leak age pow e r, s hortes t reco~ery tim e, and longes t life , and
it is too much to expect to find a s ingle gas filling that w ill s a tis fy aH of
tions . Fortunately , the s hape can be s o m od ified as to elim inate os ciHa-
$ ion s a lmos t en tire ly .
In th norm al glow d is charge the voltage d rop betw een electrod es is
nearly ind epend en t of the current, and the current d ens ity at the cathod e
L“
c
v
!
Fsc. 54S.-Volt-ttmpere wrve of d-c glow disch ar ge,
is a ls o ind ependent of the tota l current. Th is characteris tic res u lts
becaus e the glow is able to cover more and more of the cathode area as
the current is increas ed .’ Once the entire c thod e area has been covered ,
a further increas e of current is accompan ied by an increas e in vuitage
d rop, and the d is charge characteris tic tak es on a pos iti e dy nam ic
resistance.
Therefore, by res tricting the cathod e area , the current ab
w hich the V-I s lope becom es pos itive m ay be reduced , and thus , the
current a t w h ich os cill tion occu rs m ay be d ecrea sed .
Early TIZ t bes s uch as the 721A and 724A, had s imple k ungs ten
k eep-a live electrod es . S om e tim e after thes e tubes had been produced
and w e re b ein g u s ed , k e ep -a liv e re la xa tion os cilla tion s w e re “d is cov ere d .”
The critica l current above w hich os cilla tions ceas ed , w as of the order of
200 to 400 Xa , By reducing s tray capacitance to a m inimum by placing
the lim iting res is tor d irectly a t the TR tube, it w a s us ually pos s ible either
to elim in ate th e os cilla tion s or to make their frequency very high for
JCobinr, Gascswa C’on&ctora, McGr aw-H ill, N ew York, 1941, Chap.4 ,
204
ICROWAVE GAS DISCHARGES
[SEC. 517
norm al k eep-a live currents . The s pik e leak age energy w ith an os cilla t-
ing k eep-a live d is charge is illus tra ted in Fig. 5 .49a w h ereas Fig. 549fI is
for a nonos cilla tin g d is charge .
The ind ivid ual lines repres en t the s pik e
energy in s ucces s ive pu ls es .
Thes e varia tions w ere firs t m eas ured and
correla ted w ith k eep-a live os cilla tions in a s tudy of the 724A and 1B24
TR tubes . ~ Depend ing upon the repetition ra te and trans mitter pow er,
the s pik e energy d uring the ‘‘ oil period ”
of th e k eep-a live d is ch arge ma y
be 10 to 25 db greater than the normal level.
Coated k eep-a live electrod es are now us ed a lm os t exclus ively . They
are m ade by covering the electrod e w ith a glas s or ceram ic s leeve dow n
to the end , w hich is expos ed by
grind ing off the ins u la tion . Al-
f%
th ough th e os cilla tion -free region
extend s to currents as low as 30
(a)
---t
pa, opera t n g cu rren ts a re u s ua lly
main ta ined b tw een 100 and 200
Luwumu&
~a . There are tw o reas ons for
th is . he voltage d rop acros s the
(b) d is charw e is abou t 400 volts . and
FIG. 5.49.—Time variations in spike
herefore, the d -c res is tance is
leakage energy; (a) oscil a t ing and (b) non-
oscilla t ing keep -a live d is cha rge.
about 4 megohm s at a current of
100 Ma and about 20 m egohms at
a current of 20 ~a. Fo m ilita ry s ervice, it is d ifficu lt to main ta in a
lea ka ge res is ta nce la rge compa red w ith 20 m egohm s, a nd th e low -cu rren t
d is charge m ay actually be extinguis hed by s urface leak age on the TR tu be.
Figure 550 illu s tra tes ty pica k eep-a live voltampere curves for
“coa ted ” and
“uncoa ted” electrod es . The uncoa ted electrod e of the
721A tube s how s a pos itive s lope at curren ts above 200 pa. A coa ted
electrod e w ith an expos ed area of a bout 10 -~ in . Zhas a pos itive s lope d ow n
to curren ts of 50 pa or les s . The 1B24 has a coated electrod e, and the
V-I curve has a pos itive s lope dow n to 50 ~a . The dotted lines w hich
ind ica te regions w ith negative s lope, are the res ult of d -c m eas urem en ts
m ade w hile the d is charge w as os cilla ting. As a res ult, the read ingg are
a vera ges a nd have n o pa rticu la r s ign ifica nce.
Another reas on for choos ing the higher curren t is tha t in ord er to
m ain ta in a given no in the r-f gap, the k eep-a live electrod e m us t be placed
clos er to the gap for the low -curren t d is charge than for the high-current
d is charg . The m echan ica l d ifficu lties involved are ra ther s evere as can
be s een from a cons id era tion of the actual d im ens ion involved . The
accurate location of the k eep-a live electrod e w ith in the hollow cone of a
TR tube s uch ae the 1324 or 724A is a moderately d ifiicu lt tas k . The
‘
J. B .
Wiesner
and F. L. McMkn , J r., “Pre ign ition Tmrw r&ion th rough TR
Tubes ,”RL Report No. 254,Ju ly 3 , 1943 .
SEC.517]
THE KEEP-AL IVE
2435
only s upport for the electrod e is a t the m eta l-to-glas s s ea l w here it goes
through the glas s envelope of the tube. This poin t may be as much as
tw o inches from the end of the electrod e from w hich the d is charge tak es
place. S ince it is us ua lly im pos s ible to loca te the end of the electrod e by
any jigs or s pacers , it is d ifficu lt to loca te the end w ith in +0.010 in . of
500
480
320
/
x
/
721A TR tube
Exposed electrode area ~10-3 sq in
/
; //x<&=~’A-’g:”
Uncoated keep. allve electrode
Oscillates /
b,
/0 1B24 TR tube
- ‘( No
‘Q&O
4
Oscillates
300 I
!
I
I
I I 1
1
0 100
200
300
400
500
600
700 800
Keep. alive current in # amps
FIG.5.50.—Volt-ampere char acteristics of keep-alive dischar ges.
;{(!/
Og
%
I-J
IJ.025”d-
0.140”
1B27
1B24
1B26
FIG. 5.51 .— Deta ils of cones and keep -a live elect r odes of some TR tubes.
the nom inal pos ition ins id e the cone. In the 1B27, the d iameter of the
cone at the end of the k eep-a live electrod e is about & in .
In the 1B24,
h ow e ver, the corres pon ding d iameter is on ly 0 .055 in . Figure 5 .51 s how s
the pos ition of the k eep-a live electrod e w ith in the cones of the 1B24 and
1B27 TR tubes . It w ould be almos t impos s ible to mak e a 1 .25-cm TR
tu be w ith th is ty pe of cons truction .
206
MICRO WAVE GAS DISCHARGES
[SEC.517
S ince nO mus t be held w ith in the lim its im pos ed by low -level trans -
m is s ion on the one hand and low s pik e leak age energy on the other hand ,
let us cons id er w hat effect the loca tion of the electrode has upon nO.
The d is charge is s how n more or les s s chematica lly in Fig. 5 .52. The
electrons , und er the in fluence of the d -c field , d rift in the d irection of the
cone The number of electrons that pas s
through the hole in the cone in to the r-f gap
I
is a function of the hole d iam eter, the d is -
tance of the electrode from the hole, the
avera e tem pera ture of the electrons , the
electron m ean free pa th , and the d is charge
current.
In th e us ual pres s ure ra nge for TR tu bes ,
is of the order of 10–4 in . An electron
FIG, 5.52.—Structure of keep-
m ak es a grea t m any collis ions per s econd ,
a live discharge,
and the influence of the field is mainly to
in crea se the ra nd om velocity or tem pera tu re of th e electron s , in ad dition
to caus ing a rela tively s low dri t in the d irection of the field . If it is
as s umed tha t the pos itive column end s at s ome s urface, s uch as that
s how n in Fig. 552, the d iffus ion of the electrons out of it m ay be found ,
in p rin cip le , b y s olv in g th e d iffu s ion e quation .
The electron d ens ity n is
s ubject to the boundary cond itions that n = O at the w alls of the cone,
and n = j(r,z) at the edge of the
d is charge, r = ad ial and z = axia l
d im ens ions . While th is cannot be
s olved form ally , it ca n be rea liz ed
in tuitively tha t, if the d is charge
end s at a d is tance from the gap
larger than the d iameter of the
cone, the number of electrons
reach ing the gap w ill vary by a
factor of about 30 for every in -
FIG.553.-Side-a rm keep-a live elect rode,
creas e of th is d is tance by one d iam eter. 1 Thus , if the cone is large, the
perm is s ible abs olute error in loca tion of the k eep-a live electrode for a
given tolerance in rzois larger than that for a small cone by about the
ratio of th e con e d iameters ,
It is evid en t, on the bas is of thes e cons id era tions , that it w ould be
very d ifficult to m ak e a coaxia l k eep-a live electrode for a 1 .25-cm tube
becaus e of the small s iz e of the cones in s uch a tube. To avoid thes e
d ifficulties , the s tructure illus tra ted in Fig, 5 .45b w as evolved . In th is
I Th is numbe r is arrived at by a na logy wit h t he a tt en ua tion of elect rom agn et ic
wavea in wavegu idez beyond clit off.
SEC.517]
THE KEEP-AL IVE
207
cons tm ction , the electrode is placed in a fairly large hole at the s id e
of the cavity , and the exit hole through w hich electrons dMus eis Tlq in .
in d iam eter. In th is des ign, thenum ber ofelectrons en tering the cavity ,
n ., m us t be much larger than the number finally reach ing the gap, nO.
Becaus e the electric field is s o w e ak in the outer regions of the cavity , th is
large value of n . has very little effect upon low -level transm is s ion ,
Fig. 5.53.
The electrons s pread out from the exit pos t accord ing to the d iffus ion
equation , s ubject to the bound ary cond itions n = O a t all m eta s urfaces .
Becaus e the gap is partia lly s hield ed by the cones , and becaus e of the
d is tance from the w all to the gap,
:<<1.
Bes id es the ad vantage of greater eas e of cons truction in s mall tubes ,
the s id e-arm electrode has the further a vantage of allow ing grea ter
freedom in the des ign of the r-f gap. The des ign of the 1B26 TR tube
required s harp poin ts on the cones
in ord er to bring the leak age pow er
dow n to a us able level. This w ould
have been impos s ible on the cone
r
5=-$ -
s urround ing a coaxia l k eep-a live.
“/
S im ilarly , ii the 1B50 tube, ~he us e =
“w
FIG. 5.54.—Over apping gap of 1B50 TR
of a s id e-a rm k eep-a live made p os s i-
tube.
ble a des ign w ith the poin ts of the
cones overlapping, Fig. 5 .54. Th is tube has nearly cons tan t leak age
pow er over the en tire tuning range becaus e the gap length remains
unchanged as one cone m oves axially relative to the other.
Th e coa xia l k e ep -a liv e e le ctcod e and th e s id e-a rm e le ctrod e, Fig. 5 .4 5a
and c have found equal us e in bandpas s TR tubes . The reas ons for
choos ing one or the other of thes e electrod es are s till not clear. The s id e-
arm electrod e m us t be accurately aligned perpend icu lar to the electric
field in order to avoid exces s ive low -level los s es . On the other hand ,
the coaxia l e ectrod e mus t be carefully aligned w ithin the con e to prevent
s hort circuits .
Ne ith er of th es e d ifficu ltie s is in supe rable , and su fficie ntly
clos e tolerances can be m aintained w ith proper jigging of the as sem bly .
His torica lly , the s id e-arm electrod e w a s the firs t to be us ed in band -
pas s tubes . A d is charge is mainta ined betw een it and the end s of the
electrodes or c nes form ing the r-f gap.
The res onant elem ents of the
band pas s tube have low Q’s , QLZ
= 4 as compared w ith 300 for a high-Q
tube. As a res u lt, the t rans format ion ra tio is low , and no can be much
larger than in a high-Q tube for the same low -level in teraction . This is
fortuna te, s ince it tak es a large no to reduce s pik e leak age energy to a
208
MICRO WAVE GAS DIS CHARGES
[SEC.&18
sa fe va lue .
A !200+a d is charge d irectly to the end s of the con es prod uces
a bout 0.05 d b change in low -level transm is s ion .
Becaus e the cones are
the anode of the d is charge, no is practica lly independent of the d is tance
of the k eep-a live electrod e from the r-f gap, a t a cons ta t current level.
%
5
= 0.4
~
.s 0.3
~
~ 0.2
&
2
~ 0.1
u
+&
m
0.10.20.40.61 2 4 681020 40 100
Keep alive insertion loss in per cent
FIG. 555.-Efficiency of keep-a live dLs-
chiwges.
In the m any 1 0-cm ba nd paw tubes
tes ted , includ ing thos e us ed for
experim en t al purpos es and thos e
produced commercia lly , there is
no record of s erious k eep-a live
in teraction for th is s ty le of elec-
trode w ith d is charge currents of
les s than 250 va .
In bandpas s tubes it has been
obs erved that the coaxia l k eep-
a live has as much as 8 db of in ter-
action w hen pus hed too far for-
w ard . Thus , it apparently can
produce a larger va lue of no than can the s id e-arm electrod e. Tes ts
m ade on a 3-cm bandpas s tub ind ica te les s s pik e leak age energy
for a given in teraction for the coaxia l than for the s id e-arm electrod e,
F& !5.55 . Jus t w hy th is is s o is not immed ia tely obvious , s ince
in teraction is apparen tly a measure of no, unles s the electrons from
the s id e-a rm electrod e are load ing the fringing field of the gap rather than
the cen tra l portion w here break dow n tak es place. Com paris on , in the
1B55 bandpas s tube for 8 .5 cm , of the coaxia l and s id e-arm electrod es
ind ica ted little d ifference betw e en th e tw o.
6 .18 . Keep-a live Characteris tics . -S ince the gas filling of a TR tube is
determ ined by the leak age pow er and the recovery characteris tics , the
characteris tics of the d -c d is charge are m ore or les s d eterm ined by the r-f
d is charge characteris tics . Figure 556 s how s the d epend ence oft he k eep-
a live voltage d rop upon the gas filling of a 1B24 TR tube. The charac-
teris tics of other h igh-Q TR tubes are not very d ifferent from thes e.
In S ec. 5“7 it w as poin ted out that no d irect m eas urements had been
m ade of the electr n dens ity no produced in the r-f gap by the k eep-a live
d is charge. Th is is a s erious lack in the unders tand ing of s pik e phenom -
ena, From the poin t of view of TR-tube d es ign , how ever, it is s u fficien t
to measure s pik e energy and k eep-a live in teraction . Thus , an experi-
m enta l approach to the d es ign of a tube w ou ld be, firs t, to choos e an r-f
circu it w h ich has the d es ired Q or bandpas s characteris tics , and w hich
has a s hort r-f gap. Then , under h igh-pow er tes t, the gas pres sure w ould
be varied , and W. and Pa m eas ured .
For e ch gas pres s ure, the k eep-
a live curren t s hou ld be brought t a level that res u lts in about 0 ,01 db
of in teraction . If the current required to obta in th is is too high or too
SEC. 518]
KEEP-ALIVE CHARACTERISTICS
209
low , the pos ition of the k eepalive electrod e .s hQtid be read jus ted . s uch
a proced ure w ould allow truf y optim um leak age pow e r chamm teris tics to
I
I
200024681012141618 202224262830
,
Partial pressure of H2. mm Hg
FIQ. 6.56.—Keep -a live p res su r~volt age cha ra ct er ist ic of IB24 TR tube. Th e disch ar ge
cu r r en t var ies from 100 to 150 pa.
be obta in ed , bu t it requ ires an a dju sta ble k eep-a live electrod e. Alth ou gh
this procedure has not been follow ed in the pas t, it appears that the us e
of s uch an electrode w ould res ult in an appreciable econom y in d evelop-
ment tim e and in the number of experi-
Gas pressure
mental t u b es required .
It w ould ,
mmHg of N2
fu rth ermore, es ta blis h tolera nce s upon
6
8 10
electrode location. In the pas t, s uch
50
~
12
p
14
information has us ually been obta ined ~ 40
2
by mak ing a number of d ifferent tubes .=
--
--’36
w ith vary ing electrode loca tions , and
.
g 30
,/ ’
measuring Ws and interaction. /
The interaction, or low -level ins er- ~
20
/
tion los s , can be pus hed to extrem e ,0
H2-H20
15-15 mmHg
lim its by m oving the coaxial electrod e
of a 1B24, or s im ilar tube, clos er to the
r-f gap, by eniarging the hole in the end
00 0.2 0.4 0.6 0.8 1.0
Keep-alive current i nma
of the cone, and by changing the gas
FIG. 5.57,—Low-level sign al a tt en -
content of the tube. In fact, d -c-con-
us tion caus edby k eep-alivedischarge
trolled r-f sw itches have been made
in modif ied1B24TR tube.
out of 1B24 and 1B27 TR tubes .
In thes e, a k eep-a live current of
300 pa produces an r-f a ttenuation of about 40 db.’ In a 1B24,
1Tin g-Sui K~ and L. D. Smu llin ,
“A hw Pow e r X-Ban d R-f Ga s Sw itch ,” RL
Report No. 841 ,Oct . 19 ,1945;T. S . K&,“
h’ote on a Low Pow erS-band Gas Switch ,”
RL Repor t No. 979, Dec. 10, 1945.
210
MICRO WAVE GAS DIS CHA ROES
[SEC.5’19
filled w ith 15 mm Hg each of Hz and H*O, an attenuation of about 25 db
could be obta ined w ith currents of about 1 m a if the k eep-a live electrod e
w e re in the pos ition to give greates t in teraction .
If the gas content is
changed to N2, attenuations of 0 db are obta ined . Figure 5.57 s how s
the variation in a ttenuation w ith k eep-a live curren t for various gas
fillings . It s hould be noted that high interaction is obta ined only w ith
negat iue keep-alive polarit ies .
6 .19 . Keep-a live Dis charge s nd Tube Life.-LTnder the action of the
d -c glow d is charge, there is a continua l m od ifica tion of the gas conten t
of the tube. Thk change is the res u lt of tw o d ifferen t m echanism s :
s pu tterin g, a nd ch em ica l re action .
S pu ttering is a proces s in w h ich the ca thod e is heated by pos itive-ion
bom bardm ent to the poin t w here particles are boiled out of the ca thode
and fina lly condens e on the anode or on the tube w a lls . Thes e particles
m ay collid e w ith gas m olecu les and carry thes e m olecu les w ith them to
the tube w alls , w here the gas is trapped . Thus j the ra te at w hich meta l
is s pu tter d from the ca thode is a meas ure of the ra te at w hich the gas
pres s ure w ill be reduced in a given tube. Table 5“5 gives the normal
cathode fall 1 in Hz and A, for a num ber of m eta ls , and the rate of s pu tter
ing for the s am e metals in Hz w ith a ca thode fall of 850 volts .
TABLE5.5.—NoRMALCATHODEFALL IN A ANDH,, AND SPUTTERING RATE IN HZ
(CATHODEALL= 850 v) FORVARIOUSMETALS
Metal
Al
Ag
Au
Cu
Fe
Mg
Ni
Pt
Sn
w
Xorma l ca th ode fa ll
~ Spu tt er ing ra te in H,,
A
H,
!
pgr /a . sec
100V
130
130
130
165
119
131
131
124
170V
216
247
214
250
153
211
276
226
8
205
130
84
19
2 .5
18
55
16
The onlv m eta ls that have been us ed for the k eep-a live electrode are
tungs ten aid Kovar. Exam ination of the table ind~ates that, in regard
to s puttering, alum inum m ight have m ade an excellen t k eep-a live elec-
trode. It cannot, of cours e, be s ea led to glas s , and w ould have to be
w eld ed to a s uitable glas s s ea ling m etal s uch as tungs ten or Kovar. To
preven t os cilla tions , the electrode m us t be covered w ith an ins ulating
1Cobine ,Gaaw uaConductors, McGraw -Hill, New York, 1941, Chap.8.
SEC.&~]
KEEP-ALIVE CIRCUITS AND POWER SUPPLIES
211
m ateria l. Tungs ten or Kovar electrod es are s im ply glas aed right dow n
to the end . If alum inum w ere us ed , it could be covered w ith a s u itable
ins ulating cem en t s uch as Ins alu te cem ent.
To th e a uth or’s k n ow led ge,
no tes ts have been m ade w ith a lum inum k eep-a live el ctrod es ; but the
con sid era tion s pres en ted h ere m igh t w a rra nt s uch tes ts .
Tungs ten is a very unfortunate choice as a k eep-a live electrod e for
TR tu bes containing w a ter vapor.
Man y y ea rs ago lamp man ufa cturers
d is covered the s o-ca lled “tungs ten w a ter cy cle” and learned that they
could get lo g life from their tungs ten filam ents on ly if w a ter vapor w ere
carefu lly k ept ou t of the lam ps .
This phenom enon involves the form a-
tion of an uns table tungs ten oxid e and the releas e of a tom ic hy drogen in
the d is ch rge. The oxide d iffus es through the tube, and condens es on
the w alls . In tim e, how ever, the ox d e is reduced and the oxy gen and
hy drogen recombine to form w ater vapor. Thus , although the w ater
s erves as a carrier to trans port tungs ten aw ay from the cathod e or fila -
m ent, it is not cons umed . The amount of tungs ten carried aw ay in this
manner is not large enough to d es troy the k eep-a live electrode in any
rea s on able len gth of tim e.
It is s ufficien t, how ever, to form filam ents or
“hairs ” and , in a s mall tube s uch as the 1B24 or 1B26, thes e m ay actually
brid ge th e ga p betw een ca th od e a nd anod e a nd s h ort-circu it th e d is ch arge.
Exactly w hat determ ines the ra te of th is proces s is not k now n; but s hort
circu its have d eveloped after opera ting tim es of only 10 to 100 hours a t a
d is charge current of 100 pa .
The effect is mos t s erious , and w as firs t
noticed , in TR tubes w ith ins u la ted k eep-a live electrod es . Becaus e of
th is , Kovar is us ed in the tubes w ith glas sed k eep-a live electrod es , the
1B24, 1B26, 1B27, and the various band pas s tubes .
6 .20 . Keep-a live Circu its and Pow er S upplies .-The large m ajority
of a ll radar s ets have us ed s im ple, d -c k eep-a live d is charges . Thes e are
energiz ed either from a negative voltage already available or from a
s im ple a uxilia ry h alf-w a ve rectifier, s uita bly filtered . Th e volta ge a va il-
able m us t be 750 to 1000 vo ts negative, on open circu it, and the curren t
is lim ited to 100 to 200 ~a.
In a few cas es , a d evice k now n as prepuls ing is us ed . In th is d evice a
puls e of curren t of the ord er of a m illiampere is pas s ed through the d is -
charge a few tenths of a m icros econd before the trans mitter pu ls e, and is
made to overlap it. Th is pu ls ed d is charge may be us ed alone or in con-
junction w ith a low -curren t d -c d is charge. In th is w ay , a large value of
no can be produced in the gap and the s pik e energy greatly reduced
The fact that the in teraction may als o be large is unimportant, s ince it
occurs only for a few tenths of a m icros econd at the very end of the
receiving period.
Let us firs t cons id er the external circu it of the d -c d is charge. The
d y namic res is ta nce, or s lope o! th e k eep-a live d is ch arge ch ara cteris tic is
212
MICROWAVE GAS DISCHARGES [SEC. 521
small compa red w ith the s ta tic res is ta nce obta in ed by ta king th e qu otien t
of the operating voltage and current (s ee Fig. 5 .50). In the firs t approxi-
mation, it may be as s umed that the dy nam ic res i tance is z ero; that is ,
the d is charge i a cons tan t-voltage d evice. If the voltage d rop is V., the
curren t is 1 , the open circuit voltage of the s ource is VO, and the s eries
lim itin g res is ta nce is R,
~=~o– Va=A_V,
R R
ldIl
~dAV – AV
(74)
Thus , if either V. or Va is s ubject to fluctuations caus ed by pow e r-line
va ria tion s or d ifferen ces in in divid ua l TR tu bes , th e percen ta ge of cu rren t
change for a given voltage change w ill be invers ely proportional to
Vo – V.. It therefore appears d es irable to m ak e AV large by increas ing
V,, and to m aintain the proper curren t by a corres pond in increas e of R.
Mos t h igh-Q TR tubes w ith H, and HZO fillings have a k eep-a live
voltage d rop V. = 400 volts , and the operating current 1 is betw een 10
and 200 pa. How ever, becaus e of manufacturing tolerances , V. is
a llow ed to vary betw een 350 and 475 volts in new tubes , and during the
life of the tube t may increas e by 50 to 100 volts . If the des ign point is
at V. = 400 volts and 1 = 100 pa, w ith VO = 700 volts , 1 will fa ll t
67 ~a if V. s hould ris e up to 500 volts . If V, = 1000 volt , 1 w ill fa ll to
83 pa for a s im ilar increas e in Vm. This m ight be carried to tbe exten t of
m ak ing VOvery large, and thus red uce s till further the varia tion in 1 w ith
changes in V.. At th e operatin g cond ition s as s um ed a bove, if V, = 1000,
R = 6 megohms . S ince the voltage required to fire the gap initia lly is
about 600 volts , it w ould require a s urface leak age of 8 or 9 megohm s to
reduce the voltage at the tube to a poin t w here it w ould never fire.
Un der m ilitary operatin g con dition s, the a ccumulation of d irt, m ois ture,
or s alt on ins ulatin g s urfa ces m igh t ea sily res ult in lea ka ge res is ta nces as
low as 0 or 20 m egohm s. On this bas is 1000 volts is us ually cons idered
th m axim um s afe value for VO. In large, fixed , land ins tallations , w h ere
the equipm ent is ind oors , higher values of VO may of cours e be us ed .
5 .21. Prepuls ed Keep-a live Circu its .—It has been ind ica ted that the
d -c d is charge changes the gas content of the tube, and thus affects the
tube life. In fact, in h igh-Q TR tubes , the tube life is a lm os t independent
of the r-f d is charge, and is invers ely proportional to the curren t in the
k eep-a live d is charge. It thus appears des irable to reduce the average
k eep-a live current to as low a level as pos s ible. One w ay of doing this
is to turn off the d is charge betw een puls es , and to turn it on only in time
to get the required value of no in the gap w hen the transm itter puls e
starts.
Depend ing upon the repetition rate, the average current w ould
SEC. 521]
PREP II S ED KEEP-ALIVE CIRCUITS 213
be reduced by a factor of abou t 1000 if the ins tan taneous value of the
curren t w e re k ept cons tant, and therefore the tube life w ould be increas ed
by a ver large factor.
If the ins tantaneous curren t is made 10 or 20 tim es the normal d -c
va lue, the average current w ill s till be 50 to 100 tim es les s , the increas e in
tube life w ill s till be s ubs tantia l, bu t nOw ill be increas ed and the s pik e
energy decreas ed . If th is double effect, longer life and low er W,, is t be
utiliz ed , a k now ledge o W. as a function of k eep-a live curren t is neces -
s ary , Unfortuna tely , no deta iled inform ation of th is k ind exis ts . From
50 to 200 or 300 pa , the s pik e leak age energy is nearly cons tan t in mos t
high-~ TR tubes . Apparen tly no remains cons tant in th is range. Thk
may ind icate that the d is charge extend s back , away from the r-f gap,
w ith increa sing cu rrent in th is ran ge.
With currents f the order of I to
5 ma, W. is 7 to 10 db low er than at normal opera ting curren ts in high-~
tu be s w ith coa xia l k e ep -a liv es .
This reduction in W. is s ubs tantia l, but prepuls ing has found little
applica tion . There is one immed iate objection to a prepu ls ed d is charge
in w h ich no continuous d is charge is m ain tained , that is , it is incapable of
protectin g agains t h igh -pow e r pu ls es from n ea rby ra dars operatin g in th e
s ame frequency band , becaus e the prepu ls e is s y nchroniz ed to its ow n
trans mitter, but not to nearby trans mitters . In m ilitary or naval cipera-
tions , a large number of radars may be operating in a res tricted area.
Once an aircra ft is a loft, un les s a group of planes are fly ing in tight for-
m ation , there is little probability of cry s ta l burnout by a nearby radar.
On the ground , how ever, w ith planes lined up clos e together, mutual
urnout can be a s erious problem .
Becaus e of the danger of random puls es caus ing burnout, the TR
tube mus t be capable of protecting cry s ta ls con tinuous ly w ith a low -
curren t d -c d is charge. If the T tube can already protect cry sta ls w ith
a d -c d is ch rge, it s eem s that little is to be gained by reducing W, another
10 db by means of a prepu ls e s uperimpos ed on the d -c d is charge. Only
by extens ive life tes ts on a large number of TR tubes and cry s ta ls can it
be s how n w h ether or not any appreciable im provem ent in cry s ta l protec-
tion can be obta ined by reducing W..
All TR tubes now in us e a fford good cry s ta l protection w ith a d -c
k eep-a live and , although occas ional “u expla ined ” burnouts d o occur,
the s am e tube w ill again protect cry s ta ls for s evera l hund red hours m ore.
If thes e burnouts are caus ed by rare burs ts of large s pik e leak age energy ,
they m ight be elim ina ted by the us e of prepu ls ing w h ich not on ly r duces
the average value of W., but als o red uces the varia tion in energy betw e en
ind iv idual s p ik e s .
It is w orth w hile to exam ine s ome of the circuits us ed to produce a
prepu ls e. The tw o im portan t variables to be cons id ered are the rela tive
214
MICROWAVE GAS DISCHARGES
[s~c. 5.21
tim ing of the prepu ls e and the transm itter puls e, and the magnitude of
the prepu ls e current. J leas urem ents made on a 724A TR tube us ing a
prepu ls e of ~ps ec duration s uperim pos ed upon a 100-pa d -c d is charge
gave the res ults s how n in I?ig. 5 .58.
If the prepu ls e s tarts a fter the
FIG. 5.5S.—E ffect of pr epu lse t im in g on spike
energy of a 724A TR tube.
trans mitter pu ls e, it as no effect
o W,.
When it leads the trans -
m itter by about 0 .1 ps ec, as in
th is experim ent, W , is 8 db dow n
from its d -c value. As the lead
is increas ed bey ond 0.1 ps ec, the
num ber of electrons furnis hed to
the r-f ga by the d is charge be-
come s sma ller, a nd W . approa ch es
the d -c level. The increas e in
W. to values 12 db greater than
normal wh en the prepu ls e lea ds by
5 to 7 ~s ec, w as caus ed by a pos i-
tive overs hoot on the prepuls e, w hich turned off the d -c d is charge and
reduced no momentarily .
A prepuls e mus t be added to a d -c circuit in s uch a w ay that the puls -
ing circu it has little or no effect upon the d -c d is charge.
NTorma lly , Lo
preven t relaxation os cilla tions , a res is tor of ~ to 4 m egohm s is put right
a t the k e p-a live cap on the TR tube.
To prod uce a prepuls e current of
severa l milliamperes w ith a reason-
able voltage, there m us t be little
RFC
lM
lo#/ .lt
‘T
or no lim iting res is tance betw een DC
,+
To prepulse circuit
the s ource and the tube. Thus ,
‘1
if the prepuls e circu it is connected ~
betw een the d -c lim iting res is tor
and the electrode, the s tray ca-
TR tube
pacitanc of the prepu ls e circu it
—
FIG. 559. -f.3rcu t for prepu lsing TR tube.
mus t not be large enough to a low
relaxation os cilla tions to tak e place. Figure 5.59 ind icates s uch a con-
nection w ith a 10-~pf capacitor us ed to is ola te the tw o circuits .
The prepu ls e voltage may be obta ined in a number of w ay s . It m ay ,
of cou rs e, b e gen era ted by a block in g os cilla tor or s im ila r ircu it properly
tim ed w ith res pect to the transm i ter. This is pos s ible only if the trans -
m itter is triggered from some external s ource that can als o be us ed to
trigger the prepuls er. If a “s elf-s ynchronous ” trans mitter m odula tor
is us ed , s uch as a rotary or s eries s park -gap m od ula tor, there is an uncer-
tainty in the tim e betw een s ucces s ive pu ls es of perhaps 50 y sec. S ince
all trigger voltages in s uch a s et are derived from the trans mitter puls e,
there is no w a y of triggering a prepuls er s o that it w ill lad the trans mitter
SEC.5“21]
PREP ULSED KEEP-ALIVE CIRCUITS 215
by a fraction of a m icros econd .
In s uch cas es , and even in the cas e of
s ynchronous trans mitters , it is d es irable to us e s om e voltage w ithin the
m od ulator that lead s the voltage on the trans mitter tube (m agnetron) by
the proper amount. The primary w ind i g of the s tepup puls e trans -
form er that d rives the m agnetron is a convenien t s ource of s uch a voltage.
It is pos s ible, by tak ing ad vantage of t e fin ite ris e ‘tim e of the m od ula tor
puk e = * ps ec, and the magnitude of the pu ls e (s evera l thous and volts
on the primary ), to produce a high-curren t pu ls e in the TR k eep-a live
circu it that lead s the r-f ou tput pow er of the magnet on by about %lU
~sec.
Figure 5.60 illus tra tes a convenien t w ay of obtaining the neces sary
prepu ls e voltage from the puls e trans form er by m eans of a h igh-voltage
capacitor m ade from a length of h igh-voltage puls e cable. The pick -off
Cable
Brass tube
insulation
Hv pulse cable
—
To pulse
transformer
uwer
jacket
1-
Corona
To TR
tube
shield
Fm. 5.60.—Voltage divider for prepulsing TR tube.
tube has a capacitance of about 5 p~f to the high-voltage lead . Thus the
total charge that can flow in the prepu ls e circuit is q = CV where V is th e
maximum value of the pu ls e voltage. In a ty pica l h igh-pow er s et,
V = 10 k v, C = 5 ~pf, q = 5 X 10–8 coulomb. If the ris e tim e is 0 .1
ps ec, the average curren t is ~ amp (averaged ver 0 .1 y s ec), and the
average d -c current is 25 pa . It is importan t to k eep al the tim e con-
s tan ts of s uch a circu it as small as pos s ible, s ince there is probably
les s than 0.05 ps ec that can be w as ted in charging the various circu it
components.
Another m ethod of reducing the s pik e leak age energy has been s ug-
ges ted m any tim es .
Th i m ethod is to ins u la te one of the electrod es
fm rning the r-f gap through a s u itable r-f chok e, and to s trik e a d -c d is -
charge d irectly acros s the gap jus t before and during the trans mitter
,pulse.
Such a s chem e has been tes ted on the 1B27 TR tube, and more
recen tly on the 3-cm bandpas s tube. The res u lts in both cas es w ere
s urpris ing in that the s pik e energy iw emd by about 7 db w hen a d -c
216
ICROWAVE GAS DISCHARGES
[SEC.5.22
curren t of 900 ~a w as caus ed to flow acros s the gap. The explanation of
th is phenom enon is not y et k now n.
Another interes ting propos a l is to us e a rad io-frequency (about 5
Me/ s ee) h igh-voltage s upply for the k eep-a live. Th is w ould be us ed
w h ere s pace or w eight d id not perm it the us e of a trans form er, rectifier,
and filter for 60 or 400 cps . A s ingle os cilla tor tube operated from a
low -voltage s upply , and a res onant trans form er can furnis h enough
voltage and c rrent for a TR tube k eep-a live d is charge. Only rud i-
m entary tes ts have been m ade of s uch a s ys tem w ith the lternating cur-
ren t applied d irectly to the k eep-a live electrod e.
The m eas ured s pik e
leak age en ergy w a s n ot a ppreciably d ifferen t from that of a d - k eep-a live
d is charge. No attention w as paid to the problem of s hield ing this high
rad io-frequ en cy volta ge and th e d ev elopmen t of s imp le, low -capa cita nce,
high -volta ge s hield ing may be very d ifficu lt, un les s the os cilla tor and th e
TR tube are hous ed w ithin a common s hield . Th is propos a l m erits
further considerat ion.
5 .22. Rad ioactive Prim ing.-To initia te d -c d is charge, it is neces -
s ary to have a num ber of free electrons in the gap betw een the electrod es ,
or the voltage mus t be rais ed to a level high enough to caus e field em is -
s ion from the ca thode. In form ally there are free electrons pres ent in a
gas volume. Thes e are releas ed photoelectrically or by high-energy
cos mic- or -y -ray particles . A TR tube, how ever, is us ually enclos ed in a
light-tight m etal conta iner and is s urround ed by fa irly m as s ive pieces of
m eta l, th erefore th e proba bi ity of ion iz ation b y extern al ra dia tion is very
s mall. Experim enta l tubes that have been id le for s evera l d ay s becom e s o
completely inactivated that s eve a l m inutes may elaps betw een the
applica tion of the k eep-a live voltage and the s trik ing f the d is charge.
The length of tim e is determ ined by the probability of an ioniz ing ray of
s ufficient energy pas s in g through the tu be.
The TR tube w ill not, in genera l, protect cry s ta ls if the k eep-a live
d is charge is off; and , in particular, the very firs t pu ls e of leak age energy
w hen the transm itter is turned on w ill be extrem ely large. Thus , rapid
and reliable firing of the k eep-a live under all circum s ta ces mus t be
ens ured . This can be accomplis hed by producing a small amount of
ionization w ithin the tube by means of a rad ioactive s ubs tance. Tw o
m ateria ls have be n us ed for th is purpos e: rad ium brom ide and an arti-
ficia lly rad ioactive cobalt ch lorid e. The rad ium brom ide produces a -,
P-, and y ray s , w h ereas the cobalt ch lorid e is on ly & and T-ray active and
has a half-liie of 5 y ears . Although th is life is s hort com pared w ith that
of 1690 y ears for rad ium , it is ample for mos t purpos es . The cobalt
chlorid e has the im portan t ad vantage of being com pletely nontoxic a d
it is eaay to mak e in compara tively large quantities . During the w ar,
it w as produced by the cy clotron group of the Mas sachus etts Ins titu te
SEC,5.23]
TUBE LIFE AND GAS CLEANU
217
of Technology , There s eem s to be little excus e to us e the highly toxic
rad ium s alts s ince the artificia lly rad ioactive cobalt ch orid e is eas ily
available.
In practice, the cobalt chlorid e is us ed in a w a ter s olu tion and d ilu t d
to a con cen tra tion th at h as an equ iva len t ra dioa ctivity y of 0 .1 ~g of ra dium
per d rop. A d rop of the s olu tion is put on the cone ad jacent to the k eep-
alive electrode before s ealing off the tube. During the s ealing-off and
evacuating proces s , the w ater is evapora ted . Th is amount of rad io-
activity is s ufficient to guarantee the s ta ting of the tube w ithin les s than
5 s ec after the application of the voltage.
5s 23. Tube Life and Gas Cleanup:-The life of a TR tube is d eter-
m ined by the rate at w hich the gas cen t ent changes .
Th is ra te is d eter-
m ined by the action of the r-f or the c d is charge. With continued
opera tion either the leak age pow er becom es too large or the recovery
tim e becom es too long. Occas ionally , a tube m aybe found in w hich the
d is charge has depos ited a thin lay er of m eta l upon a glas s s urface and
thereby has decreas ed the low -level transm is s ion . How ever, th is
phenom enon is s o rare as to be cons id ered a freak .
There is no quantita tive in form ation on the rate at w hich the r-f d is -
charge changes the gas conten t of the tube. It is k now n that a high-Q
tube opera ted w ithout a k eep-a live d is charge may be run for s evera l
th ou sa nd h ours w ithout s eriou sly changing eith er its leak age pow e r or its
recove~-t ime characteris t ics .
The s ame tube w ill have a life of on ly 500
to 1000 hours w ith a d -c k eep-a live d is charge curren t of 100 ya even if
there is no r-f d is charge. The usual k eep-a live voltage d rop is about 400
volts and the pow er d is s ipated is about 40 mw . The pow er d is s ipa ted
in the r-f d is charge is equal to the geometric mean of the transm itter
and the arc leakage pow er. Ty pica l va lues for thes e are 100 kw and 40
m w , res pectively , and therefore the puls e pow er d is s ipa ted in the d is -
charge is about 60 w atts . If a duty ra tio of 1 to 1000 is as s umed , the
a vera ge pow er d is s ipa ted in 60 mw .
Th us , th e a vera ge p ow ers d is s ipa ted
in the r-f and d -c d is charges are roughly equal, and the d ifference in the
rate of gaa cleanup m us t be attributed to s om e other factor.
The proces s that ta lies place m os t rapid ly in TR tubes is the cleanup
of the w ater vapor. Th is apparen tly tak es place by chem ical action ,
s in ce th e copper con e that s erves as th e a nod e for the k eep-a live d is charge
becom es oxid iz ed , and the pa rtia l pres s ure of hy d rogen in creas ed s a that
of the H20 d ecreas es .
The proces s involved is probably the follow ing one. Under the
action of the d is charge, OH ions are produced . In the d -c d is charge of
the k eep-a live, them ions drift acros s to the anode. They are highly
~W. G. G~dIIw , “The Chznge in Compos itionof the Gas Resen t in a 721AType
Tube es a R.emd tof Operation,”BTL MM-43-MO-98,S ept.2 2,1 943 .
218 MICROWA VII GAS DISC HA RGl?S
[SEC. 523
active, and therefore, they react w ith the copper, form ing copper oxid e
a nd releas in g a tom ic h yd rogen .
n the r-f d is charge the mas s ive ions
a re un affecte by th e electric field and th eir m otion is completely ra nd om ;
the num ber reaching the electrodes w ill be roughly proportiona l to the
s olid angle s ubtend ed by the electrod es .
It is probably this d ifference
in the motio of the ions that mak es the d -c d is charge s o much more
effective than the r-f d is charge for d es troy ing the w a ter va por.
The r-f d is charge acros s the low -Q input w ind ow of the pre-TR, 1ow -Q
ATR, or ban pas s TR tubes is much more in tens e than in the high-Q
tubes . When the transm itter pow er is 10s w atts , the pu ls e pow er d is s i-
pa ted in a 10-cm pre-TR tube (lB3t3) is about 7 kw . Furthermore, the
expos ed electrod e area, the area of the tube w a lls , is m uch grea ter than in
the h igh-Q tubes . In thes e tubes , the r-f d is charge play s the m ajor role in
the d ecom pos ition of th w a ter vapor.
An example of the compara tive activity of the d -c and the r-f d is -
charges is furnis hed by a conven tiona l duplexer in w hich the s ame TR
cell is us ed for both the TR and the ATR sw itches : a 721A tube, fo
instance.
In the TR tube a k eep-a live d is charge is m aintained and , as a
res ult, a fter about three hundred hours the tube w ill have to be replaced ,
becaus e the recovery tim e w ill have becom e too long. In the ATR tuber
on the other hand , no d -c d is charge is m ainta ined , and although the r-f
p w er d is s ipa ted in the d is charge is about 50 per cen t greater than that
in the TR tube, the recovery tim e remains unchanged even after 1000
to 2000 hours of opera tion .
An obvious w ay to increas e the life of a TR tube is to increas e the
volum e of gas cen t ained in it, s ince the life of a tube is proportiona l to its
volume of gas . In a cell TR tube, the volume is lim ited ra ther s everely
by the des ired tuning range and by the cavities in to w hich it mus t fit.
In tegra l-cavity TR tubes , how ever, may have protuberances on them
s ince there is no externa l cavity in to w hich the tube mus t be clamped .
Table 5.6 lis ts s om e of the m ore comm on high-Q TR tubes and gives the
volumes of th eir en velopes .
TABLE 5.6.—VOLUMES OF VARIOUS HIGH-Q TR TUBES
Tube
I
Type
I
Volume, cm’
7 24A/ B
&cm cell
1 .5
1B27
I&cm cell 5 .3
1B26
1.2&cm integral cavity
18
1B24
3-c integral cavity
19
721A/ B
M-cm cell
25
It is to be noted that the 1B27 , w hich has to a large extent replaced
the 721A in new equipments , has on ly about one-fifth the volume of the
SEC.5.24]
CHEMICAL RESERVOIRS
219
721A. This reduction in volum e res u lted from the des ire to mak e the
tube tune dow n to8 .0cm or les s , w hereas the721Aw ou1d go only as low
as 8.7 cm ; it a ls o res u lted from the fact that the tun ing mechani m
occupies one end of the tube and is a t a tm os pheric pres s ure, w h ich red uces
the effective volum e to tw o-th ird s tha t of a fixed -tuned tube of the s am e
s iz e. This reduction in volume w as rea liz ed w hen the tube w as firs t
in troduced , bu t the advantages of s mooth , s ingle-k nob tuning, and the
w id e range of frequencies that cou ld be covered w it various cavities
m ad e it s eem worth w h ile to examin e th e pos s ibility of a rtificia lly in crea s-
ing the tube life. A s im ilar problem had been faced in the cas e of the
1B24 and 1B26 TR tubes . In thes e tubes the cavity proper is very
s mall, 1 cc or les s ; ow e ver, the us e of an external res ervoir increas ed the
gas volume to about 25 cc, and res u lted in excellen t tube life. Such a
s olu tion w as not pos s ible for the 1B27 tube.
5 .24. Chem ical Res ervoirs .-The life of the 721A tube w as barely
long enough to m ak e it a us able tu be, for, a fter a pproxim ately 300 hours of
opera tion , the recovery tim e becam e exces s ive.
The 1B27 tube, w ith
only one-fifth the volum e, w ould be com pletely us eles s if its life w ere cor-
res pond ingly reduced . R. Levine s ugges ted tha t a chem ical w ater
res ervoir in the form of a hy d ros copic s a lt be incorpora ted in to the
1B27 tube. In th is w ay a large quantity of w ater could be s tored
in a few m illigram s of s a lt and the effective volume of the tube w ould
be greatly increas ed . An inves tiga ti n of pertinen t data w as made to
d eterm ine if there w ere any s a lts w ith s u itable characteris tics . The
mos t importan t characteris tic to be cons idered w as the varia tion of
va por pres s u re w ith tempera tu re.
Military cond itions require tubes to
w iths tand temperatures of —55°C to 100°C, and to give s a tis factory
opera tion w ith in a range of – 10”C to 1 0” . Therefore, a hy dros copic
s a lt, in order to be us efu l, mus t have a maximum vapor pres s ure of 20 to
30 mm Hg at 100”C to preven t the leak age pow er from increas ing to the
poin t w here cry s ta l burnout is lik ely to occur. On the other hand , the
vapor pres sure at — 10”C m us t be of the order of a few m illim eters to k eep
the recovery tim e reas onably s hort (s ee Fig. 5 .34).
Data on various s a lts ind ica ted that above 40°C, the increas e in
vapor pres s ure w as s o rapid as to mak e mos t of the s a lts us eles s .‘,z
F@re 5.61 is a ty pica l curve of HZO vapor pres ure plotted agains t
temperature. Nick el and cobalt perch lora tes have s a tis factorily fla t
pres sure characteris tics , bu t their explos ive nature w ould probably
d ecreas e ra ther than increas e the life of the tube.
1International Critical Tables, McGraw -Hill, 1933.
i R. Levine, F. L. McMillan , “Chemica l Me thods for Main ta in ing the F%rtia l
Re s ew s of Water in TR Tubez ,”RL Rqort No. 5 93 ,J uly 1 3, 19 44 ,
220
MICRO 1$’A VE GAS DISCHARGES
[SEC,524
Water can be obta ined by an equilibrium reaction w ith H,O as an end
prod uct, for example
TlOH e T120 + H20.
Here too, how ever, the rate of evolu tion of H!() is too great at tem pers ,-
tu res a bove 6 0°C.
Finally , abs orben ts and abs orben ts w ere cons id ered . In the firs t
50.
group are activa ted alum ina and
s ilica ge~. Figure 562 gives the
* 40
Zu
,/
p re s s ure -tempe ra tu re chara ci,e r-
.s
is tics for thes e s ubs tances . The
eE30
‘E
EI
.2 0
& =. 20
w as d ried in a vacuum at 100”C”
before being charged by expos ure
-; ~
&
10
to an atm os phere of 23 mm Hg of
H20 at 90°C. Thk charge gave a
o
0
10 20 30 40 50 60
w a ter-va por con ten t for th e s ilica
Temp ‘C
gel of 2 .6 per cen t by w eigh t. The
.5.61 .—~apor pr essu re BS a func-
activa ted a lum ina w as 8 to 14
t ion of temperature for a typical hydra te:
NiClv4H,0 = NiClr2Hz0 + 2H 0.
mes h, and a fter having been d ried
at 10O°Cw as charged in an a t m os -
phere of 18 mm Hg of HZO at 98°C; the w a ter-vapor con ten t of the
a lum ina w as 1.33 per cen t by w eigh t.
Although far from perfect, both of thes e s ubs tances s how ed enough
prom is e to w arran t life tes ts in TR tubes . The 11327 TR tubes w ere
us ed w ith 0.5 g of s ilica el. If the gel was charged w ith 22 mm Hg of
$;= filw
20 40 60 80 100
Temp. ‘C
12345
Hundreds of hours
FIG. 5.62.—Vapor pressure of alumina and
FIG. 5.63.—Life tests of 1B27 TR tubes
Silica gel.
ueing silica-gel reservoirs.
HzO at a. tempera ture above 90°C, at room tempera ture the recovery
tim e w as poor. On the ther hand , charging w ith the s am e pres s ure at
75°C caus ed exces s ive leak age pow er t 100°C. Tubes w hich w ere
charged to 22 mm Hg of HZO at 85°C protected cry s a ls a t 100°C a d
s how ed good recovery tim e at 5“C.
Figure 5%.3 s how s the tim e after the transm itter pu Iae w hich ia
requ ired for the low -level trans mis s ion through the TR tube to olim b to
SEC.525]
INERT COATINGS 221
w ith in 6 db of its cold va lue, fo five tubes . Thes e tubes w ere opera ted
at 500-kw pu ls e pow er w ith a duty ra tio of 1 to 2500 and w ith a k eep-
a live curren t of 150 pa . During the las t 200 hours of thes e tes ts , the
tubes w ere main ta ined at a tem~era ture of 100”C. Although the
recovery tim e and the leak age pow er w ere s atis factory for the dura tion
of the tes ts , it w as found that the un loaded Q of the TR tubes and
the cavity had fa llen from 2500 or 3000 to 1400 or 1900 , and the copper
cones had becom e covered w ith a redd is h copper oxid e.
Th oB e tu bes
charged in itia lly w ith the m os t w a ter s how ed the larges t change in QO.
At various tim es , a number of other chem ica ls and other m ethod s of
s torin g w a ter w e re p rop os e d .
S ilver oxid e is an uns table com pound tha t
m ain ta ins an equil brium pres s ure w ith 02; and th is oxy gen could be us ed
m the electron -capture agent. Copper s u lpha te w ith one molecu le of
H,O, is a very s table compound tha t gives off its w a ter very s low ly ; (no
quantita tive data for copper s ulphate are ava ilable}. h f. D. Fis ke s ug-
ges ted and la ter us ed as bes tos as an abs orbent; it is s im ilar to s ilica gel
but has a fla tter vapor-pres sure curve. S om e evid ence exis ts tha t z inc
ch lorid e , w hich is s ometim es pres en t in TR tubes as a s old er flux, m ay
giv e off C12s low ly .
If z inc ch lorid e w ere us ed in a tube w ith bras s w a lls ,
s uch as a 10-c.m bandpas s TR tube, an equilibrium w ould be reached as
the releas ed chlorine reacted w it h the tube w a lls to form ZnCla again .
With the exception of th e a s bes tos , th es e ch em ica ls h ave been th e s u bject
of s pecu la tion , bu t have not been us ed in d efin itive experim en ts .
5 .2 5. In ert Coa tin gs .
—The chem ica l res ervoirs of H?O, in ad{ltion
to their uns atis factory pres sure-tem pera ture curves , are undes irable
becaus e the continua l evolu tion of H20 res ults in the form ation of a th ick
copper oxid e on th e tu be electrod es .
Th is res u lts in a low er Q,, and the
Hz p res s u re is con tin ua lly in crea s ed .
The preferred m ethod of im proving the life of the tube is to m ain ta in
the H90 pres sure cons tan t by preven ting a reaction vith the electrod es .
Th is w as trea ted in a report by Guldnerl of the Bell Telephone I,abora -
tories , and w as applied to the 1B27 tube by H. J . lIcCarthy of the S y l-
van ia 131ectricProducts Co. The earl tubes tha t w ere tried had a lay er
of black copper oxid e (CUO) on the cones of the tube. The oxid e w as
made w ith a commercia l a lk a line s olu tion “ 1 3bonol.”
Thes e tubes
opera ted w e ll except th at, a fter a bou t one h un dred h ou rs of opera tion , th e
re covery time decreased and the leak age pow er increased, thus ind ica ting
an increas e of the partia l pres s ure of HZO. S imultaneous ly , the black
oxid e w as red uced in pa tches to a red cuprous oxid e, C’U20 .
The other tubes w ere made w ith a coa ing of Cu@ ins id e the cone
w h ere the k eep-a live electrod e is loca ted .
Thes e tubes s ho}ved a s ub-
‘ W. G. Guklner, “The Changein Compos itionof the Gas Presen t in a 721 .1Type
Tube as a Resu lt of Opera t ion ,”BTL hfk f -43-120-98 ,Sep t .22 ,1943 .
222
141RO$$7AVE GAS DISCHARGES
[SEC.5.25
stantially increased life, aslongas 7~hours with good recove~-timemd
leak age-pow er characteris tics . F gure 5:64 s how s the recovery tim e,
k eep-a live voltage d rop, and tota l leakage pow er as a function of
opera ting tim e for a ty pica l 1B27 ttibe w ith a CU20 coating.
Keepahve ~Cu20 coating
30 (a)
20 (b)
10
~+ [$ [l:W
(c)
200
‘02468101z
o
0123’ 456789
Hundredsof hours
Hundreds of hears
FIQ. 5G4.-Life test of 1B27 TIt tube;
FIG. 565.-Life test of 721A TR
(a ) keep-a live volt age dr op; (b) t ot al lea k-
tuhe with un t rea ted rones; (a ) r e-
age power , mm,, 1 ,usec pulses; (c) loss in covery t ime in ,usec for —6db trans-
signal, db, 6 psec after t r an smis sion puls e.
mission; (b] total leakage power In
mw.
Figure 5 .65 is a plot of recovery tim e and leakage pow er for an
unoxid ized 721A TR tube. Figure 5.66 is a s im ilar plot for a 721B tube
w hich is the s ucces sor to the 721A, and w hich has oxid ized cones .
~[~Ocoating
eep-alwe
I
‘:-
4 8 12 16 20
Hundreds of hours
FIG. 566. --Liie test of 721B TR
tube; (a) total leakage powrr iu mw;
(b) recovery times in pbec.
quenching to com plete fa ilure
A peculiar fea ture of thes e tubes is
the fact that the leak age pow er and
recovery tim e are cons tan t up to the
end ,of life, bu t then s ud denly increas e
rapid ly . In the unoxid ized tubes , the
recovery tim e increas es
continually
from the tim e the tube is firs t turned
on. A s im ilar phenomenon has been
obs erved in Geiger-Mueller counter
tubes w ith oxid ized anod es in w h ich , at
th e en d of life, th ere is a ra pid tra ns ition
from normal opera tion w ith good
to uuench .
.
S ince the developmen t of the Ck@ coating, it has been fo nd that
gold -pla ting the copper cones is a lmo t as effective as the CU20 in pre-
ven ting cleanup of the w a ter vapor.
Other d en se, inert coatings s uch as
m onel m eta l s h uld als o prove effective.
Alth ou gh th e cu prou s -oxid e
a nd gold -pla te tech niqu es h ave mult ip]ied th e lives of th e 1 13 27 ,7 21B, a nd
the 3 -cm bandpas s TR tube many tim es , they have not done s o for the
3-cm cell TR tube, the 72413. The life of th is tube has a maximum
value of 250 to 300 hr. Then , no matter how the cones are treated ,
the leak age pow er becom es exces s ive.
No explanation exis ts for this
SEC.526]
BANDPASS AND PRE-TR TUBES
223
d ifference; it may resu lt from the cleanup of the gas by s puttering. A
better unders tand ing of th is problem could be obtained if life tes ts w ere
run w ith a manometer s ea led to the tube s o that the partia l pres s ure of
HZ and H*O could be continually check ed . The tw o pres s ures may be
obtained by obs erving the total pres sure and then freez ing the HZO to
get the Hz pres sure.
The tife characteris tics of the 1.25-cm and 3-cm high-Q TR tubes are
quite d ifferen t from thos e of th 10-cm tubes . In the 10-cm tube, the
recovery tim e is u su ally th e lim it-
ing factor. In the higher-fre-
quency tubes , d iffus ion play s a
m uch s tronger rol in the recovery z
proces s than it play s in the larger E
1 0-cm tube, and con sequen tly the
recovery tim e is les s s ens itive to
the amount of w ater vapor in the
tube. The 1B24 3-cm tube has ,.,
r
1
500
‘w”’
8 12 16 20 24
Hundreds of hours
FI~. 567.-Life t es t of 1B24 TR tube;
keep-a live volt age dr op; (b) total leakage
a volume only 0.8 that of the ‘-’
ower in mw for +psec pu lse,
721A tube; but its us efu l life is
alm os t s ix tim es as great, a lthough no attem pt is m ad to inhibit the HZO
cleanup by inert coatings . Figures 5.67 and 568 are curves of leak age
pow er and k eep-a li e voltage d rop during the li~-es of ty pical 1B24 and
1B26 TR tubes . The recovery tim e after 2000 hours of opera tion is only
5 to 10 ~s ec for T = – 6db at a transm itter-pow er level of 40 kw .
6.26. Bandpas s and Pre-TR Tubes .—It is the intens e r-f d is charge
acros s the 1ow -Q input w indow that play s the dom nant role in
, 500
~ 300
0
Hundredsof hours
FIQ. 56S.-Life test of 1B26 TR tube;
(a ) keep-a live volt age dr op; (b) t ot a l leakage
power in mw for $-psec pulse.
changing the gas content of the
bandpas s and the pre-TR tubes ;
the k eep-alive d is charge has a l-
mos t no effect, The volumes of
thes e tubes are very large: the
1B38 pre-TR tube has a cubic
content of 110 cc and the 1B58
bandpas s TR tube has a volume
of about 400 cc, w h ereas the 721B
has a volume of only 25 cc. De-
s ~ite th is 1a r~e volume. the
.,
recovery time of a 1B38 pre-TR tube may becom e exces s iv ly long in
200 to 500 hours of operation at l-lIw pul e ow er w ith a duty ra tio of
1 / 2 500.
It is im portant to note the qualify ing \ erb “ may ” in the above s ta te-
m ent. If he 1B38 pre-TR tube is filled initia lly w ith argon and H,O,
the recovery tim e of th is tube w ill a lm os t invariably becom e too long in
224
MICROWAVE GAS DIS CHARGES
[SEC.526
the 200 to 300 hours. Fortu na tely , prod uction tu bes , w h ich w ere n om i-
na lly filled w ith argon alone, cou ld be opera ted w ith good recovery tim e
as long as thos e contain ing argon and HZO and very often longer.
In fact, s uch “argon filled” tubes often s how ed a s horter recovery tim e
after s om e tim e of opera tion .
Th is , of cours e, is as sum ed to ind icate
the evolu tion of gas from the tube w a lls .
Mea s urem en ts on commercia l
1B38 tubes ind icated for one of the tubes tes ted an increas e in pres sure
Time inusec
()
,;
T–
-
—
<
1
0 hours
)
1
-+
1
)
120 -
180 240
0
(
u
/
~
~, / ‘
/
f
FIG.5,69.—Recovew-t ime cu rve of lB3s p,e-’rR t ube f lled ~~t h 5 mm argon and
2 mm H?O.
of 15 per cen t a fter one hour of opera tion; for another tube, an
increas e of 38 per cen t after 1000 hours w as m eas ured .
It is not s ur-
pris ing that the recovery tim e remained fa irly s hort in thes e tubes .
What, is s urpris ing is that, w hen H,O is added to argon , the life is d efi-
n itely lim ite to a few hund red hours .
Figures 569 and 570 are ty pica l
curves for a 1B38 tube filled w ith 5 mm Hg of argon and 2 mm Hg of HZO,
and for a production tube filled \ vith 10 m m Hg of argon.
Bmd pa ss tu bes h ave received compa ra tively few con clu s ive life tes ts .
A 3 -cm tube, w hich had been gold -pla ted , ran for m or,e than 500 hours
a t 30-k w pu ls e po}ver, ~vith little or no change in perform ance.
Th e
1F, L, llcllillm , ~. H. Pearsall, 1 .H. lkarn ley , 10C. , Se r. 5.15,
SEC.5“26]
BANDPASS AND PRE-TR TUBES
225
10-cm bandpas s tubes , w h ich had no trea tmen t of the bras s w a lls , and
w ith in itia l fillings of 5 and 3 mm Hg, re pective ly , of A and HZO, an
for s evera l hund red hours w ith no change of recovery tim e. How ever,
the res u lts are s till inconclus ive and further s tud y of thes e tubes is
needed . One s erious cons id era tion is w hether a hard -s old ered 10-cm
Time inA sec
12
24 36
48
1
/
/
1
/
I
,
0 hours
I
/ ‘
I
/930 hou
rs
/
I I
[
1
/ -
/’ff
/
FIG.570.-Example of change of recovery t ime with life of a IB3S tube filled with
10 mm argon .
tube w ith its w a lls fa irly w ell ou tgas s ed w ould have a s horter life than
the pres en t tube. Although the pres en t “d irty ” tubes apparen tly have
long lives , th is is an ins ecure bas is for genera liza tion s o long as the
quality and the quantity of the
“ d irt” are not k now n and are not
controllable.
CHAPTER 6
THE TR AND ATR TUBES AT HIGH POWER
BY L. D. SMULLIN AND W. C. CALDVJEL
6.1 . In troduction . -Th is chapter w ill pres en t, in add ition to a s um -
m ary of the h igh-pow er characteris tics of the various h igh-Q TR tubes ,
a deta iled d s cus s ion of bandpas s and pre-TR tubes , and of ow -Q ATR
tubes at h igh pow e r.
The h igh-Q tubes to be d is cus s ed are the ty pes 72 B, 724B, 1B24,
1B26 , and the 1B27. Thes e tubes are all des igned to protect the mos t
s ens itive cry s ta ls now in us e and to protect them at any pow er level from
z ero up to a m axim um d eterm ined by d irect-coupled pow er, by harm onic
lea k age pow e r, or by the es tablis hm ent of s econd ary d is charges w h ich
m ight s horten the life of the tube.
Th e es ta blis hm en t of prod uction tes ts and s pecifica tion s that en su red
uniform tube quality Jvasa d ifficult tas k s ince the tes ts had to be d es igned
for us e by rela tively uns k illed pers onnel, and w ith on ly the s im ples t pos -
s ible equ ipm ent, As a res ult, recovery -tim e ch ara cteris tics a re s pecified
only as a ty pe approva l tes t und er the joint Arm y-l-avy (JANT) s pecifica -
tions , ~vhereas leak age pow er is a production tes t on mos t T R tubes .
In s om e of the earlier s pecifica tions , con id erable effort w as m ade to
d evis e [‘ equiva len t tes ts ” th at w ou ld m ea su re certain in trin sic qua lities
of the tube but at the s am e tim e w ould not requ ire the us e of pu ls e and
oth er comp lica ted techniqu es .
310re recen tly , how ever, the tend ency
interes t w hen the tube is in us e, and to meas ure thes e quantities under
s im ila r con dition s of u se. Th e va riou s tes ts and s pecifica tion s cu rrently
u sed w ill be lis ted .
In the s econd part of the chapter, the characteris tics of band pas s TR
tubes, pre-TR tubes , and 1ow -Q ATR tubes w ill be d is cus s ed . Thes e
tubes are characteriz ed , in genera l, by the fact that their m inim um oper-
ating pow e r level is cons id erably in exces s of that for high-Q tubes , that
they can be us ed at cons id erably h igher peak pow ers , and that their
d irect-cou plin g a tten ua tion is pra ctica lly in fin ite for both th e ca rrier a nd
the harmonic frequencies of the transm itter. Th is las t feature w as
s hared by only one high-Q tube, a tube de~-eloped by J. La}vs on and
B. Cork at the Rad iation Labora tory .
Becaus e it w as d eveloped at
about the s ame tim e as the bandpas s and the pre-TR tubes , it \ v as
n ever pu t in to prod uction .
226
SEC. 6.2]
HIGH-POWER CHARACTERIS TICS 227
The las t part of the chapter w ill pres en t a brief d is cus s ion of m anu-
facturing techniques and m echan ical d es ign techniques for both h igh-Q
a nd low -Q tu bes .
6 .2 . High-pow er Characteris tics of High-Q T Tubes . —Table 6 I
lis ts the various high-Q tubes and their characteris tics . Thes e charac-
teris tics are tota l leak age pow er (fla t plus s pik e leak age for s om e given
puls e length ), arc leak age pow er, s pik e leak age energy , recovery tim e,
k eep-a live voltage d rop, and gas con tent. The “s tarred” item s are
specif ied quantit ies .
The 721B tube, as can be obs erved from the table, does not have a
puls ed -lea ka ge-pow e r s pecifica tion . In s tea d, a m eas urem ent of the c-w
leak age pow er is m ade and is converted in to a quan ity PO (or P,). This
quantity is the reactive pow er s tored in the cavity , and is proportional
to the s quare of the arc voltage. 1 ,2
Tw o read ings are tak en, one at room
TABLE6.1.—HIGH-LEVELCHARACTERISTICSFVAEIOUSHI~H-(J ‘rlt TUBE+
Tube
721B
724B
1B24
1B26
1B27
1B50
Total
[;.s filh.g
Keey:,live
:::;; ttP.
leakage RP -
, t t rnHg
m mw
ilVr Es ~:ynt
inp~-a
AP,/PiCOvery
-oltge
in cm
drop a t
tinwt
100@
mm-
H, H,O
10
30t o40 0,04 .,, .,, *7t o30*o.5t oo.7
*3dh at 350 10 10
7 Alsec
3
20
0.05
’40 ma. 3db at 400
10 7
3
10
4 AISec
0,02
*3Oma,
*3 dh a t +325 t o 450
15 15
‘1LIs,.
1.25 15
0.05
*2,5ma, ...
,. .,,.
*3 (ill a t *32.5to480
1[)
10
4PSec
10 15
0.03
*25 ma. ,. *3 db at .370 t“ 480
1,5
10
5 IIs, .
4 18 ZVK
300 to 425
20
2(I
* See Pa r&graph1 , Sec. 6.2.
t t Th e 721A a nd 1B27 wer e m ?z,u red wit h (], = 2500, L=–1.5 cIII,mat ched input.
t P,,lseengt h 0.5 w.. for a ll t ul,es except for t he 1B50 wher e it is 0.35 ~e.,
I The t ransmit te r -power Ievcl is 501iW {m the721Band lB2i, 101iW for t he 1B24, a nd 8KIV for
tem pera ture, and one ~vith the w ater vapor frozen out at d ry -ice tem -
perature. The va lue Pi at room temperature, and als o the change
AP/ Pj w hen the w ater is condens ed , are s pecified . Together, thes e
va lu es give a rea s on ably a ccu ra te in dica tion of th e rela tive proportion s of
H~ and HZO in a tube of a given ty pe, tes te under k now n cond itions .
Th is tes t s u ffers from the fact that Pi is a s ens itive function of the
1Samue l,L1cCrw , and [umford , “Gas Discharge TR Swit ch , ” BT1, ilfh l--l2.
140-26,+pril 27, 1942.
2 Sinclair, Garoff, Gilbarg,
“ Xreasurc. mrnts of ~T:M Fillings in 721A ‘rI1 TtI}ws,
(XS1, Repor t No. T-18, Sept . 11, 1943.
228 THE TE AND A TR TUBES rt T HIGH POWER
[SEC.62
incident pow er level if it is les s than about 0.5 to 1 w att (s ee Fig. 5 .23);
furtherm ore it gives no ind ication of k eep-a live effectivenes s , and con-
s eque tly no ind ica tion of s pik e leak age energy . 1
The other tubes have a s pecified total leak age pow er at s om e definite
line puls e pow e r and puls e length .
At the tim e thes e s pecifica tions w e re
w ritten, beca us e of the com plica ted apparatus and techniques involved ,
it w as not deem ed advis able to a ttem pt to m eas ure s pik e leak age energy
a nd a rc lea k age pow er s epa ra tely .
For s ome time the method for meas -
uring tota l leak age pow e r at tw o d ifferent pu ls e lengths and then com pu t-
ing W. and Pa on the as s umption that Pa is cons tant had been know n , but
ha never been applied (Chap. 9).’
An attempt w as made to determ ine the quality of the 1B27 tube, the
gas conten t, and the k eep-a live effectivenes s , by measuring the tota l
leakage pow er w ith the k eep-a live on and w ith it off. .41though the
s pecifica tion has rem ained in force, the conclus ion m us t be draw n that
th is tes t w as not too s ucces s fu l, and that only the tes t w ith the k eep-
a liv e on had any s ign ificance .
Th e tes t in dica ted , h owe ver, th at n o d ra s tic
change in production technique occurred from day to day .
Th e fip eci-
fica tion s for the 72 4B, 1B2 -!, and 11326tu bes requ ire on ly a m ea su rem en t
of tota l leak age pow er w ith the k eep-a live on.
In the tunable tubes , w ith the exception of the 1B50 tube, the leak age
pow er is a function of gap s pacing.
Xo particular gap length in inches
is s pecified , but it is r qu ired that the tubes be tuned to a s pecif[ed fre-
quency in ord er that the leak age pow e r m eas ured w ill be tru ly ind ica tive
of th e op era tin g p erformance.
The maximum pow er at w hich thes e tubes may be opera ted is d iffi-
cult to define exactly , The 1B24 tube w as initia ly rated (unofficially )
at a pow er near 100kw , at w hich level a s econdary d is charge is es tab-
lis hed jus t back of the input w indow . When high-po!rer 3 -cm magne-
tron s (2 00kw ) became a vaila ble, th e 1B24 tube w as tes ted at the higher
polver level. In initia l tes ts , tu bes a~aila ble at the Rad iation La bora tory
failed after 10 to 10 hours . In all the tes ts the leakage pow er increas ed
m ark ed ly , and in m os t tubes the ins ertion los s increas ed .
La ter, in tes ts
on tubes of m ore recent m anufacture and ~vith care tak en to k eep s older
flux and exces s s older out of the cavity ,
tubes \ vere run for 500 hours .
I Although this test gave a good correla t ion ~vlth leak~ige po\ ver ancl recovery time
in the 721.1 tube, the correla t ion changed completely when the oxide coating was
wdded to make the 72111. his ~vas olmcrved ~t E~-ms SWml Lal)ora tory in 1945,
but no explanation of it ~ras advanced up to the end of the war .
z This m~thod was apparcnt [y developed inctcpelldcr it ]y at th? Radiat ion Labora-
tory and at the Bell ‘~elephone Ltilmrator ics.
J . W’. (’la r k,
“The Gas J )isch t irge S\ r itch ; VJ II. A \ Iet hod of Arudyzing I.ca!i-
r ige Power Data, ” BTL hf }1-43-1 40-5 , (X>t . 11, 1943.
s Sn lu llin u nd I,eit c, r ,
“ Tl,c 11127 TR T{ IFw, ” RI, Repor t \ -(). 5!)4, (M. 4, 1944.
SEC. (Y2]
IIIGH-POfi’ER CHA RA CYERIS T ICS 229
Th es e tu bes ga ve n o ind ication of s eriou s d eteriora tion , alth ough a fa irly
in tens e d is charge w as m ain tained acros s the input ~vind ow .
Whether
or not s uch performance is characteris tic of all production tubes w as
never de fin ite ly e s ta~>lished .
The 721R and the 11127tubes are us ed s ucces s fu lly a t pow er levels
of the ord er of 1 31w S(J long m the harmonic conten t of the transm itter
is low . At pow e r le~els greater than 1 31N-them is , in the s mall-d iam eter
cavities , a tendency for a d is charge to s trik e acros s the glas s cy linder
ad ja cent to th e inpu t cm lplin g.
It is belie~-ed th xt th is d is ch arge a ppre-
cia bly s hortens the tu lw life.
Som e magnetrons , Jvhen opera ted at high pow er levels , s how a
tend ency to s park occas ionally and als o to jump in to an inefficien t
electron ic m ode that is very rich in harmonic conten t.
A magn etron
w h ich opera ted in th is Ii-a y w a s
firs t n oticed ~vh en J i O-cm duplexer u s in g
1B27 TR and ATR tulw s ;~:w t e ~tm l \ rith the -LJ44 s eries of m agnetrons
at pow e rs near 1 31v:.
J 1’h eu :1 h au l-tu be modu la tor ~va su s ed , th e 1 13 27
tube protected cry sta ls [or long period s at a line pow er of 1 MN-. When
a s park -gap modula tor lras us ed ,
holvever, cry s ta ls u’ere burned out
a lmos t ins tan tly . A long s eries of experim ents by L. D. Smullin and
A. }Y. La~vs on fina lly es tabl s hed the fact tha t thes e burnouts w ere
coincident w ith the s park ing of the magnetron , and that during thes e
period s exces s ive lea ka ge po]rer d id n ot occu r at th e n om ina l w a velen gth
of 10 .7 cm , but w as pres en t a t the s econd , th ird , and fourth harmonics
of a 9 -cm mode. That th is w as another magnetron mode that could be
excited und er certa n cond itions of the r-f load ing and exciting circu its
w as s how n la ter by Clogs ton and Riek e. .~ number of a ttempts to put
harmonic filters in to the TR cavity \ \ -eremade, but none of the filters
gave enough attenuation over a s ufficien tly large frequency range. It,
w as es timated that a m inimum of 30 db of add itional a ttenuation at a ll
harmonic frequencies w as needed to ens ure cry s ta l protection , This
particu lar problem w as fina lly s olved by the us e of a pre-TR tube’
ahead of the 1B27 TR tube. The pre-TR tube w ill be d is cus s ed further
in the s ections on 1ow -Q and bandpas s TR tubes .
Tube life w as s till a ra ther indefinite quantity even as la te as the
end of the w ar. Although laboratory life tes ts on dozens of 1B24 and
1B26 tubes ind ica ted a usable life of 2000 hours or more, the life of the
1B24 tube in the field s eem ed to be on ly a few hundred hours . Com -
paratively few tubes w ere returned for exam ination but thos e few tubes
ind ica ted that about 40 to 50 per cen t of the tubes mark ed 1’bad” w ere
bad tubes originally , and m os t of thos e had air leak s at crack ed w ind ow s
or s older join ts . As a res u lt of th is xperience w ith the 1B24 tubes , a ll
1L. D. Smullin , “’The 1B38 P re.TR, ” RL Repor t h ’o, 641, Dec. 5, 1944.
230
THK TR A.VD A TR TUBES AT HIGH POWER
[SEC. 6.3
TR tubes w ere requ ired to pas s a ty pe approva l tem pera ture-cy cle tes t
of half-hour expos ures to – 55°C, to room tempera ture, and to 100”C.
Thes e tes ts had to be repea ted fifty tim es \ vithou t fa ilure.
Res ults obta ined w ith 721A tu bes ~~ere th e oppos ite of th os e obta ined
!rith the 11324tubes . Labora tory tes ts had s how n that recovery tim e
l)ecame unduly long after a life of abou t 300 to 400 hours , a lthough
cry s ta protection w as good for more than 1000 hours .
It ~vas very
d ifficult to pers uad e s ervice pers onnel to replace the tubes frequen tly
enough.
Th e 72111 tube has a life of 1000 hours or more, and the 1B27 tube
opera tes for a out, 700 hours .
The 724B has a life of approximately
250 hours , a t the expira tion of w h ich it w ill no longer protect cry s ta ls .
6 .3 . High-level Characteris tics of Bandpas s and Pre-TR Tubes and
Low -Q ATR Tubes . —I3 rea k clow n a nd recovery a re fu nd amen ta l p roces s e s
of both the high-Q and the IoN-Q or bandpas s tubes .
Th es e ph enomena
are, in genera l, m ore com plica ted in the hand pas s tubes s ince as m any as
three or four d ifferent d is charges m us t be cons id ered , w hereas in the
h igh-Q tubes on ly one d is charge need be cons id ered . The in tens ity of
the various d is charges in a band pas s tube varies hy ord ers of m agnitud e,
and s om e probably las t for on ly a fraction of the period of the trans -
m itter p uls e ,
The loaded Q’s of the res onant elem en ts in bandpas s tubes are low er
than th os e of con ven tion al high -Q tu bes by factors of 5 0, a pproxim ately ,
As a res ult, the voltage bu ildup acros s the gaps follow s the m agnetron
ris e w ith a lmos t no tim e delay and cons equen tly the en tire s pik e-
trans ient analy s is becom es qui e d ifferent from that of the h igh-Q tube.
The fact that s evera l gaps fire in s equence w ithin a tim e interva l of
abou t 10–s s ec probably m ak es the “fine s tructure” of the s pik e of a
ba nd pa ss tube very complica ted in deed .
One of the mos t s trik ing features of the low -Q tubes , as they exis t
today , is the d is charge w hich covers the inpu t w indow . At very low
pow er levels , the d is charge is jus t a filament acros s the cen ter of the
~~ind ow .
As th e pow e r is in crea sed , the d is cha rge s prea ds un til it covers
the en tire w indow w ith a smooth glow . The pow er d is s ipa ted in the
d is charge is very large. An argo -filled 10-cm tube s uch as the 1B38
pre-TR tube may have a puls e d is s ipa tion of 5 to 7 kw , as compared
w ith 5 to 10 w atts for an argon-filled h igh-Q tube, or 50 to 60 w atts for
h igh -Q tu bes filled w ith an H2-H10 m ixtu re.
The arc leak age pow er of a ty pica l bandpas s tube is 30 mw or les s ,
and s pik e leak age energy is about 0 .1 erg. Corres pond ing va lues for
h igh-Q tubes are 20 to 30 m and 0 .03 erg. It is w ell k now n that both
Pa a nd W , in crea s e ra pid ly a s th e loa ded Q (Q~Z) in h igh -Q tu bes d ecrea s es .
In fact, the 1H24 or 1B27 tubes no longer protect cry s ta ls if QL2 is m ade
les s tha n a bou t 2 00 . IIo~~-cry s ta l protection is obta in ed ~vith th elo~\ -fJ
elem en ts in band pas s tubes has not been com pletely d eterm ined .
It is found tha t the s pik e leak age energy varies invers ely w ith Q.,
(m ore s pecifica lly the outpu t Q, Q..,) w hen no is k ept cons tan t, bu t tha t
it d oes not vary in th is w ay w hen the equi~a len t conductance, or k eep-
a live in tera ction , is k ept con sta nt.
Practica lly a ll m eas urem ents of W.
vs . QOU,have been m ad e w ith cons tan t k eep-a live curren t and loca tion
(con s tan t rzO).
Thes e experim en ts , therefore, cannot be us ed to give a
curve for high va lues of Q.z that cou ld be extrapola ted to m eet the
obs erved va lues of W, for very low QLZ. R ugh ca lcu la tions s im ilar to
thos e ind ica ted in S ec. 56 s how that for a cons tan t va lue of in teraction ,
W , changes very s low ly w ith Q..,.
The arc lea age pow er of a 7Z1A TR tube filled w ith an H,-H,()
m ixture is about 40 mw , for QLz = 300 and”an ins ertion los s of 1 .5 db.
Th is corres pond s to a voltage acros s the d is charge of 100 volts rm s .1
The s ame tube filled w ith argon m ight hay -e a voltage d rop of approxi-
ma tely 3 volts . Convers ely , a ty pica l bandpas s tube filled w ith argon
has a fla t leak age pow er of 1 mw or les s , w hich corres pond s to a gap
voltage of abou t 3 .5 volts , if the elem en t trans forma tion ra tio is tak en
as 5 . A m ixture of A-HA3 gives P= = 20 mw and a gap voltage of about
]5 volts. Thes e num bers becom e rough ly com parable if a correction is
made for the gap length , w hich is abou t 0 ,030 in . in the h igh-Q tube,
and 0 .008 in . in the bandpas s tube. How ever, the neces s ity to explain
a s e lf-s u s ta in ing d is cha rge w h ich
has a tota l voltage d rop les s than
Keep.al;ve
)
the ion iz ation poten tia l of the gas
rem ains . Th is effect has a ls o been
High ~er
To receiver
v
X!/
W2
obs erved in electrod eles s d is -
A
91 tJ2
charges a t low er frequencies and
h as b ee n rep orte d in th e litera tu re
Fm . 6 .1 .—Cro.s sectionof a 3-cInba ndpa ss
b y va riou s a uth ors .
TR tube , 1B63 .
In ad dition to arc leak age pow e r, h igh-Q tubes have d irect-coupled
and harmonic leak age pow ers , and either one may be larger than the
arc leak age pow er. Band pas s tubes nd pre-TR tubes have practica lly
in fin ite d irect-cou plin g a tten ua tion beca us e of th e d is ch arge tha t covers
the input w ind ow s . Harm on ics a ls o are very h igh ly a ttenuated .
Figure 6 .1 is a cros s s ection of a 3 -cm bandpas s tube (1B63) w ith
tw o res onant gaps and tw o low -Q res onan t w indow s . The k eep-a live
electrod e is at the gap clos es t to the receiver.
Although no d irect
experim en ta l d eterm in ation s h ave been ma de of th e brea k dow n s equ en ce,
it is believed to be as follow s . In the in terva l tO< t < tl, Fig. 62 , the
1H. A Bethe, R. E. Marshak, and J . Schwinger
“Th eor et ica l Resu lt s on t he TR
Boxj” NDRC Repor t No. 14-116, 10C.cit ., Cor nell Un iv., J a n. 20, 1943.
232
Tlffi TR A Xll A TR T1”BE,Y AT IIIGIi POWER
[SW 6.4
voltage build s up acros s the gaps and is in phas e w ith the transm itter
voltage. At about II the electron ic conductance of the s econcl gap gz ,
w h ich has th e k e ep -a live e lectrod e, be gin s to in crea s e ra pid ly , a s d es crib ed
in S ec. 56. During the in terval t, < t < tz , the impedance acros s th is
gap is very low , and the s tand ing w a ve w h ich res ults d oubles the voltage
at the firs t gap gl. Th is gap depend s for its in itia l ion ization no upon
ca rry -ove r from th e p re viou s d is ch arge and pos s ib ly u pon photoe lectron s
releas ed by the light from the d is charge in the s econd gap. Although no
is very small, t he doubled voltage which resu lt s from the breakdown of
the second gap probably breaks down the fir st gap almost instan t ly.
This, in tu rn , causes the volt age to double at the inpu t window wI, and
th is, t oo, fina lly breaks down .
The d irect-coupling attenuation through a fired gap is about 30 db.
Thus , the pow er incid en t upon the s econd gap ga is the s um of the arc
leak age pow er of g, and the w indow leak age pow er attenua ted by 30 db.
This pow er is probably 20 to 50 mw w hich is not s ufficie t to maintain
the d is charge at gz . The electron ic load ing at gz , how ever, does not d is -
appear ins tan tly ; therefore ~vh ile the gap is recovering, the le k age
pow e r, incid ent upon the receiver, varies from about 0 .001 of the leak age
pow er through gl up to the fu ll leak age po}ver through gl. Th is is illus -
tra ted in curve A of Fig. 62 , Curves s im ilar to B and C are obs erved
w hen the amount of HZO in the
tube is reduced , w ith a cons equent
‘L
increas e in the recovery tim e. In
1 0-cm tu bes , the fla t leak age pow e r
is us ually too small to be s een on
an os cillos cope. Although t e s ts
to
t~ t~ t~
t4
have not been made, it is believed
Time
that w ith a 5 -ps ec tra nsm itter pu ls e
FIG. 6 2.—Leakage power envelope of
a
the leak age pow er envelope of a
3-cm bandpass TR tube.
10-cm tube w ould be s im ilar to that
of th e 3 -cm tu be a nd th at th e a rc lea k age pow er wou ld be come a pprecia ble.
In the 3 -cm tube th e ch aracteris tics illu stra ted in Fig. 62 can be obs erved
w ith O.5 -p s ec tra nsm itter p uls e s .
6 .4 . Spik e Leakage Energy .-In bandpas s tubes as in high-Q TR
tubes , the margin betw een cry s ta l protection and burnout is much
narrow er for the s pik e leak age energy than for the fla t leak age pow er.
As a res ult, m os t experim en ta l effort w a s d irected tow a rd s the red uction
of W,, and the fla t leak age pow er received more or les s perfunctory
attention.
The experim enta l w ork can be clas s ified in three main d ivis ions :
gap des ign, gas con ten t, and k eep-a live des ign. The firs t d ivis ion , ga
d es ign , involved the problem of d eveloping res onant elem ents w h ich had
$EC. 64]
S PIKE LEAKAGE EM7RGY 233
the s malles t product of QLZ . W,.
I?orth es e experim en ts , it w a s tacitly
as s umed (and th is as s umption w as Mer partia lly verified ) that a gap
des ign w hkh gave optimum performance for one gas w as equally good
for all other gas es . This s implified the experim ent al technique, for
aft e r the gap des ign w as chos en , it ~vas n eces sary on ly to determ ine the
gas filling of the tube for the lon es life, the s hortes t recovery tim e,
and the leas t leak age pow er.
In Sec. 6 .3 it w as s een that the fla t leak age pow er w os far from corl-
s tan t d ring the puls e. Becaus e of th is , it w as d ifficult to s epara te the
s pik e trans ien t from the arc link age pow er by the us ual techniques of
cancella tion or puls e-length increment (s ee Chap. 9). The us e of pure
argon , how e ver, res ulted n a very s m a l arc leak age pow e r, and the s pik e
leak age energy cons titu ted more than 95 per cen t of the tota l energy in
the ieak age pu ls e. Thus , s ince there is uncerta in ty concern ing cm Iy a
small percenta ge of the pow er, it can
be as s umed tha t the tota l energy is
equal to the s pik e energy .
Window Leak age.—The des ign
of the input w indow has been bas ed
p rimarily upon low -le ve l con s id e ra -
tions of QL2 and upon d is s ipa t ve
los s . The leak age pas t a ty pica l
w indow is of the order of hund red s
of ergs com pared w ith the tent s of
an erg that is actually incid ent
upon the receiver. Figure 6.3
s how s the tota l leak age energy
through various low -Q res onant
w indow s for various pres s ures of
argon . Curve A k the leak age
energy through a 1B38 pre-TR
tube, in w hich both w indow s have
Q., ~
1 and a height of 0 .875 in .
The m eas urem ents w ere m ade w ith
a trans mitter-pu ls e pow er of 50 k w
at 10.7 cm bu t ch eck mea s uremen ts
m ade at 1000 k w agreed w ith thes e
d ata w ith in th e experim en ta l ‘error
&o
6000
-m
4000
A 0,875
B 0.250 in.
2000
C 0.125 in.
D 0.063 in . ,
,1
1000
0
---
I
AIM
L I
Y
cl
Argon pressure in mm of mercury
FKO. 6.3.—Leaka ge-ener gy cha ra ct er -
ist ics of var ious 1ow-Q glass windows. A
is for a 10-cm window, and 1?, C, and D are
for 3-cm windows .
of about A 1 db. The arc leak age pow er w as about 50 w atts t a
pres sure of 10 mm Hg of argon, and t us cons titu ted about one-th ird the
tota l energy for a l-~s ec puls e.
Curves B , C, and D of Fig. 6 .3 give the tota l leak age energy for three
Ii fferent w indow s meas ured at a w avelength of 3 .2 cm . Their heights
234
THE TR AXI) A TR TL’BES AT HIG[{ IWII’ER
[SEC. 64
w ere 0.250 in ., 0 .125 in ., and 0.063 in ., res pecti~-ely , and Q~2 WaS 1.1 ,
2 .1 , and 6. There is not the l-to-l ra tio bet w ecn s ucces s il-e curves that
w ould be expected if the break dow n voltage w ere a linear function of
the w indow height, one tes t a t 8 .5 cm d id give a fourfold change in
total leak age pow er w hen a w indow w ith one-half the height of the
s tandard one w as us ed . At the pres en t w riting it is not clear w hether
th is repres en ts poor experim ental technique or w hether it res ults from
th e fa c th at brea k dow n a long a d ielectric s u rfa ce is a h igh ly comp lica ted ,
a nd litt e u nd ers tood ph enomenon .
The curves illus tra te pres s ure dependence of the us ual ty pe w ith
fa irly w e ll-de fined min ima .
For the 10-cm tube at leas t, in ~~hich the
arc leak age energy is about 3 per cent of the total leak age energy , the
m in imum has little th eoretica l importa nce.
This m inim um is the res ult
obta ined by add ing the curves (autom atically ) of W. and pa w hich have
d ifferen t s h ape s a nd d ifferen t m in ima .
The data pres en ted in thes e curves w ere obtained w ith the leak age
energy of the w indow d is s ipated in a m atched receiver load .
In actu al
us e, as in the input w indow to a handpas s tube, the voltage buildup
acros s t e w indow follow s the m agnetron very clos eiy until the break -
dow n of t e res onant gap one-quarter guide w avelength aw ay from it
ca us es the voltage to d ouble
This m us t undoubted ly change the s pik e
tra ns ien t, an d it proba bly red uces th e s p]k e !ea ka ge en ergy in cid en t u pon
the next gap. The extent of th is reduction in energy is not k now n, nd
is p robably of little pra ctica l importa nce.
A ca th od e-ra y os cillogram of
the s pik e trans ient in a 1B38 pre-TR tube w as s how n in Fig. 511 and a
d is cus s ion of this trans ient is found in S ec. 56.
Carefu l cons ideration of Fig 63 em phas iz es the fact that at a w ave-
w ould be about 1 to 2 ergs .
Furtherm ore, if thin m ica is us ed ins tead
of glas s , the height of the w indow may be reduced by a factor of almos t
tw o and thus the tota l l ak age through a w indow w ould be w ell below
1 erg.1 This , together w ith the fact that 1 .25-cm cry s ta ls (1 N26) can
w iths tand about 0 .3 erg of s pik e energy , s hould mak e it pos s ible to
des ign a very s im ple band pas s TR tube for th is w avelength .
The pre-TR tube is us ed in conjunction w ith a high-Q TR tube in
ord er to m inim iz e both harm onic and d irect-coupled leak age pow er. To
ens ure proper opera tion , the trans m is s ion line betw een the tw o-tubes is
ad jus ted s o that the d etuned high-Q cavity prod uces a voltage m axim um
at the input w indow of the pre-TR tube. S ince the pre-TR tube is one-
quarter guide w avelength long, the connecting line is m ade one-half
guide w avelength long. It has already been s een in Chap. 5 that the
I
Some u npu blish ed r esu lt s of exper im en ts by C. W. Za bel a t t he Ra dia tion La bor a-
t or y con firm t his.
SW. 65] ,~PIKE LEAKAGE E,YERG F, GAI’ l) ES IG.Y
235
inpu t admit t ance to a TR cavity dur ing the en f ir e spike t ransient is very
Ii)r~e compared \ r it h 1’,; th erefore, the prc-TR tube is working in to an
open circu it du r ing the en t ir e t ransmit ter pu l~e, and the leakage energy
is presumably smaller than when it is termina ted in a matched load.
6.5. Spike Leakage Energy. Gap Design . —Early exper imen t s on
bandpass TR tubes were concerned pr imar ily w-ith the developmen t of
a tube tha t wou ld \ vork . The pressu re of ~~ar rna (lc it necessa ry in th is
exper imen ta t ion to use many in tu it ive deduct ions and ext rapola t ions
based upon insufficient da ta .
on ly a fter a usable tube had been pro-
duced was it possible to make a systemat ic study of the in fluence (jt ’
va r ious pa rameters on Iea lmge energy character ist ics. This systemat ic
invest iga t ion 1 begin in 1944 and ended at the close of the war in 1945.
The leakage pow er through a complete bandpas s tube is a compli-
ca ted fu nction and res ults from th e s uperpos ition of s evera l d ifferent d is -
charges . From a narrow pragmatic poin t of view onl the tota l leak age
energy is importan t, and n fact m os t leak age-pow er data \ \ -eretak en
w ith complete tu bes .
There can be no d oubt, ho~vever, that a com plete
und ers tand ing of w hat happens w ith in a s ingle gap w ould im plem ent the
des ign of a better tube than any now in exis tence.
Figure 6 .4 s how s the leak age energy from 3-gap, -cm bandpas s TR
tubes w h ich have d ifferen t gap des igns , as a function of argon pres sure.
The arc leak age pow e r is negligibly s m all, and therefore the tota l energy
is nearly equal to the s pik e leak age energy . .111gaps are of the ty pe
illus tra ted in Fig. 331 and all the curves exh ibit the fam iliar s hape of
lea k age-p ow er cu rves w ith ra th er pron ou nced m in ima .
Figure 6 .5 is a plot of the s quare root of the leak age pow er (W~~)
agains t gap s pacing at an rgon pres sure of 10 mm Hg and is bas ed upon
data tak en from Fig. 64 . With the exception of the smalles t gap
s pacing, the poin ts define a s traight line pas s ing through the origin .
Th is is to be expected if the voltage trans form ation ra tio is cons tan t for
the various gaps , and if the grad ient increas es linearly as g-’.
The poin t for the s hortes t gap (0.0017 in . ) lies above the s traigh t line
defined by the other three poin ts and the origin . It may be pos s ible to
clarify further this behavior by a cons id era tion of the electrons los t to
the electrod es . In general the electrons in an r-f d is charge s uffer a lm os t
no net d is placem ent in the d irection of the field , and therefore very few
are los t to the electrodes . There is a small region ad jacent to the
electrod es , w hich is o the ord er of one mean free path long, through
wh ich el ctron s may be a ccelera ted and th us rea ch the electrod es .
With
I Most of the leakage power data , par t icula rly on 3-cm tubes, were obta ined at the
GE Resea rch Laboratories by the group under M. D. Fiske. W. C. Caldwell of the
Radia t ion Labora tory worked with th is group for a lmost a yea r on the development
of the 3-cm tube.
236 T{[E TR A Y ll A TR T1’RE,$’ AT TI[C17 P(?W177i’ [S E(-. 65
lnutn frcv paths d t}m oi-d cr of ().(Ni in ., the tw o regions ad jacen t to
th e clectm d es ocru l)y a ]a rg(, pu tt, (If tile tot id g~p of (),0 ()4 7 in ., bu t for
larg r gaps they are les s im porttin t. ‘IIe low of electrons by th is m ech-
a nism requ ires a h i@f~r ra te of elcrtron prod uction a nd , th erefore, h igh er
gap voltages m d higher s pik e leak age rnergy . Th is phenom enon is ver
s im ilar to tha t w hirh mus es the m in imum f the Pmchen curve for d -c
breakcloli-n. S im il:lr eflert,s frere obs erved by Pos in in a s tud y of r-f
b rez k d ow n in ~va veg~lidw a t a tmos ph eric p res s u re . 1
10.0
8 ,0
6.0
4.0
%
.: 2.0
&“
@ l,fJ
$ 0.80
& 0.60
~
& 0.40
~
.-
$0.20
0.10
0.08
0.06
2 4 6810
40
Argon pressure in mm o;%ercury
FZQ.
6.4.—Snike leaka~e
ener zv
u mroils
FIC. 65.-The square root of the spike
th rough 3.cm bandpass TR- tubes f&
leakage energy of Fig. 6.4 plotted against
va ri0u8 gap spa cin gs.
gap spacing for a pressu re OJ 10 mm Hg of
argon.
The in fluence of the particu lar s hape of the end s of the electrod es
upon s pik e leak age energy has been for s om e tim e the s ubject of con tro-
versy .
It rema ins an open ques ti n . It is argued tha t if poin ted elec-
trod es are us ed , the gap length required to tune a given res onan t elem en t
w ill be les s becaus e of the s ma ller capacitance betw een the end s .
Since
l?’,% decreases a lmos t linearly w ith gap s pacing, the s m alles t gap s hou ld
give the s ma lles t va lues of leak age energy .
Bu t there is a ls o evid ence
to s upport the conten tion tha t th efective volum e of a gap has a s trong
1D. Q. Posin , 1. Mansur , 11. Clarke,
,, Exper imen ts in Micr owave Breakdown,”
RL Repor t No. 731, Ifov. 28, 1945.
SEC.66]
DIRECT-COUPLED SPIKE LEAKAGE ENERGY
237
influence upon the s pik e. That is , for equal gap lengths , the gap w ith
the larges t volum e s hould break dow n at the low es t voltage s ince the
probability of fin din g an electron w ith in th e region of h igh field is grea tes t.
No d efin ite com paris on of thes e tw o argum ents has been m ad e although
s ome ind irect experim ental evidence e is s in s upport of each point
of view .
The 3-cm tube (1B63) us es truncated cones , and the 10-cm
tubes (1B55, 1B58, and the 9. l-cm tube) have pointed electrodes ; but it
is not pos s ible to d eterm ine from their perform ance w h ich gap is better.
A d irect comparis on of the tw o gaps made at the s am e w avelength and
w ith the s am e m eas uring equipm ent w ould be a s traightforw ard experi-
m ent, and w ould be w ell w orth w hile.
The analy s is res en ted in S ec. 3”3 ind icates that the s pik e energy of a
low -Q res on an t ga p s hou ld va ry d irec ly w ith th e s us cepta nce of th e in du c-
tive iris , and invers ely w ith the area of the electrodes w hich form the
gap. If the valid ity of th is rela tions hip could be es tablis hed it m ight
elim inate fruitles s experim entation w ith odd gap s hapes in the effort to
com bine m inim um QL2 w ith m ini-
m um leak age energy .
1 .0
6.6 . Direct-coupled Spik e 0,8
Leak age Energy . -In Chap. 3 it ~ 06
w as s een that the d irect-coupling ~ OA
attenuation t h r o u g h a ty pical ~
resonant gap is 25 to 30 db. The ~ oz
s pik e leak age energy pas t an input 5
w indow is about 1000 ergs in 10- 0 12
4 6S10 20
40 60SO100
cm tubes , and about 100 ergs in
Argonpressurein mmof Hg
3-cm tubes . Thus , it is evid ent
l~lu,6.6.—Spikeeakageen er gy t hr ou gh
s ngle gap 3-cm bandpass TR tubes with
that the energy leak ing Pas t the &fferentinpu t -window heigh t s,
firs t gap can not be les s than
about 1 erg and 0.1 erg res pectively , for the tw o tubes , even if the gap is
‘ completely sh ort-circuited.
Figure 6.6 s how s the s pik e leak age energy through on e-gap ban dpas s
tubes w ith input w indow s of d ifferent s iz es . Curve A is for a tube w ith
an input w indow & in. high, and c rve B is for a tube w ith a ~-in .
w indow . The gap us ed in each tube had the follow ing d im ens ions :
o = 45°, d = 0.030 in ., w = 0.250 in . (Fig. 3.33) and it had a d irect-
coupling attenuation of 35 db. By referring to Fig. 6 .3 , it can be s een
that at a pres s ure of 10 mm Hg of argon, the w indow s pik e leak age
energy is 90 ergs for the ~-in . w indow and 25 erg for the &-in . w indow ,
res pectively . Thus , if the gaps are s hort-circuited during the entire
puls e, leak age energies of about 0 .3 and 0.08 erg through the tw o tubes
can be expected . The obs erved values w ere 0.24 and 0.13 erg. Although
the curves of Figs . 63 and 606 w ere tak e at d ifferent tim es and none of
238 THE TR AND A TR “TUBES AT HIGH POWER
lSEC.&7
the tubes w e re bak ed ou t before filling, there is nevertheles s good agree-
m ent betw een the m eas ured and the pred icted r s ults .
At th is poin t the ques tion that m os t naturally occurs to the tube
d es ign er is w h eth er it is p s s ible to m eas ure s e a rately the lea ka ge pow e r
ch ara cteris tics of a w in dow and of a res ona nt gap, and to pred ict for a tube
w ith one or m ore gaps the res ultant leak age characteris tics . At pres en t
th is is not pos s ible. Although fa irl com plete data on w indow leak age
ha ve been com piled ver little accurate in form ation exis ts regard ing the
leak age characteris tics . of a s ingle res onan t gap. M. D. Fis ke has m eas -
ured the leak age characteris tics on 3-cm gaps , and L. D. Smullin and
C. Y . Meng made S im ilar m eas uremen ts on 10-cm gaps . The experi-
m en ts w ere m ain ly explora tory and have not been publis hed .
One of the m os t s erious d ifficu lties encoun tered in the early experi-
m en ts for the com paris on of the leak age energy of various gaps w as the
fact tha t the tubes w ere not clean .
Th is d ifficu lty d id not occur w ith
glas s tubes s uch as the 721A s ince the tubes had to be clean in ord er to
form the copper -gla ss seals. The bandpass tubes, however , a re, except
for the windows, of a ll-meta l c nst ruct ion, and a ll pa rt s a re assembled
y solder ing. Unless grea t precaut ions a re taken, the leakage charac-
terist ics of a soft -soldered tube will be ser iously a ffect ed by many imp ri-
t ies in its gas cont en t . Hard-soldered tubes a re easy to keep clean but
it is difficult to modify them after they are assembled. It is, t herefore,
oft en desirable t o use soft -soldere exper imenta l tubes, but it is neces-
sa ry to clean the tubes thoroughly after solder ing.
A grea t dea l of informa t ion can be obt a ined from resonant gap that
can b adjusted without breaking thevacuum sea l.
The gap le gth may
be var ied by br inging one of the elect rodes out t hrough an r -f choke and
a flexible bellows, or t he gap point may be dr iven in and out by a screw
mounted in a tapered, lapped join t sea led with vacuum-pump oil. The
induct ive ir ises, a lso, may be moved in and out th rough flexible, vacuum-
t ight bellows. All of these adjustable elements were made, but there was?
no oppor tun it y to make complete measurements of their character ist ics.
6.7. Arc Leakage Power .—In 3-cm bandpass tubes, as in h igh-~
tubes, t he a rc leakage power is much grea ter for dia tomic than for mona -
tomic gases. In 3-cm bandpass tubes the fla t power is negligibly small
when pure a rgon is sed, F igure 67 however , gives typica l result s’ for
th ree dia tomic gases used in a 3-cm tube; t he gases used were hydrogen ,
oxygen , a d n it rogen. The powers shown here for t hese gases a re many
t imes grea t er than the powers f r a rgon or helium. It has been seen in
Fig. 5.28, that a ra t io of 20 or 30 to 1 may be expect ed in the arc leakage
powers for a rgon and hydrogen in h igh-~ tubes. Here, however , t he
1M, D. Fiske, “Fina l Repor on OSRD Cont ra ct OEMsr 1306,” GE , Sch enect ady,
Nov. 7, 1945.
SEC.68] EFFECT OF GAS -FILLING
239
ra tio s eem s to be much larger. It may be pos s ible to expla in th is by
m eans of the recovery -tim e ph enom enon pos tu la ted in S ec. 6 .3 .
810 20
40 6080100 2
I
c
Pressure in mm of mercury
FKG.6.7.—Arc leakage power through a 3.cm ban dpass TR tu be for var iou s diat omic gaa&.
5
In a practica l tube, how ever, in ord er to s horten the recovery tim e ~
to a us able va lue it is neces s ary to employ w ater vapor. The us e or i
w ater vapor res u lts in a s ubs tan tia l increas e in arc leak age pow er ovek ~
that for argon a lone. Figure 6 .8
s how s the s pik e leak age energy W,,
and arc leak age pow er P. thr ug a
3-gap tube (the s ame tube us ed for
cu rve A of Fig. 6 .4 ) as a function of
argon pres su re, w ith a partia l pres -
s u re of 4 .5 mm Hg of HZO. It can
be obs erved that the s pik e leak age
energy is on ly s ligh tly h igher than
for pure argon , Fig. 6 .4 curve A,
and tha t the m in imum value of W,
occurs a t abou t the s am e tota l pres -
s ure in both cas es .
Becaus e, in genera l, it has been
pos s ib le to mainta in Pa below an
approxima te va lue of abou t 30 mw ,
there has been little incen tive to
s tud y the problem in grea ter d eta il.
2.00
0
1.00
!61111
“.7”
&
< 0.20
100
%
~ 0,10
Ro -
,S 0.08
~= 0.06
0.04
,- -
0,02
20
0.O11 ~
4 6810 70 41160
Argonpressure-inm-mof-rnercufi --
l?KG, 6.8,—Spike leakage en er gy an d
arc leakage power through a 3-cm band-
pass TR tube with a part ial pre sure of
H,O of 4.5 mm Hg.
l?@re 6 .9 gives W, and P. as functions of t ot al ga s press ure f or various
m ixtures of argon and HZO in a 1B55 (8 .5 -cm ) tube.
6 ,8 . Effe ct of Ga s -fillin g upon High -pow e r Cha ra cte ris tics .-B ecau s e
of the com para tively in tens e d is charge at the inpu t w ind ow s of band pas s
240 THE TR AND A TR TUBES AT HIGH POWER
[SEC.6.8
TR tubes , pre-TR tubes , and 1ow-Q ATR tubes , it is neces sary to choose
a gas fillin g th at w ill not on ly min imize the p ow er d is s ipa ted in this dis-
80
0.40
70
0.35
$
$3
E60
a 0.30
.G
g 50
“~0.25
240
~ 0.20
$
$
% 30 % 0.15
*
*
; 20 .S 0 .10
n
10 m 0.05
0
0
123456789
123456789
Total pressure in mm hg.
Total pressure in mm hg.
FIG,6 9.—Spike an arc leakage th rough an 8.5-cm bandpass TR tube for va r ious mixtures
of argon and H?O.
ch arge, in ord er to avoid crack ing t he w ind ow , but w ill also increase t he
genera l tu be life .
F@re 6.10 shows the arc loss in t he discharge across the window of
a 1 0.7-cm t ubej opera ting in ser ies
with a line carry ing 50 kw of pu ls e lo
power.
The curve for argon is obvi-
ously much lower than for any of o g
the other gases. Pr imar ily on the “
0.2
I
1
I
I
10 20
30
40
0
Pressure in mm of Hg
0
r
‘3
~
10
20
30 40
Pressurein mm Hg
FIG. 6.10.—Arc loss in the discha rge FIG. 6.11.-–Arc loss in the discha rge
across a 10-cm low-Q window (h = 0,875”) across a 1B35 tube window at X = 3.2 cm
fo var ious gases a t a line power of 50 kw,. and 3-kw line power .
basis of these tests, argon was chosen as the major component of the gas
filling of a ll tubes in this genera l a t egory.
F igure 6.11 is a similar curve for the arc loss in the window of a 1B35
(3.2-cm) 1ow-Q ATR tube measured at a line power of 3kw. F igure 6.12
I
I
I
SEC.
EF ECT OF GAS -FIL LING
241
shows W, for var ious noble gases in a 3-cm bandpass tube. For this
tube a lso, a rgon is clear ly the best of the gases tested. No tests have
been made with xenon or krypton , or mixtures of these gases with argon .
Some mixtures of this kind have very low d-c breakdown voltagea .
Because a shor t r ecovery t ime is required for this tube, the use of a
gas such as water vapor which has a Klgh elect r n-capture cross sect ion
is demanded. Up to the present , H20 is the on ly gas used for th is pur -
pose, a lthough there are other gases which may be more stable and which
may have equal or grea ter capture-cross sect ions, as has been indica ted
in Chap. 5.
Measurements on high-Q TR tubes indica te (Fig. 5.13) tha t the spike
leakage energy through a hydrogen-filled tube is not much grea ter than
tha t through an a rgon-filled tube. Some ra ther old measurements indi-
4,0
2.0
~ 1,0
~ 0.8
\ 0.6
:
c 0.4
.-
g
0.2
0.1
2
46810 20
4 6080100
Pressure in mm of mercury
FIG. 6.12.—Spike leakage energy th rough a 3-cm bandpass TR tube as a funct ion of gas
content.
cate tha t in bandpass tubes IV. is about five t imes grea ter for Hz than
for A. No explana t ion for this differ ence in the behavior of the two
tubes has been advanced.
It is much simpler to choose the gas filling for pre-TR and low-Q ATR
tubes than for bandpass tubes.
There are three condit ions that must
be met: (1) low fir ing power , (2) low arc loss, and (3) shor t r ecovery
t ime. The filling genera lly adopted for a ll these tubes in the 1.25-, 3-,
and 10-cm bands is about 10 mm Hg of arg n . If these tubes were to
be ca refu lly made and ca refu lly cleaned, their r ecovery t ime wou ld be
much too long. Most tubes, however , conta in enough impur it ies to
ensure fast r ecovery of the tubes for hundreds or even for thousands of
hours. It has a lr eady been poin ted out in Sec. 5.26 tha t the argon -
H,O-filled pre-TR tubes had shor ter tube lives than did “ commercia lly
dir ty” tu es.
The arc loss in a rgon-filled pre-TR and ATR tubes is so low that no
tubes have ever fa iled because of cracked windows, even at the very
—
242
THE TR AND A TR TUBES AT HIGH POWER [SEC.68
highest t r ansmit t er -power levels. The addit ion of HZO grea t ly increases
the a rc loss, and ca re must b taken to keep the window cool enough to
pr even t cr ackin g.
Table 6.2 illust ra tes the effect of water vapor and of window dimen-
sions upon the arc loss in 3-cm low-Q tubes. If it is assumed tha t the
TABLE62.-Artc Loss IN DISCHAIWESCROSS-cM Low-Q WINDOWS
Window
Gas con ten t , mm Hg
Transmitter
height
I
Arc loss
A H ,0
pu lse power
l-–
1
1
1
0.250 in .
15 4
70 kw 0.35db
0.125
15 4 70
0 19
0.250
15
4
150
0.27
0 125
15
4
1.50
0.09
0 250
10 0 70
<0.09
volt age drop across the discha rge remai s constan t , t hen the loss PL
shou ld va ry wit h the squa re root of the t ransmit ter power P ~.
If t he
loss ra t io a t any given power level is known , the ra t io at any other power
level may be found as follows: If P~, = v’P~, then
PQ _
d
g
P. – K’
and
which is the loss ra t io and is expressed in decibels in the table. The
exper imen ta l loss ra t ios for the two line powers given in the table obey
th is r ela t ionship very closely.
The O.125-in . window is the one in actua l use in the 3-cm bandpass
TR tube. At 150 kw the pu lse power dissipa ted in the a rc (P.) is 3 kw.
If the du ty ra t io is ~, th is indica tes an average power dissipa t ion of
3 wat t s at the input window. In a typica l insta lla t ion , th is dissipa t ion
re ult s in a t empera tu re r ise of the window of more than 50”C. Simila r
test s made on 10-cm pre-TIl tubes w-h ich opera t ed at 2 NIw line power ,
with a du ty ra t io of ~&, indica t ed window tempera tu res in excess of
100”C with an ambient t empera tu re of 25°C.
Although dir e resu lt s were predict ed for the addit ion of severa l
millimeters of mercu ry of wa ter vapor to the a rgon filling of 10-cm band-
pass tubes, no tube fa ilu res due to window cracks a t h igh t ransmit ter
powers resu lt ed .
SEC.6.9]
EFFECT OF LINE POWER
243
6.9. Effect of Line Power upon Leakage Character ist ics. -It has
a lready been seen tha t the power lost in the window discharge var ies as
the square root of the line power . Tests on pre-TR tubes indica te
essen t ia lly constan t values of W. and Pa from about 5 kw to more than
1000 kw of line power . Below the minimum fir ing power (about 5 kw),
the leakage power becomes approxima tely ha lf t he line power , and the
tube offers no prot ect ion. Simila r ly, below a cer ta in power level a TR
tube wiU not fire, and about half of t he incident line power goes to the
receiver . It is an accept ed necessity that a TR tube must protect it s
receiver at any level of line power below the maximum rat ing of the tube.
For a bandpass TR tube, this means that a t least one of t he gaps must
fir e a t a powe~ level low enough to ensure crysta l protect ion, even though
the window does not fir e a t powers below 1 kw.
1000 mw
z
g
n
%
M 100 mw
x
;
2.
a
10 mw
10 mw 100 lW
10 w 100 w
1 kw 10 kw 100 kw
Line power
FI~. 6.13.—Arc leakage power th rough a 2-gap 3-cm bandpass TR tube as a funct ion of line
power.
F igu r e 6.131 shows the arc leakage power th rough a 2-gap 3-cm tube
as a funct ion of line power .
The tube was filled with a mixture of
5 mm Hg of Hz and 10 mm Hg of A. This, hotvever , is not a standard
gas filling, and the arc leakage power is almost 10 t imes tha t from a
standard filling. Up to a line power of approximately 1 wat t , t he leak-
age power i creases linea r ly. At h igher power levels the gaps b eak
down , a ft er wh ich Pa remains constan t for all h igher power levels,
F ig, 6.142 shows the var ia t ion of spike leakage energy with line
power , in an argon-filled 3-cm 2-gap tube. The nega t ive slope of the
curves, just beyond the point of aximum energy, may be expla ined,
according to Fiske, by the na ture of the exper iment . The line power
was adjusted in these exper iments by passing the power from a 30-k\ \ -
magnet ron through a power divider r a t tenua tor . Thus, when the line
power was about 0.1 wat t , t he gap broke down near the top of the pulse
ra ther han a t the foo of t he expon en tia lly r isin g fr on t.
As a resu lt the
volt ag bu ildu p wa s a ppr oximat ely lin ea r.
It was seen in Chap. 5 tha t a
1 I f. D. Fiske, H, h’, Wallace. and A. D, Warner ,
“ Final Technical Repor t on
Contract OEMsr-1306, N“ov. 7, 1945.
z Fiske , op. cit.
144
THE TR AND ATR TUBES AT HIGH POWER
[Sn l c. &9
inea r voltage r ise on th e magnet ron pulse results in a spike leakage en ergy
tha t var ies inversely a the square root of the transmit ter pulse power .
The dashed lines represen t such a square-root var ia t ion .
0.25
0.20
g
al
.E
&
g 0.15
~
~
.=
w 0.10
0.05
0.01 0.1 1 10 100 1000
10,000
Line power in warts
FIG. 6.14.—Spike leakage energy through a Z-gap 3-cn l })andp ss Tf-i tube s a funct ion
of line power . Tube is t illed with pure argon,
(G:*P No, 1 is closer tot hein pu t win cfow,)
Measurements on 3-cm tubes at pcnyer levels up to 250 kw, and on
10-cm tubes at po~ver levels up to 1000 kw, have shown no increase in
leakage power o~rer tha t at 10 to 50
(OE
1
2 3
4
(Linepowerin kw)!zl
l;f~, &15.-.\ r r 10SS i~~ the diwl~argc
of a 1B35 ATR t ube win dow. as a fu nct ion of
line power for var ious gases,
kiv. It is felt that the maximum
transmit ter po~}-ers now in use
may be doublecl with no increase
in the leakage power of the TR
tubes,
The m i n i m u m transmit ter
power at which these tubes may
be used is determined by the fir ing
of the input window.
Detailed
specifica t ions will be given later ;
but nominal minimum values are
about 1 kw. 5 kw. and 10 kw at ,
1.25 cm, 3 cm, and 10 cm, respect ively,
F igure 6.15 shows the var iat ions in v-indo~v a c loss in a IB3.5 ATR
tube as a funct ion of the sqlla re root of the line power for var iolls gas
fillings. The xper imenta l poin ts lie \ -cry closely IIpon straight lines
and thus indica te the correctness of the assumption tha t the discharge
SEC. 610]
KEEP-ALIVE ELECTRODES
245
voltage is essen t ially constant and that the arc loss is direct ly propor -
t ional t o the cu rren t in the mainline.
601O. Keep-alive Elect rodes.—The problem of the keep-a live has
already been discussed ingeneraIter rnsin Chap. 5. In this sect ion some
of the more
presented.
det ailed con sider at ion s a pplica ble-t o ba ndpass t ubes will be
Figure 6.16 illust ra tes the side-mm and coaxia l elect rodes
FIG. 6. 16.—Side-arm and coaxial keep-a live elect rodes u sed in 10-cm band pass TR tubes.
used in the 10.7-cm and 8.5-cm (1B58 and 1B55) “l% tubes. Figure 6.17
illust rates the coaxia l elect rode used by the Genera l Elect r ic Co. in one
var ia t ion of the 3-cm tube. The 3-cm tube made by the Sylvania Elec-
t r ic Product s Co. ut ilizes a coaxial elect rode very similar t o that used in
the 1B24 TR tube.
The end of the side-arm keep-a live elect rode used in 10-cm tubw is
ben t towards the gap as shown and it ends about & in. from the axis of
the gap. The low-level signal loss (in teract ion) due to the d-c discharge
246 TIIE TR AND A TR UBES AT HIGH POWER
[SEC.610
is a lmost complet ely in depen den t of th e posit ion in g of an elect r ode of th is
type. The coaxia l elect rodes differ in th is r espect , and the low-level
signal loss increases rapidly as the elect r ode t ip approaches the gap. At
a discharge cu r ren t of 100 pa, the in teract ion can be as h igh as 5 db for a
M
Glass
,.,.
:..
.’” ., .
.,,”,,,, ,.
,7., : =.
4 “’”
,- Fernlco
L___ Ceramic
insulator
J t -
opper cone
0.010” dia.
FIG. 617,-Coax al keep-a live electrode for the GE 3-cm bandpass TR tube.
coaxia l elect rode while it can hardly exceed 0.1 db with a side-arm
electrode.
F igu re 5.55, cu rves A and B, show’s the spike leakage en er gy th rough
a 3-cm tube tha t has t runcated-cone elements. Both a coaxia l and a side-
arm elect rode a re mounted at the same gap. The coaxia l elect rode
appears to be by far the more efficien t of the two. The nu bem along
0,15
0
-5 0 +5
+10 +15 +20
Keep -aliveet ractiond) in mik
FIG. 6.18.—Spike leakage energy vs.
distance of coaxial keep-a live elect rode
from the end of the cone in a 3-cm bandpass
TR t ube.
the cu rve represen t th e keep-a live
cur ren t . Curve C, however , is for
a side-arm elect rode in a tube
using con ica l-post resonan t ele-
ments. Although it is dangerous
to compare thk curve with the first
two curves direct ly, it is obvious
tha t the last st ructu re a t least
approximates the efficiency of a
coaxia l elect r ode in a t runcated-
cone gap.
No clear explanat ion
for th is di ference has been ad-
van ced. A reason able explan at ion
is based on the fact tha t all of the elect rons from the coaxial elect rode
a re fu rn ished to the gap, whereas many of the elect rons from the side-arm
type reach the conica l elect rodes by paths tha t a re not in he region of the
h ighest r -f elect r ic field. Thus, in the t runca ted-cone gap , it is difficult
to send elect rons in to the r -f gap from a ide-arm elect rode. If poin ted,
SEC.&ll]
HIGH-POWER CHARACTERIST ICS
247
conical elect rodes are used, a grea t er no can be produced in the gap with
the sidearm elect rode than in the
t ru nca ted-con e ga p, sin ce t he post
diameter is much smaller and the
per forman ce begins t o approach
th at of t he coaxia l elect rode.
F igures 6.18, 6.19 and 6.20
represen t the resu lts of another
in terest ing exper iment by Fiske.
A coa xia l k eep-a live elect rode wa s
mounted in a bellows ar range
ment at the second gap so that it s
a xia l posit ion cou ld be va ried fr om
0.020 in . away from the gap to
0.010 in . in to the r -f gap. The
keep-a live elect rode was in its
normal posit ion at gap No. 1 and
Keep-alive retraction (d) in roils
Fm. 6.19.—Low-level kee~alive inter -
act ion vs. coaxial keewdive posit ion for
t he same t uba as in F ig. 6.18.
was main ta ined at ; cu r ren t of 50 pa. F igure 6.18 shows the var ia t ion
of W. for differ en t keep-a live cu rr en ts as a fu nct ion of elect rode posit ion .
The distances back from the gap are plot t ed as posit ive. F igure 6.19
3
0.15
$0.10
E 0.05
~
E
a-
0
-5 0 +5
+10 +15 +20
Keep-aliveretraction(d) m LA
FIG. 6.20.—Data of Fig. 6.19 trans-
formed to resemble spike energy curves of
Fig. 6 .18.
sh ows t he cor respon din g va lu es of
low-level loss (in teract io ). If
Fig. 6.19 is r eplot t ed by a r ecipr o-
cal t ransformat ion
~ = 0.021
L’
where L is the fract iona l t rans+
mission loss given in Fig. 6“19,
then Fig. 620 is der ived. The
sim ila rit y between th is figu re a nd
FIE. 6.18 is st r iking, and it pro-
vides fa ir ly convincing proof that both phenomena are go~erned by-the
elect ron density in th e gap.
6.11. H igh -power Ch ar acter ist ics.-Th e h igh -power ch ar acter ist ics
of a TR tube that can be specified are as follows: leakage powe~fla t and
spike; arc 10SS; r ecovery t ime; minimum fir ing power ; minimum and
maximum oper at in g power s; keep-alive volt age dr op, keep-a live cu rr en t
an d keep-a live in ter act ion ; ga s fillin g; a nd life.
The tubes now in use maybe divided into low-Q ATR tubes, pre-TR
tubes, nd bandpass TR tubes.
Table 6.3 gives the per t inen t character ist ics of the var ious ATR
tubes. The gas filling is 10 mm Hg. of a rgon in all cases.
248
THE TR AND ATR TUBES AT HIGH POWER
[SEC. 6.11
TARLE 63.-HIGH-POWER CH.4RACTER1S’HCS OF LoTv-~ ATR TUBES
Tube No.
Min. fir ing Ar c loss
power , kw
db
1B35
1B37
1B36
1B44
1B52
1B53
1B56
1B57
4
4
1
10*
10*
10*
10”
10*
07
07
0.5
0.3
0.3
0.3
03
03
Power level a t
wh ich a rc loss
s mea su red, k v
4
4
1
50
50
50
50
.50
\ I in . oper a tin g
power , kw
5
5
2
20
20
20
20
20
*Approximate.
FIG. 6.21
.—1 O-cm du plexer using 1
B38 pr&TR t ubs.
SEC. 6.11]
HIGH-POWER CHARACT ERIS TICS
249
The 1B35 and 11337 3-cm tubes, and the 1B36 1.25-cm tubes are
requ ired to fire within 5 sec after the power is applied at the minimum
fir ing power level indicated in the table. After they have fired, the arc
loss of the tubes must be less than the value indicated. It was planned
or iginally to requ ire the var ious tubes in the 10-cm band to undergo
simila r t est s.
The appara tus for these tests was so bulky, however , that
a much simpler test was devised in which the fir ing voltage of a 7 Me/see
elect rodeless disch arge was corr ela t ed with th e actual opera t in g charac-
ter ist ics of the tubes (see Chap. 9).
F]
[G.6,22.—1B38 and 1B&l p re-TR tubes for u se a t 10.7 cm and 8.5 cm r espect ively. ‘1
1B3S tube has contact spr ings at both ends.
?he
At presen t , no upper limit to the power level at which the tube can be
opera ted has been reached. Tube life is indeed an unknown quant ity,
for lit t le is known about the r ecovery t ime of ATR tubes. Tubes have
been run for thousands of hours a t h igh power levels withou t breaking
and withou t increasing the arc loss; howeve;, for thes long per iods of
opera t ion , no recovery-t ime measurements were made.
If the exper i-
menta l results with the 1B38 pre-TR tubes are applied to these tubes, it
can be concluded that tubes assembled with soft solder should average
good recovery-t ime life, approximately 1000 hour~. Tubes assembled
by hard solder ing, however , for exa ple, the Sylvania 1B36, 1B35 and
1B37 tubes and the 1B52 and 1B53 tubes a e probably “too clean” and
the recovery t ime is withou t doubt long even when the tubes are new.
The pre-TR tubes that were pu t in to product ion were the 1B38 at
10.7 cm and the 1B54 at 8.5 cm. Figure 6.21 shows a typical duplexer
employing a 1B38 pre-TR tube in con junct ion with a high-Q tube,
250
THE TR AND .4 TR TUBES AT HIGII POli”ER
[Sw. 611
Figure 6“22 is a photograph of the 1B38 and 1B54 tubes. The 1B38 tube
has cen t act spr ings a t both ends, whereas the 1B54 tube has a cen t act
spr ing a t the h igh -power end, and a flange connect ion a t the receiver end.
Table 6.4 gives data per t inen t to the opera t ion of pre-TR tubes. The
recovery t ime of these tubes has a lready been discussed in Chap. 5.
The 1B38 tube is requ ired to pass a leakage-energy test in order ,
pr imarily, to determine whether th init ia l gas filling is cor rect and also
to ensu re that a ir has not leaked in to the tube. The 1B54 tube which was
developed la ter was requ ired to pass only the 7-Me/see discharge test .
Very few test s have been made on the 1B5+ tube since it is very similar
to the 1B38 tube and therefore it is assumed tha t a ll the importan t cha r-
a ct er ist ics a re a lik e.
TABLE64.-CHARACTERISTICSF1B3S (10.7 CM) AND1B54 (8,5 CM) PRE-TR ‘I%BES
Characteristic
Value
Gas filling . . . . . . . . . . . . . . . . . . . . . . . . . . . ...10 mm Hg of argon
Tota l leakage energy . . . . . . . . . . . . . . . . 1500 ergs
ArclOSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. O.3db
Power for arc-loss measurement . ., . . . . . 50 kw
Minimum opera t ing power ...,.. 20kw
Since the 1ow-Q windows used i all 10-cm tubes in this group (TR,
ATR, or pre-TR tubes) hav the same heigh t and the gas fillings a re the
same, minimum opera t ing power levels a re the same.
No upper limit
for the opera t ing power level has yet been reached.
Table 65 gives per t inen t h igh-level data on the var ious bandpass TR
tubes.
TABLE6.5.—HIGH-LEVELHARACTEIUSTICSF BA~~PASSTR TUBES
Gas filling,
Recovery
P o\ ver for
Tube Band, h-o. of Keep-alive
mm Hg w., pa,
t ime to
r ecOvery -
No. cm gaps
elect rode erg mw
6 db
time meas-
A H,O
urement
1B63 3 2 Coaxial 15 4 0.1 30 < 2 ~ec
40 kw
1B55 8.5 3 Coaxia l 4 2 0.1 5 10 700
9.1 3 Side-arm
6 0
0.1 <1 < 100
50
1B58
10.7 3
Side-arm 4 2
0.1 .5 10
700
The th ree tubes in the 10-cm band are of the 3-gap type and have
low-Q input and outpu t windows, whereas the 1B63 3-cm tube has a
h igh-Q input window and has two resonant gaps. At the end of the war ,
work had just begun on the design of a 2-gap 1 -cm tube using a high-Q
input window. The advantages of th is tube would have been: a shor ter
tube (about 1+ in. shor ter in the 10.7-cm tube), and a longer tube life.
It was believed tha t the use of a high-Q input window, about ha lf the
SEC.6. 11]
HIGH-POWER CHAR ACT ER IS TICS
251
heigh t , or less, of the presen t windows, would reduce the a rc loss by a
factor of about four , and the cleanup of HZO would be cor respondingly
reta rded. Unfor tuna tely, on ly preliminary low-level test s had b~en
made befor e all developmenta l work was stopped.
The 9. l-cm tubel is filled with a rgon a lone, This tube was designed
for use in radar beacons and was to be opera ted at about 50 kw of line
power . A recovery t ime of approxima tely 100 psec was tolerable; bu t
tube life had to be thousands of hour in order to meet t e r igid require-
ments of a ircra ft beacon systems.
The tubes were assembled b-y soft -
solder ing and the impurit ies in t roduced in to the tube were sufficien t to
keep the recovery t ime below 20 psec during severa l thousand hours of
opera t ion . Under normal opera t ing condit ions, the beacon t ransmit ter
is o only while it is being in ter roga ted by an a irplane. The du ty
rat io which result s is very low.
At a busy airpor t the ra t io of “ on” to
‘‘ off” t ime averaged over severa l hundred hours is cer t a in ly less than
~. Thus, the r -f discharge plays a negligible par t in the gas cleanup
process; and the 100-Pa keep-a live discharge opera t ing on the 260 cc of
gas shou ld give a tube life of a t least 5000 hours if an extrapola t ion may
be made from the 11327 or 721B tubes (Sec. 5.23).
The 1B55 and the 1B58 tubes were designed for h igh -power radar sets
to be opera ted a t line powers of 500 to 1000 kw, and du ty ra t ios of a t
most ~~. Prel minary test s on th ree or fou r hand-made, soft -soldered
tubes of ea ch t ype sh owed cont in ued crysta l protect ion and good r ecovery
t ime a fter 500 hours a t 1000 kw, and a duty ra t io of ~lm. For wha t
length of t ime it is possible for clean , ha rd-soldered tubes to give good
recovery t ime is not known . This t ime can probably be extra ola ted
from test s on the 1B38 pre-TR tube which has one-fou r th the volume of
these tub s, and appears to have a life of 100 to 200 hours when filled
with an A-HZO mix ure.
The 3-cm tube has a volume of about 7 cc, or about & the volume of
the 1B58 tube. On the other hand, the window heigh t is about one-
seven th tha t of the 10-cm tube. Therefore, if a square- aw varia t ion of
a rc loss with window heigh t is assumed, the a rc loss will be less by a factor
of 40 or 50, approxima tely, for equiva len t line powers in the 3-cm tube.
Thus, a t equa l line powers, tube life should be about the same for the two
tubes. At presen t , 3-cm magnet rons with an outpu t power of 300 kw are
availab e, while 1000-kw tubes a re in use a t 10 cm. Developmenta l
magnetrons tha t have twice the powers have been tested. On this basis,
the 3-cm tube might be expected to have about th ree t imes the life of the
lo- m tubes, ij thetubes are clean an d h ard -sol&red , and a re filled with
a rgon and water vapor .
I L. D, Smul l in ,
“S -Ban d Bandpass TR Tubes,” R.L Repor t No. 971, J an . 23,
1946.
252
THE TR AND ATR TUBES AT HIGH POWER [SEC. 6,12
Actual life test s have been too few in number to allow any defin it e
conclusion to be drawn. Some tubes opera t ed at 30 kw for more than
500 hours. A few gold-pla ted tubes (th is pla t ing preven ts oxid t ion)
have run severa l hundred hours at 180 kw with lit t le change in recovery
time.
Although considerable thought was given to the use of water r eser -
voir s in these tubes (Chap. 5), any idea of their use was abandoned
because of the danger of excessive HzO pressures at t empera tu res near
100”C, and also becau se t he cont inu al dissocia t ion of t he HZO r esu lt s in an
increase of par t ia l pressure of Hz in the tube. This resu lt s in excessive
arc loss and leakage power . F iske has proposed the use of a palladium
window in the tube in order to “dra in” ou t the hydrogen .
Th e possi-
ility of using other gases than HZO and the mer its of iner t coat ings have
already been discussed in C ap. 5.
Ml possibilit ies of gold-pla t ing to
increase tube life have not yet been fu lly rea lized.
In la rge tubes such
as the 11M8 it is probably necessa ry to pla te on ly the region around the
inpu t window.
6.12. P resen t and F ture Sta tus of Low-Q and Bandpass Tubes and
ATR Tube . —There does not seem to be any immediate prospect of
improving in any \ vay the low-level per formance of these tubes, for it is
not possi le to lower , t o any mark d degree, t he loaded Q. A sub-
stan t ia l reduct ion in arc loss and minimum fir ing power wou ld make it
possible to use these tubes in low-power ( < lkw) beacon installa t ions.
This reduct ion might be obta ined either by an extension of the tube
designed by Samuel (Chap. 4) or by the use of nar rower wi dows-a
possibility if mica is used instead of glass. The methods of mount ing
th at in volve cu rr en t-ca rr yin g con tact s n eed fu rt her in vest iga tion . Th er e
is a t presen t no informat ion available on how these con tact s withstand
the r igors of ext reme var ia t ions in climat ic condit ions, a lthough they
per at e wit h n o difficu lt y u nder n ormal in door con dit ion s.
Pre-TR Tubes.—These tubes were in t roduced as a stopgap and were
esigned to prot ect crysta ls from cer ta in h igh - ower magnetrons. It
was felt tha t their usefulness would end when bandpass tubes of cor re-
sponding frequency coverage became available. These tubes are now
available, and there is lit t le poin t in the fu r ther development or use of
r e-TR t ubes.
Bandpass TR Tubes.—These tubes in th eir presen t sta te of develop-
ment hve andpass character ist ics of about 10 to 12 per cen t and pro-
t ect crysta ls a t h igh power levels for per iods of more than 1000 hours.
Recovery-t ime life is st ill a n un r esolved p roblem , a lt hough , in va r iou s ways,
it is possible to improve the recovery-t ime life of these tubes. T ese
methods for improvement include, t he use of iner t coat ings or pla t ings
inside the tube; t he discovery of a captor gas ess chemical] y act ive than
SEC.&12]
STATUB OF BANDPASS TUBES 253
H*O; the development of water reservoir s plus a suitable means of get t ing
r id of Hz; and the reduct ion of the intensity of the window discharge.
Of these, the first and the last will in all probability give posit ive result s.
Gold pla t ing has already been t r ied with some ~uccess. Chromium
Because of the poor r -f loss character ist ics of chromium plat ing, it can
not be put on resonant ’ elements, but can be used only cm the walls
adjacent to the input window, No exper iment have been made with
pr eoxidized su rfa ces sim ila r t o t hose
used
in the 1B27.
The intensity of the window discharge may be reduced by decreasing
t he window heigh t .
The use of the same thickness of dielect r ic resu lts
in an increase of loaded ,Q &nd in an increase of r -f loss in the dielect r ic.
In 10-cm bandpass TR tubes, it is possible to use a window with two o
three t imes th Q of the presen t windows; this r educes the arc loss y a
large factor and probably increases the tube life about 5 t imes. The r -f
loss in the windows would probably be less than 0.1 db if 707 glass were
used. In 3-cm tubes, t he presen t windows, ~ in . high, a re probably the
best tha t can be made with glass.
The loss increases rapidly with any
fur ther decrease i heigh t . The presen t th ickness is 0,023 in. The use
of thinner giasa reduces the loss, but glass windows 0.010 in. th ick are
very fragile.
The r -f loss of quar tz is considerably less than tha t of 707 glass.
Therefore, with quar tz it would be possible to make a smaller window
than can be made with the glass and to do so without incur r ing excessive
losses. The Q would be increased, of course, if t he thickness were not
redueed. Since the presen t 3-cm windows already have a Q,,z of 2, it is
not possible to proceed indefinitely in this direct ion. Even if the higher
Q can be accepted, the problem of sealing the quar tz t o metal st ill remains.
Almost the only pract ica l method available is to metalize the edge of a
quar t z or a “ Vlcor” (Corning 709 glass, about 90 per cen t quar tz) window
and then to soft -solder it t o an Invar frame. A much more promising
solut ion of this problem may be found in the use of mica in st ea d of gla ss.
The technique for making vacuum-t ight mica windows was applied by
Malter ’ in the const ruct ion of a magnet ron coupling window. M. D.
Fiske used this technique to make TR-tube windows. A window reso-
nant a t 3.33 cm, + in. high, and covered with mica 0.004 in. th ick, had a
Q~z of ~.3, and no measurable loss.
It thus appea s that , by the use of
mica , a window& in. high or even less could lx made.
Although this appears to be a very at t ract ive solut ion a number of
problems involved with this design remai . The mica sheet is sealed to a
n ickel-steel frame with a specia l low-melt ing point (550°C) glass. This
~L. Mal er , R. L. J epson , L. R. Bloom,
“ Mica Win dows for Wa vegu ide ou tpu t
Ivfagn et r on s,” NDRC Div. 14, Repor t 366, Dec. 5, 1944.
254
THE TR AND A TR TUBES A T HIGH POWER [%C, 6 .12
makes it impossible to hard-solder the frame to the tube by ordinary
techniques. 1 Because the mica is sea led to the steel a t the edges only, it
should be on the outside of the frame in order to relieve the sea ls from the
ext ra st rain of a tmospher ic pressure.
This, however , requires tha t the
ent ire inside of the frame be c ated with glass to preven t sput t er ing by
the discharge. A window of this type has not yet been made, but at
least it seems possible to use this as a method of const ruct ion . The
higher-Q (about 2) window would be usefu l in TR tubes, whereas the
1ower -Q (about 0.3) window would be usefu l in ATR tubes.
Table 6.6 is a summary of the ar ious pa rameters involved in TR-
tube design and the in ter rela t ion of these parameters with the various
TABLE6.&-DESIGNVARKABLESORBROADBANDR TUBES
No. elemen t s.
Qm of elemen ts.
Gap.. . . . . . . . . . . .
Kin d of ga s.,....
Ga s p res su r e
K-a cur ren t and
posit ion ...,.,,.
Peak power .
Aver age power .
Window size. .,
Spike
Band-
leak-
width
age
en erg,
x
x
x
x
x
x
x
x
x
Flat
leak-
age
jower
x
x
x
x
i
Ii-a
Arc
10ss
10ss
.
—
x
x
x
x
x
x
x
x
x
Re-
ovcr:
time
x
x
x
Life
x
x
x
x
x
x
Llax.
and
min.
]Owel
x
x
x
[nsm-
tion
10ss
per formance character ist ics of the tube. Thus the number of element s
a ffects the bandwidth and the spike leakage energy but does not affect
the other proper t ies. Fur ther improvement of these tubes, in addit ion
t o t he improvements just discussed, will most likely consist of an increase
in the bandwidth with no definit e increase in the leakage power . A
10-cm 3-gap t be whose pass band extended from 9.4 cm to 11,1 cm was
t est ed a t t he Radia t ion Labora tory.
It spike leakage energy was high,
about 0.8 erg, but , because no carefu l study of keep-a live loca t ion and
gas filling has been made, it has not yet been established tha t such a tube
cannot be a lt ered to protect crysta ls,
The exper iment s did indica te
however tha t with careful design , a lmv-Q gap ith low spike leakage
energy could be made.
1Extensive research has t iecn done in the develop ent of low-melt ing-poin t hard
solders, and a m)itah]e solder may already exist .
SEC.613]
METAL-T04LAS S SEALS
255
6.13. Const ruct ion Techniques-Meta l-to-glass Seals.-The metal-
to-glass seals used in microv. ave TR tubes may be classified under th r ee
main h ea din gs: (1) wir e feed-t hr ou gh sea ls, (2) ba la nced copper -t o-gla ss
seals, and (3) Kovar or Fern ico window seals.
The first type, the feed-
th rough seal, is used mainly for keep-a liv elect rodes. Such seals a re of
fa ir ly simple const ruct ion and will not be descr ibed here.
The balanced seal is ext remely useful in tha t it a llows a but t join t to
be made between a glass cylinder and a copper disk as in the 1B27 TR
ube. In th is seal, advantage is taken of the fact tha t glass is st ronger
in shear than it is in tension .
If a disk of copper were sealed direct ly to
one glass cylinder , when the cylinder cooled the copper would expand
radially more rapidly than the glass.
Th resu lt ing bendi g of the
copper disk puIls it away from the glass and breaks the seal.
If now,
however , the disk is sea led between two glass cylinder s, it can no longer
pull away from either one and the differen t ial expansion of he two
mat er ia ls r esu lt s in a ra dial for ce wh ich exer ts essen tia lly pu re sh ea r u pon
the glass. Such seals will withstand tempera tu res varying from severa l
hundred degrees cen t igrade down to – 50”C or less.
There are two impor tant methods for making balanced seals: the
“bera ted” and the “beaded” sea l techn iques. These have been used
extensively in TR tubes of the cell type. The bera ted seal is prepared
as follows:
washed in wa ter and alcoh ol,
2. The copper is oxidized in a gas flame and is then allowed to cool.
3. The flanges are dipped in to a solu t ion of sodium tet rabora te,
Na,Bi07, 1.5 gr to 100 cc of H,O.
4. After drying, the flanges are heated by a gas flame or an induct ion
coil to form cuprous oxide of a deep red color .
5. The flanges and glass cylinder s are then stacked in the assembly,
jigged and heated by r -f induct ion to make the seals. This is done
in an a tmosph er e of COZ t o pr even t excessive oxidat ion .
6. After annealing, the en t ir e tube is cleaned with acid to r emove the
oxide.
7. If an iner t coat ing is desired (Sec. 525), the sect ion to be left
oxidized is coa ted with a lac uer befor e the acid clean ng, a fter
wh ich t he lacqu er is dissolved in a lcoh ol.
The beade sea l is considerably st ronger than the bera ted seal,
a lthough it is slight ly more difficult to make. It is used almost exclu -
sively now in all cell TR tubes. The seal is made by sealing th in glass
r ings t o ea ch side of th e oxidized copper disk in a direr .t copper -glass seal.
A hydrogen flame is used to make th is seal. The glass cylinders a re then
256 T E TR AND A TR TUBES AT HIGH POWER
[sm . 613
sea led to the beads in a hydrogen flame. Aft er annea ling, the tube is
.
clea ned a s a bove.
I
tube. This tube
is an excellen example of the use of the balanced copper -glass seal. (Cour tes~ ASLJ wznia
ElectricProdu cts Co.)
In a ddit ion t o bein g mech an ica lly st ron ger , t he bea ded sea l over comes
the main defect of the bera ted seal in tha t it cannot be spoiled by long
exposure to warm, moist a ir . Bera ted sea ls can be dissolved in boiling
\ ra ter , of course, and t ere was some evidence tha t prolonged exposure
to moist a ir in the t ropics a lso weakened them, Figure 6.23 shows the
SEC. 813]
METAL TO-GLASS SEALS 257
par ts and stages of manufacture of a 11327 tube, a good example of the
u se of copper -gla ss sea ls.
The th ird group of seals involves the use of glass-sealing alloys with
su it able coefficien t s f expan sion .
Th e balanced copper -glass seals can
be made with any glass, bu t Corn ing 707 glass & commonly u ed bec use
of it s low loss factor . Kovar ’ is designed to match 706 (705AO) glass,
which has an expansion coefficien t of 5 X 10-G per “C; but successfu l
seals have been made to 707 glass which has a coefficien t of 3.1 X 10–8
per “C.
F la t windows sealed in Kovar frames are used in the 1B24,
1B26, and in the 1B50 in tegra l-cavity TR tubes, and in all the low-Q
ATR, pre-TR, and bandpass TR tubes.
The genera l process of making these windows is as follows:
1. The Kovar frame is hea ted in air by an induct ion coil t o oxidize
it . The proper depth of oxida t ion is impor tan t and must be
recogn ized by the proper shade of grey.
2. The glass blank is then placed on the frame and the combinat ion
is heated in a COZ atmosphere unt il t he seal is made
For low-Q windows in ATR and other tubes it is necessary to add a
fu r ther refinement . The in tensity of the window discharge is so grea t
that if the window consists simply of a piece of glass in a Kovar frame,
the discharge cleans up the gas very rapidly by what seems to be a
spu t ter ing act ion . To preven t thki, M. D. F iskez coa ted the inside
su rface of the Kovar frame with glass. Th is coat ing is now used in
all tubes of th is kind. The glass coa t ing may be applied in one of two
ways. F iske’s method consists of spraying the oxidized metal with
a suspension of powdered glass in alcohol.
The edges must first be
masked so that the frame can subsequen t ly be soldered in to the tube.
The frame is then hea ted in air t o a tempera tu re of 950”C for 10 minu tes.
The next step is t o place the frame on a graph ite block, set the glass
window in place, and then cover it with another graph ite block. The
assembly is again hea ted to 950°C for 15 minutes.
A much simpler method for 3-cm Iow-Q windows was devised by
McCar thy of the Sylvan ia Co. It consist s simply of placing on the oxi-
dized frame a glass bl ck that is bigger than the open ing. It is then
induct ion hea ted in a C02 a tmosphere. The most in tense hea t is gener -
a ted around the per iphery of the frame and this causes the glass a t first
to run ou t towards the edges of the frame and then finally to soften at
the cen ter . When this soften ing occu rs, a lavite paddle is used to press
i “ Kovar” is used here as a gener ic t erm to include both Kovar aud Fern ico.
2 M. D. Fiske,
“ Resonant W_indows for Vacuum Seals h Rectangular Wave-
guides,” GE Repor t , Feb. 10, 1945.
258 THE TR AND A TR TUBES AT HIGH POWER
[SEC,614
it in to place. Although th is method is sa t isfactory for small windows, it
is a ppa ren tly impra ct ica l for 10-cm win dows.
Afthough 707 glass has a lower coefficien t of expansion than Kovar ,
ligh t st ra in an lyzer , a good window made with 706 glass shows a lmost
no signs of st a in . Windows made of 707 glass, however , show marked
stra in lines tha t indica te tha t the glass is under compression a t room
tempera tu re. Although there are no defin it ive exper imen ts, it is reason-
able to suppose tha t the 707 windo~w are st ronger since the lass can
never be under tension . The most tha t can be said is tha t windows of
both types, when they a re well made, meet all possible service
requirements.
6.14. Solder ing of Windows in to Cavit ies. -In Sec. 2.12 it has been
seen tha t in order successfu lly to solder the Kovar window frame in to
th copper block of the 1B24 and 1B26 TR tubes, the frames must have
wrinkles (F ig. 2.69) tha t a llow the ou ter edges to move in and out with
the copper block without cracking the window. The linear coefficien t
of copper is about 16 X 10–5 per degree C, or appr ximately 3 t imes tha t
of Kova r .
The actual solder ing process consists of hea t ing the tube body by
means of a la rge elect r ic hea ter , such as a solder ing iron , or a hot pla te.
This is done with the pret inned window frame in place. When the desired
tempera tu re is reached, addit iona l solder in the form of a fine wire is
applied to the edge of the frame.
On the 1B50 tube which has a steel body, it is possible to hard-solder
th }vindow in to place, This makes a much st ronger sea l, and it elimi-
na tes th e possibility of soft -solder flux get t ing in to th e tu be cavity.
The 1oN--Q windows in pre-TR and simila r tubes a re soldered in to
th ends of rectangula r wavegu ides. In the or igina l tubes made by
Fkke, pu re t in solder ~vas used.
The window was dropped in to a sea t
formed by cut t ing he gu ide wall t o ha lf it s th ickness. Because of the
rectangu la r shape of the window and because of the rela t ive st iffness
of the Kovar frame, it is very impor tan t to make the hea t ing uniform
in order to pre}~en t cracking of the glass.
Since the solder must be fed
in by hand while the tube is hot , gas hea t ing is impossible, and elect r ica l
hea t ing only can be used.
The technique of sof -solder ing the fla t frames in to the waveguide
recesses was never rea lly per fected from a product ion standpoin t except
in the smaller tubes such as the 1B35 and 1B36 tubes. The fir defin ite
var ia t ion from th is technique was made by Sylvania in the 1B35 and
the 1B36 tubes. The 1B36 tube was of a ll-steel const ruct ion , except
for the frame, and was completely assembled with hard solder . The 1B35
body was brass waveguide but the Sylvania engineers succeeded in hard-
SEC,6.15]
TUNING TECHNIQUES 259
solder ing the window direct ly to the end of the waveguide, in a but t
joint.
Engineers both of Sper ry and ylvania designed 10-cm ATR tubes
and bandpass TR tubes tha t were completely assembled with hard
solder . None of these tubes reached the product ion stage.
In the Sylvania 1B52 nd 1B53 ATR tubes, the 1B54 pre-TR tubes,
and the 1B55 bandpass TR tubes, the brass wavegu ide was replaced by
steel tubing, and the fla t Kovar frame was replaced by a rectangular cup
or dish, whose cross sect ion matched tha t of the waveguide. 1
The two
were but ted together and the steel mounting flange was slipped over the
outside. This th ree-piece combina t ion was then soft -soldered togethe .
This const ruct ion is apparent ly much st ronger than the const ruct ion
just descr ibed. One indica t ion of th is is the fact tha t few 10-cm tubes
with fla t window frames and brass bodies can withstand more than 20
tempera tu re cycles from – 40”C to 100”C without failing, whereas tubes
made with th is new type of const ruct ion have withstood severa l hundred
such cycles .
6.16. Tuning Techniques.— he 721B and 724B tubes, since they are
fixed-tuned tubes, must be ~retuned in standard cavit ies to standard
frequencies, This is accomplished by pushing one of the cones in or out
by means of a specia l tool pushed in-through-the pumping tabula t ion .
The 1B24, 1B26, 1B27, an 1B50 tub s a re tunable tubes. The
tuning is accomplished by pushing one of the cones in or out with a
differential-screw mechanism.
Th e complet e r an ge is cover ed in a mot ion
of .030 in. or less. In the 1B24 tube for instance, a mot ion of approxi-
mately 0,015 in. resu lts in a change of tuning of 1200 Me/see. With
Q.,
= 300, the half-power bandwidth of the tube is about 30 Me/see.
Thus, a mot ion of 0,0001 in. of the cone results in a detuning of about
8 Me/see, and in an increase of inser t ion loss of about 1 db. .41though
the different ia l screw provides a convenien t method for producing such
small in cr emen ts of mot ion , u nless ver y a ccu ra te, a nd a lso ver y expen sive,
threads are used, it is necessary to use spr ing loading to elimina te back-
lash. This is shown in Fig. 2.68. The diaphragm through which the
mot ion is t ransmit ted to the cone exer t s an axial force upon the screw,
but as the diaphragm passes th rough it s neut ra l posit ion t he for ce becomes
ze o and then changes s gn; consequent ly, there is a region in which it
is very difficu lt to tune accura tely. Spring loading can be used to over -
come th is d ifficu lty.
The tuning of bandpass TR tubes is the final opera t ion before e acua-
t ion and sealing. The 10-cm gaps are of the form shown in Fig. 6.16
\ vith one of the posts ar ranged to screw in or ou t ,
After the gaps a re
1 Sylva ia Elect r ic Products, Inc., “ Repor t on OSRD Tube Development Sub-
con t ract on Radiat ion Laborato y Purchase Order DIC 182032, ” Feb. 5, 1946.
260
THE TR AND A TR TUBES AT HIGH POWER
[SEC.6“16
tuned, the posts must be Iocked and sealed. This was done or iginally
by soft -solder ing the screw to the outs de of the guide; however , unless
the screws were very t ight there was danger of moving the screw. L.
Sor of Sper ry Gyroscope CO. suggested simply locking the post with a
lock nut , but at the same t ime surrounding it by a lit t le cylinder , hard-
soldered to the o tside of the guide, on which a lid may be solder d after
t he in al t un eu p.
The 3-cm ba dpass tube uses cones similar to the hollow cones in the
1B24 tube. The movable cone is sea led at the apex and is pushed in .
and out from the outside by means of a screw that is soldered after
being adjus ted .
The Iow-Q ATR tubes may be tuned in two ways. One method is
to make the cavity accura tely to dimension and to gr ind the windows
accura tely to the proper thickness, with the resu lt that when the tube is
finally assembled it is automatically tuned cor rect ly. This was the
technique used by the Genera l Elect r ic engineer s in the const ruct ion of
the 11335, 1B37, lB36, and the 1B38 tubes. 1 It was possible in this way
t o make most of the ATR tubes tune to within i 0.5 per cen t of their
nominal frequency.
The engineers at Sylvania , however , chose to allow more tolerance
in window tuning by eliminat ing the gr inding operat ion , and by tuning
the final tube after assembly, as descr ibed in Chap. 4. This method was
accepted as completely sat isfactory unt il some time after the end of the
war , when it was observed th t the var ia t ion in the thickness of the glass
resu lted in a much larger er ror than was desirable in the posit ion of the
effect ive shor t circu it of the fired tube. It thus appears that unless closer
con tr ol of glass th ickness can be maintained in the scaling pr ocess, it will
be necessary to gr ind the windows to defin ite th icknesses in order to
maintain t he n ecessa ry t oler an ce in a rc posit ion .
6.16. Mount ing Devices.-The methods for mounting the var ious
low-Q ATR tubes have alr eady been descr ibed in Chap. 4. The coiled-
spr ing contact used on the var ious 10-cm ATR tubes is also used for all
the 10-cm TR and pre-TR tubes.
The pr in gs a r ber yllium-copper ,
wound of iVo. 26 (0.0159 in. ) wire to 0.125 in. o tside diameter , 40 turns
to the inch. If the spr ings are proper ly mounted, and the seats in the
duplexer are accurately machined, excellen t con tact is assured. It is
felt , however , that a soft er contact mater ial is preferable, and some
thought has been given T,Othe use of a woven-metal gasket about + in.
square, made of Monel r ibbon. Although such gaskets make excellen t
developed.
] T, P. Cur t iss, F, E . Dickey, G. H, Floyd, W, T, Posey, ‘( F inal Technical Repor t
on OSRD Cont ract 0EMsr-1306, ”
Tube Division Sect ion, Nov. 1945.
-.
SEC.616]
MOUNTING DE VICEAS
261
The 3-cm bandpass TR tube has standard waveguide flanges on either
end for coupling to waveguide choke connector s.
These flanges a re
in the planes of the windows. Because of their size., t he flanges a re very
st iff and can exer t severe radia l st r esses pon the windows.
Early
exper imenta l tubes had brass flanges.
The life of these tubes a t high
power levels was rela t ively shor t , and almost all fa ilures resulted from
cracked windows. The use of Kovar flanges relieved the ext ra t em-
pera tu re st ra ins and almost no more fa ilures of this kind occur red. The
present 1B63, tube, which is made by Sylvania, uses st eel flanges and
hard-soldered window frames. Although the expansion f st eel is twice
tha t of Kovar , these tubes withstand about 50 tempera tu re cycles with a
tempera tu re range of – 40° to 100”C.
THE PRINCIPLES OF
BY
Th e gas-filled swit ch es
CHAPTER 7
BRANCHED DUPLEXING CIRCUITS
H.4ROLD 1<. F.~ItR
commonly used in duplexers have been
discu ssed; t he cir cu it s u sed t o con nect t hese sir it ch es t ; ot her compon en ts
and to each other will now be examined,
To a la rge exten t duplexing
circu it s have been built around t he fundamental st ruct ure of a t hree-way
t r ansmis siofi-line junct ion or ‘r-jUIICtiOII wit h t he arms leadin g t o an ten na,
r eceiver , and t ransmit t er and with a su itable swit ch in the receiver arm
and possibly also in the t ransmit ter arm.
This chapter will be con-
cerned with duplexers of this type \ vhich will be refer red to as branched
circuits to dist in gu ish t hem fr om t he so-ca lled balanced ci rcu it s t o be dis-
cussed in Chap. 8.
It will be assumed that the rea er is familiar with the t ransmission-
Iine impedance char t s of the two types represen t ing the complex imped-
ance plane and the complex reflect ion -coefficien t plane respect ively.
The notat ion used in Chap. 4 will a lso be employed here. This means
all ot her r ela ted qu ant it ies a ccor din g t o t he equa tion s
z,= R,+jx8=; =—’—
s
G. + jB,’
~=z ,s z”
I + Ir,l
a
z, + z,’ ‘s = ] – Ir,l”
7.1. The J unct ion Circu it . -Since the sa lien t fea tu re of a branched
duplexer is the th ree-way junct ion , the proper t ies o this circu it will be
discu ssed, Let u s con sider fir st a per fect ly gen er al Iossless lin ea r n etwor k
with th ree pairs of terminals designa ted as (l), (2), and (3) for an tenna,
t ra nsm it t er , a nd r eceiver .
Du rin g t ra nsm ission t he lin e lea din g t o t he r eceiver is sh or t-cir cu it ed
at some poin t by the TR tube as in Fig. 7.1. This places a pure reactance
at t he terminals (3) which can be made any value desired by adjust ing
the distance 1 from the junct ion to the shor t -circu it . The fir st require-
ment for the junct ion is that there be some value of 1 which will give
per fect t ransmission from (2) t o (1).
On recept ion it is necessary tha t there be a pure react ance at the
terminals (2), and it is required of t he jun ct ion tha t per fect t ransmission
take place from (1) to (3) for some value of th is reactance. In pract ice
262
SEC.71]
THE JUNCTION CIRCUIT
263
the impedance a t the terminals (2) may not always be a pure reactance,
because of the w ong t ra smit ter impedance or an inadequate ATR
circu it , bu t , for the presen t , it will be consider ed purely imaginary.
In the t ransmission case the impedance due to the TR switch is actually
very close t o a pure reactance.
The requ irement for t ransmission is fu lfilled for any sor t f lossless
t hr ee-wa y ju nct ion pr ovided on ly t ha t it is symmet rica l a bou t t he r eceiver
circu ited such a device becomes a
non dissipat ive
symmetrical
four-
terminal network. Such a circu it
(3)
T
1
always has a character ist ic imped-
ance R which is either purely rea l
I
or pu rely im agin ar y.
I R is con-
q
A—* L
+
q
net ted across the ou tpu t pa ir of ter -
(1)
(2)
minals, the impedance seen at the .“
*
q
4
input pair will a lso be R. It migh t
be expected that , by adjust ing the
FIG. 71.-Representa t ion of a waveguide
junction.
posit ion of the shor t circu it on the
r eceiver a rm , R could be made equal t o 20, the character ist ic impedance
of t he t ra nsm ission lin e.
To prove th is the th r ee equat i ns a re wr it t en
3
Ei =
z
z,,r~
(i = 1 , 2, 3), (1)
j=l
exp essing the voltage at any pair of terminals in terms of the cur ren t
a t each of the th ree pairs of terminals.
Because Zii = Zji a nd because of
the symmet ry of terminals (1) and (2), t e impedance matfix can be
wr it t en as
[1
ABD
(Z,l)=Z= B A D.
DDC
A gen er ator will be connected to terminals (1), a matched load of imp d-
ance unity to terminals (2), and an arbit rary r eactance z = jz to terminals
(3). The condit ion that the input impedance be unity is then imposed.
This gives t he t hr ee equ at ions
E = 11, E, = –Iz, E8 = –zIs,
which allows the eliminat ion of the E~’s from Eqs. (1) with the resu lt
(A – 1)1, + III, + DI, = O
}
BII+(A+l)l, +D1, =O - (2)
DI1 + D12 + (C + Z)~J = O
264
BRA ,VCIII?I) D UPLEA’1,>’G CIR CIT,S
[S W. 71
Since there must obviously be coupling between any two arms,
B # O and D # 0. It is therefore impossible for any row or column of
coefficients to vanish. Hence the necessa ry and sufficient condit ion
tha t the equat ions have a solut ion 11 # Ois tha t their determinant vanish,
Since there is no loss, the elements of (z,,) a r e all imaginary, and A = .@}
B = jb, . . ~ where a, b ~ ~ are rea l.
The rendition for solut ion is
then
(U+j) ~
d
b
(a – j] d
= 0,
d
d
(c + x)
If the determinant is expanded, the imaginary terms cancel out , per -
mit t ing a rea l solut ion for r of the form
(c +x)( ’ – b’ + 1) + 2d’(b – a) = O.
In case az – b’ + 1 = O, it is merely necessa ry to open-r ircu it termina ls
(3) for then 1, = O and the condit ion tha t the fir st t~vo of I@. (1) have a
solu tion is
(a+j) b
b (a – j)
=a’–b’+l=O,
This shows tha t there is a lways a react ance ~ which makes the system
of Eqs. (2) consisten t under the assumption tha t the input and output
impedances a re unit y; tha t is, t here is a reactance tha t matches the
junction.
For m chanica l reasons it is quite natura l to const ruct a junct ion
by adding a side arm for the receiver to a st ra igh t sect ion of the t rans-
mission lin e wh ich r uns fr om t ra nsm it ter t o an ten na .
In su ch a “T-ju nc-
t ion” the symmetry condit ions for t ransmission are sa t isfied auto-
mat ica lly and the junct ion may be matched for recept ion by some
dev ce, such as an induct ive ir is, in the receiver arm. After this device
has been added, the distance from the junct ion to the TR switch can
be adjusted o match the junct ion for t ransmission. Most T-junct ions
have ra ther small recept ion loss even without the addit ion of a matching
device. In some cases th is may permit the mount ing of the TR switch
at the closest posit ion which gives good transmission since it is unneces-
sa ry to leave room for matching. This close posit ion usua lly has the
window of the TR cavity approximately flush with the wall of the wave-
guide or outer conductor of the coaxia l line since the window presents a
shor t circu it when the switch is fired.
The requirements for reflect ed power are ordinar ily much more
str ingent dur ing t ransmission than dur ing recept ion , because the im ped-
ance pres n ted a t the t ransmit ter has a very marked influence on the
SEC.7’2]
COAXIAL JUNCTIONS
265
t r an sm it ter efficien cy and st abilit y.
In viewof the con t r ibut ions made
to the reflect ed power by the other r -f component s, a voltage standing-
ave ra t io above 1.10 dur ing t ransmission may somet imes be considered
excessive for a TR junct ion and 1.05 may be a desirable figu re. In
cont ra st to th is, a VS}VR of 1.10 would cause a recept ion loss of only
0.010 db, a va lue which would hardly be considered ser ious. This
makes clea r the advan tage of mount ing the TR cavity so tha t the win ow
is flush with the su r face of a st ra igh t sect ion of t ransmission line.
The
symmet ry makes possible a good match for the t ransmit ted signa l and
the matc can be main ta ined over a wide frequency band because of the
pr oximity of win dow and t ransmission line.
An obvious extension of t e symmet ry pr inciple leads t o a junct ion
in wh ich any two arms a re symmetr ica l with respect t o the th ird. The
junct ion is then matched for either t ransmission or recept ion if the arm
not in use is shor t -circu ited a t the proper poin t . This elimina tes the
need for any matching device and, consequen t ly, finds applica t ion in
wideband systems. Since the th ree arms are a t angles of 120° with one
another , this Y-junct ion lacks the mechanica l simplicity of the T-junc-
t ion , with arms at angles of 90° or 180°. The pr inciple of th ree-way
symmet ry has not had much applica t ion to coaxia l duplexers, but has
been u sed in wa vegu ide cir cu it s.
&
—
(a)
FIG. 7.2.—Cavit y couplin g
(b)
to a coaxial line; (a ) loop-cou pled ca vity; (b) iris-coupled
cavity.
7.2. Coaxisl J unct ions.-Coaxia l duplexers have been used pr inci-
pa lly a t wavelengths of 8 cm or longer . At shor t er wavelengths, wave-
gu ide circu it s a re usua lly simpler .
A coaxia l line can be coupled to a
TR or to an ATR cavity by a loop connected between inner and ou ter
conductor s, or by an ir is.
With an ir is, no direct connect ion is made to
the inner conductor , but an open ing i the ou ter cond ctor establishes
266
BRANCHED DUPLEXING CIRCUITS [SEC.72
coupling between the field in t he cavity and tha t in t he coaxia l line.
The
ir is coup ing, which has mechanica l advantages, may not be feasible
where ra ther t igh t coupling is desir ed or where small-diameter lines a re
used. These two types of coupling are illust ra ted schemat ica lly in
Fig, 7.2. When the cavity fires, a shor t circu it appears across the loop,
an since the loop is connect ed across the side arm which is in shunt with
the main t ransmit ter line, t he loop must be placed a t a poin t effect ively
a qua r ter wavelength from the main line.
This type of coupling is
r efer r ed to as a shunt cir cuit .
In the ir is-coupled coaxia l junct ion , t he
ir is is somet imes considered as being in ser ies with the ou ter conductor ,
When the switch is fired in this case, t he shor t circu it which appears a t
t he ir is gives cont inu ity to the coaxia l line.
R. V. Pound of the Radia t ion Labora tory has developed a coaxia l
T-junct ion , based on the pr inciple of his broadband T-stub, for &in.-
diameter , 46.4-ohm line for a loop-coupled TR cavity, This is a quar ter -
wavelength st b used as a mechanical suppor t for the cen ter conductor
of a coaxia l line as shown in Fig.
7.3. According to the symmetry
pr inciple just discussed, the length
of the stub may be adjusted to
secur e a good match; and since the
stub is in shun t with the line, th is
A
-T
length is about one-quar t er wave-
q+
Y4+
length . If it is set for a good
FIG, 7.3 .—Broadband T-s tub.
match at the cen ter of a f equency
band, however , ther e will be some
mismatch at fr equencies toward the edges df the band. To comp nsa te
for th is, a t r nsformer consist ing of a sleeve one-ha lf wavelength long is
To underst and the act ion of the ha lf-wavelength t r ansformer , let
YI and Yz be the character ist ic admit tances of the main coaxia l line
and of the sect ion with the t r ansformer respect ively.
Therefor e Y2 > YI
since the character ist ic admit tance of a coaxia l t r ansmission line is given
by
1
= 60 In
(
r adiu s of ou t er condu ct or
7
r adiu s of in ner condu ct or
)
If t he r ight -hand end of the line of Fig. 7.3 is termina ted in a matched
load, then the admit tance looking toward the r igh t a t var ious point s
moving from the r igh t-hand end toward the left can be determined.
F igure 7.4a shows the locus of this admit tance in the complex plane
determined a t the cen t er fr equency of the band. The admit t nce is
YI unt il t he t ransformer is r eached. It then moves around a cir cle
SEC. 7 .2]
COAXIAL J 11NC7’IOX8
267
cen ter ed near Y2 and, since the stub has no effect a t th is frequency,
returns to Y1 at t e other end of the t ransformer .
At t he low-fr equ en cy edge of t he band t he effect ive elect rica l lengt hs
l/x of both the stub and the t ransformer a re reduced. Hence, in moving
from the r ight -hand end to the cen ter f the t ransformer , the admit tance
poin t t r avels less than halfway around the circle to the point Ys of
Fig. 7.4b. To get Y,, the admit tance jB. of the stub must be added to
Ys. Since the stub is now shor ter than one-quar ter wavelength , it s
admit t ance is induct ive, and B. is nega t ive.
This makes it possible t o
(a)
(b)
FIG. 74.-Admittance diagram for a broadband T-stub; (a) at cen ter frequency; (b) at
low-fr equ en cy edge of th e ban d.
adjust the diameter of the t ransformer to give a value of Y2/Y1 such that
B~ = – B ,/ 2 . The complex con jugate of Y, is then Y,, and the admit -
t ance at the left end of the t ransformer will again be Y1. A similar
condit ion will be rea lized at the other end of the band so that the T-stub
is p er fect ly ma tch ed a t t h r ee fr e u en cies.
In t his wa y it h as be n possible
to design a single T-stub which can be used anywhere in the wavelength
region from 9.0 to 11.1 cm (9.2-cm,
10.O-cm, 10.7-cm bands) with a
VSWR less than 1.08.
F igure 7.5 illust ra tes a duplexer T junct ion which uses th is broad-
banding technique. At high power level the situat ion is similar t o that
for the simple T-stub. However , in addit ion to the quar ter -wavelength
stub, wh ch is reta ined for mechanical suppor t , the TR arm acts as a
t hr ee-qu ar ter -wa velen gt h st ub sin ce t her e is in su fficien t spa ce t o mou nt
268
llR A.h ’CIIl?I) I)[J PI/ n XI.Vf7 CIRC[’IT S
[SW. 72
he avity at the one-quar t er -wavelength posit ion. This means tha t
the tota l stub susceptancc at the band ccfge is four t imes tha t for a
simple T-stub and tha t the diamete of the half-wavelength t ransformer
on the main line must be much grea ter .
At low power level the distance from the junct ion to the t ransmit ter
must first be adjusted so that the admit tance of the t ransmit ter arm is
7
=-&&J
ntenna y
1
-V2
7
A
zero.
It is then necessary to add
another quar ter -wavelength trans-
former A t o the TR arm to match
tha t por t ion of the half-wave-
r
len gt h t ra nsformer in t he a nt enn a
arm. Without such a t ransformer
a matched TR cavity and receiver
would result in a VSWR, as seen
:A
from the antenna , of (Y,/YJ ’.
The presence of the t ransformer
A, however , increases the ra te of
change with frequency of the sus-
ceptance of the TR arm at high
power level.
This ma kes it n eces-
FIO. 7,5.—Coaxia l T-junct ion with broad-
band t r a ns former .
sa ry to increase the diameter of
t he ha lf-wa velen gt h t ra nsformer
and hence of A. But this, in turn
necessita t es a st ill la rger ha lf-
waveleng-t h t ra nsformer and a st ill
la rger t ransformer A. The proc-
ess converges S1OW1Vo a diam-
eter giving a good match for both high level and low level.
F or a t ra nsf or rn er of 0.555-in . diamet er , t he h igh -level VSWR r emain s
below 1.25 from 8.5 to 12.2 cm wavelength . Si ce such a large t rans-
former redu es the power tha t can be t ransmit ted without breakdown,
and since a na rrower band permits a smaller t ransformer , it was decided
to se a separa te design for each of the 9.2-cm, 10.O-cm, an 10.7-cm
bands in the wavelength region from 9.0 to 11.1 cm. A diameter of 0.486
in. was sa t isfactory for the reduced bands, giving a VSWR below 1.20
over the band from 10.4 to 11.1 cm, for example.
It is possible t o elim in at e t he t ra nsformer A by ch an gin g t he cou plin g
of the input loop of the TR cavity. If the admit tance of the TR switch
as seen at the junct ion is YTR, then in order tha t this resu lt in a match
(admit t ance YJ as seen from
Y,/Y,. = Yz because of the
antenna arm. To sat isfy this,
the junct ion is th ree quar ters
the antenna arm, it is necessa ry tha t
qua r ter -wavelength t ransformer in the
YTR must be larger than Y1 add since
of a wavelength from the TR cavity,
SEC.73] WA VEGUIDE J UNCT ION S
269
the admit t ance a t t he loop must be less than Y1. This means tha t the
loop should be made la rger in order t o increase the coupling. Thk was
don e a nd some impr ovemen t r esu lt ed a lt hou gh difficu lt y wa s en count er ed
in making the loop l rge enough because of the small space available in
the cavity. If t he loop could be adjusted to match the T-junct ion with-
ou t the t ransformer A, the ha lf-wavelength t ransformer coul be made
con sider ably smaller for a given ba ndwidt h.
It will be not iced that a t high level t he T-junct ion is matched over
the band while a t low level it is matched only a t the band cent er . This
is because of the necessity for much bet t er matching at high level.
Although it is not so important to match the T-junct ion at more than
one frequency for the low-leve opera t ion, it is usually necessa ry to
employ some matching procedure to match at one w velength , and to
pr event t he signal losses fr om becom ing t oo high.
It is possible t o use a design similar t o that of Fig. 7.5, but with
the t ransmit t er connect ed to the side arm and the antenna and TR switch
connected to the main arms. In this case modera te reflect ions may be
tolera t ed for power t ransmit t ed between the two main arms (low-level
condit ion) but t he best possible mat ch should be sought for t ransmission
“ around the corner” from the side arm to one of the main arms (high-
level condit ion). This is the reverse of t he requirement for the junct ion
with the TR cavity on the side arm.
7.3. Waveguide J unct ions. -Waveguide duplexers a t microwave
frequencies a re of necessit built with ir is coupling, since there is no
cen t er conductor t o connect to a oop. The iris may be coupled either
t o the end of a side a rm or to the main t ransmit t er line. Rectangular
wa veguide in t he fundament al Tl?lo-m ode is t he usual t ype and coupling
may be made either to the broad or to the nar row side of the waveguide.
A waveguide junct ion in which a side arm at taches to the broad side of
another waveguide is ca lled an E-plane junct ion since all th ree arms lie
in t he plane of t he elect r ic vector .
Similar ly, connect ion t o t he n arr ow
side is ca lled an H-plane junct ion in reference t o the magnet ic plane.
It was pointed ou t in Chap. 4 in connect ion with the ATR switch
that an E-pla e junct ion has some of the character ist ics of a simple
ser ies branching circuit and tha t t he H-plane junct ion displays shunt
proper t ies. Since this turns ou t t o be a very convenien t concept for
duplexer design, t will be examined more closely a t this t ime. A qualita-
t ive understanding can be gained by a considera t ion of the fields and
curren t s in a waveguide. In the TE,,-mode the current s in the cent ra l
por tion s of t he two br oa d sides flow lon git udina lly in opposit e dir ect ion s,
:md t he elect ric field ext ends a cross t he int er vening spa ce fr om one of t he
br oa d si{les t o t he ot her .
These t wo cent ra l st r ips thus resemble the t wo
halves of a simple t ransmission-line pa ir . In terms of t hese st r ips the
270
BRAN CHED DUPLEXZN G CIRCUITS
[SEC.73
ser ies and shunt character ist ics of the two junct ions of Fig. 7“6 appear
quite p laus ible.
It can be observed that the side arm of the shunt junct ion meet s the
wall of the main waveguide at a cer t a in distance from the cen t ra l st r ip.
If the side arm is shor t -circu it ed in the plane of the main waveguide wall,
energy will t ravel down tha t wavegu ide without in t er rupt ion .
For
that reason the distance from the cent ra l st r ip ou t to the side arm is
though t of as being one-quar ter wavelength in the shunt junct ion . 1%
such phase sh ift is assumed in t he ser ies junct ion .
To just ify this equ iva len t -circu it concept , it is necessary t o refer t o
the ex~er imenta l data . Here the resu lt s depend on the wavelength and
@-
-IL
(b)
I:t@ 76.-Waveguide as a trans-
m ission -lin e pa ir ; (a ) ser ies ju nct ion ,
E -pla ne; (b) sh un t ju nct ion , If-pla ne.
—
t he dimensions of, t he waveguide.
Fu r thermore, a cavity a t t ached to the
side arm one-ha lf wavelength from the
main wa vegu ide may give r esu lt s wh ich
differ from those for a cavity moun ted
flush with the wall. The simple wave-
gu ide cir cu it wit h all t erm in at ion s k ept
a t a distance from the junct io has
been studied theoret ica lly and exper i-
mentally.
Th e resu lt s a re embodied in
the equiva len t circu it s of Figs. 410CZ
and b wh ich wer e con sider ed in Ch ap. 4.
At fir st glance these circu it s do not
seem to resemble a simple ser ies or
sh un t ju nct ion bu t t hey do a ppr oxim at e
them in cer ta in respect s. The network
for the E-plane junct ion would be a
Simple Ser ieS branch if B., Xt ,, xd wer e
zero and X, infin ite. It s seen from
Table 4.1, Chap. 4, tha t B. is small, X, is la rge, and Xb and x. would
a lmost cancel if Xc were l rge enough to be neglect ed. Th s junct ion ,
t her efor e, closely r esembles t he simple ser ies br an ch .
The H-plane junct ion is not so simple, for , a lthough X. and xb are
small, X, and X~ are fa r from negligible. These last two quant it ies a re
near ly equal and opposit e. Thk means tha t a s or t circu it placed at
terminals (3) resu lt s in a lmost complet e cancella t ion , and leaves only
a ver y h igh impedan ce a cr oss t he main lin e in a gr eem en t wit h t he idea lized
circu it of Fig. 7.6. The simple shunt represen ta t ion would a lso require
tha t an open circu it a t t erminals (3) resu lt in a shor t circu it across the
line, whereas it actually shunts the line with a react ance of about one.
Of cour se, t here is a poin t on the side arm where an open circu it \ vould
S sc. 7-3]
WA VEGUIDE J UNCTIONS
271
result in a shor t circuit across the main line but it is about five eighths of a
wa velength fr om th e main wavegu ide r at her than one-h alf wavelength .
If such a junct ion were used in a duplexer , th is depar tu re from ideal
behavior might not be not iced.
At high level the shor t circu it a t the
window of the TR or ATR cavity would be placed at the waveguide wall
since for this case the junct ion resembles an ideal shunt circu it . At low
level it would be necessary to dd a match ing transformer to the junct ion
if it were to be used as a TR mount . As an ATR junct ion, however , it
would be necessa ry on ly to tune the ATR cavity unt il it s reactance
r eson at ed wit h t he ju nct ion .
In Sec. 7.10 it will be shown that the differ -
ence between the actual TR junct ion and a simple ser ies or shunt branch
ca n n ever th eless be impor ta nt in br oa dban d a pplica tion s.
The equivalent circ it s of F igs. 4“10a and b can be used to calcula te
the minimum standing-wave rat io that can be obta ined looking into arm
(1) with a matched load on arm (3) and an adjustable shor t circu it on
arm (2), but with no addit ional matching devices.
According to the
symmet ry pr inciple the match between arms (1) and (2) (st ra ight
through) can be made per fect but the match’( looking around the corner , ”
as in the ordinary case for recept ion,
will depend on the par t icular
junction.
If an impedance unity is connected across terminals (3) of the ser ies
junct ion, the admit tance seen looking out toward arm (3) from the
t ermin als of jXC is
If the values in Table 4.1 are sed,
R, =
jy:
1 + (xc + x,)’
= 0.78.
The shor t circu it in arm (2) can be adjusted to produce any desired
reactance in ser ies with Z1. If Z; = R, + jX’ where X’ may have any
value, the admit tance seen looking into arm (1) is Y2 = Y; + jB~. The
locus of Z; on a Smith char is simply the resistance con tour RI = 0.78.
If th is circle is rota ted 180° to give Y; and then displaced an amount
B. = – 0.096, the result ing locus is Y,. The point on the locus which
appr oaches closest t o th e or igin gives t he minimum at tainable standing-
wave r at i .
The value of this quant ity in voltage is r = 1,3 for a ser ies ju nct ion
and r = 1,7 for a shunt junct ion when the constants in Table 4.1 are
used. Apparent ly the ser ies T-j nct ion is super ior a lthough the reflec-
272 BRANCHED DUPLEXIN G CIRCUITS
[SEC.?3
tion loss from a sh nt junct ion would be only 0.30 db even with no
mat ch in g ir is.
Although the r ight -angle T-junct ion can be ma tched with an ir is
so tha t t he t ransmission is the same as for a symmetr ica l 120° type, the
behavior over a band of fr equencies will be infer ior t o tha t of the sym-
18 -
16
\
1
I
90° 1.125”X 0.500”
~ 14
-0
“: 12
~
\
; 10 -
g
~8
\
%
900 0.9001’x
0.400”
$= 6,
.
8
\
/
4
2
li!oQ 1.125” X0.500”
0
3.1 3.2 3.3 3.4
3.5
Wavelength in cm
(a)
6
\
I
I
90° 1.250”X 0.500”
A
U5
.G
:4
s
900 0.900” x 0.4001
I
:3
~
S ’2
[/
~
\ ~
~
gl -
1
120 1.125”X
0.500”
0 -
—2
3.1
3.2
3.3
3.4
3.5
Wavelength in cm
(b)
FIQ. 7.7.—Standing-wave-ra t io curves
f m T-j unct ions of var ious t ypes; (a ) H-pla ne
j unctions; (b) E-p lane junct ions ,
met r ica l junct ion .
A set of da ta
rela t ive to this quest ion is r epro-
duced in Fig. 7-7 from a repor t by
D. H. Ring of the Bell Telephone
Labor ator ies. 1 Measur ements
were made, on a number of differ -
en t ju nct ion s, of t he va ria tion wit h
wa velen gt h of t he st an din g-wa ve
ra t io seen looking in to one arm
wit h a n a djust able sh or t-cir cu it -
ing plunger in a second arm and a
m a t c h e d load termina t ing the
third. The plunger was adjusted
to give the minimum possible
standing-wave ra t io a t the cen t er
wavelength of 3,33 cm and kept
a t t he same posit ion for all the
ot h er wavelen gt hs.
This cor r e-
sponds to the use of the junct ion
in a duplexer where a single posi-
t ion must be chosen for the ATR
cavity for opera t ion over a band
of frequencies. Righ t-angle T-
junct ions and 120° Y-junct ions
wer e tested in waveguides of two
sizes—O.400 in. by 0.900 in. ID
and 0.500 in. by 1.125 in. ID.
The 90° junct ions were t ested
“lookin g a rou nd t he cor ner ” fr om
one of the main arms to the side
arm. No” m atch ing devices were
used. If the standing-wave ra t ios a r e conver ted to vo tage, the values
for ser ies and shunt a re 1,2 and 1.6 for the 0.400 in. by 0.900 in.
T-junct ions at 3.33 cm. These agree approximately with the va lues
of 1.3 and 1.7 previously ca lcula ted on the basis of the constant s for
3.2 cm .
‘ D. H. Ring, ‘(ProgressRepor t on a Broad Band TR-RT S}vitch ,”BTL hfiM-43-
16&189,Oct. 9, 1943.
SEC.7.3]
WA VEGUIDE JUNCT ION S
273
It w ll be seen tha t the 120° junct ion is much super ior to the 90°
junct ion because, even if t he la t ter were matched a t t he cen ter wave-
length , it would give high reflect ions a t other wavelengths. Of the two
120° junct ions, the H-plane type is super ior , wherea s bet ter resu lt s with
90° junct ions are obta ined if the E-plane branching is used. Fur ther -
more, the small waveguide is bet ter than the la rge. It is concluded
that for nar row-band work the 90° junct ion can be used by matching
a t on e wavelength ; other wise the 120° design is be ter .
The high-level standing-wave ra t io can be made good with either
the T- or the Y-junct ions. For work over a band of fr equencies, how-
ever , a cavity (either TR or ATR) mounted one-ha lf wavelength from
the junct ion on a side arm can lead to object ionable standing waves a t
the band dges because of changes in elect r ica l length of the side arm.
In such a case the volt age standing-wave ra t io can be readily ca lcula ted
a t a wavelength dif er ing by AX from the wavelength a t which the junc-
t ion is matched if the simple ser ies r epresen ta t ion of the junct ion is
assumed. The react ance of the side arm is Xl = tan P, where@ = 2rr l/k0
is the elect r ica l length in radians from the junct ion to the window. Since
8 = rm + AD where A(3is small,
because of Eq. (46). If a matched load is assumed for the antenna, the
impedance seen by the t ransmit ter is Z2 = 1 + jXl, and the cor respond-
ing reflect ion coefficien t is
~,=zz–l= jxl
22+1 2 + jx,”
Since Xl is small, II’,1 = [X@ and the volt age standing-wave ra t io is
The shunt junct ion ives the same result . For 1 = ~./2, @ = m, and
for a 2 per cen t bandwidth AA/h = 0.01, and a representa t ive va lue of
(ka /k)’ is 2. These values give r = 1.06.
In pract ica l applica t ions o the 120° junct ions it is advantageous for
mechanica l reasons to pr serve the outward form of the 90° junct ion .
This can be achieved by making addit ional 30° bends in the t rans-
mit ter and the antenna arms quite close to the junct ion. A so-ca lled
“ vest igia l” 120° junct ion, in which the 120° sect ions are considerably
abbrevia ted, s illust ra ted in Fig. 7.8 as designed for branching in the
H-plane. In place of the receiver a rm there is a choke coupling for
274
BRANCHED DllPLEXING CIRCUITS
[SEC.7.4
mounting a 1B24 TR tube close to the junct ion.
On the outside cor ner
of each 30° bend, a reflect ing plate is added at an angle of 15° to either
sect ion of wave guide and placed so as to match the bend. For trans-
mission between the two para llel arms, the voltage standing-wave
ra t io remains below 1.05 over a band of wavelengths from 3.13 to 3.53
cm. For test ing transmission be-
tween the side arm and one of the
parallel arms,
a shor t -cir cu it ing
plunger was placed one-ha lf wave-
len gt h ba ck fr om t he closest cor rect
posit ion, to simulate an ATR
cavity, which must be at a distance
FIG.7.8.—Vestigial120°junction.
of space. With fixed plunger posi-
t ion the var ia t ion of the standing-wave ra t io with fr equency was then
found to be about the same as tha t to be expected from an ideal shunt
ju nct ion wit h a t hr ee-qu ar ter -wa velen gt h st ub.
It will be not iced tha t the 120° junct ion provides more room for
a t tach ing the TR cavity than is provided by a 90° side arm. In the
la t ter ar rangement , there may be some difficulty in mount ing the cavity
so that it is flush with the waveguide wall, and easily removable for
maintenance.
For tuna tely, it is found possible in some cases to obtain
a ra ther good match between transmit ter and antenna with the window
of the TR cavity placed a small distance back from the inside wall of
the waveguide on a 90° side arm.
When a TR or ATR tube is mounted with the window flush with the
aveguide \ vall, t he constants in Table 4.1 no longer apply. It was seen
in chap. 4 tha t for a t least one such ATR switch , the simple ser i s
representa t ion held accura tely. The simple circuit seems to apply as
well in such cases as for the isola ted junct ion. This does not mean
tha t a cavity mount d out on a side arm ~rill show exact ly the same behav-
ior as when flush with the waveguide, but a proper readjustment of the
circuit constants will st ill a llow an approximate shunt or ser ies
representation.
In the next few sect ions it will be assumed, for simplicity, that the
T-junct ion can be represented as a simple shunt or ser ies circu it . In
Sec. 7.10 a mor e a ccu ra te r epr esen ta tion will be discu ssed and a compa rison
ill be made between an actua l junct ion and the ideal circu it .
7.4. Duplexing Loss without an ATR Tube.—In radar opera t ion the
losses suffered by either the transmit ted or the recei ed signa l a re of
int crest . The simple dissipa t ive losses in waveguide a re common to
both of these signals but , except for the cavity losses, they make an
in sign ifica nt con tr ibu tion t o t he duplexin g losses.
SEC.7’4]
DUPLEXZNG LOSS WITHOUT AN ATR TUBE
275
On transmission, the on ly impor tan t loss istheso-ca lled arc loss due
to the power dissipated in the arcs of the TR and ATR tubes. This is
a lso small, ordinar ily, and the impor tance of the effect resu lt s not so
much from the power dissipa ted as from the dependence of t ransmit t er
efficiency on the reflected power . As the subject of a rc loss is discussed
in connect ion with TR and ATR switches it need not be considered at
t his t ime.
On recept ion , the duplexing loss can be conven ien t ly divided in to
two par t s: the TR loss, caused by dissipat ion in or reflect ion from the
TR switch , and the “branch ing
loss, ” du e t o im pr oper im pedan ce
of the t ransmit ter branch. The
TR loss is ade uately covered in
t he ch apt er on t he low-level oper a-
t ion of the TR tube and branch-
ing loss will be discussed in the
next few sect ions of this chapter .
A duplex radar system may
be oper at ed sa tisfa ct or ily wit hou t
an ATR switch if the t ransmit t er ,
as seen fr om t he a nten na , pr esen ts
the cor r ect impedance at the TR
junction.
The received signal
will then be conducted from an-
tenna to r eceiver withou t any
appreciable loss at t r ibutable to
t h e t r an sm it t er .
This situat ion is indicated in
Fig. 7.9, which represen t s TR
junct ions of the ser ies and shunt
type. For the purposes of this
sect ion , it will be assumed that
the r eceiver is matched, as seen
from the TR cavity, and tha t the
Receiver
1.0
Antenna
1.0
(a)
Receiver
1.0
10
:1.0
Zt ::
Antenna
Transmitter
(b)
Ft~, 79. -Du1>lexing circu it s a t low
levc?; (a) with ser ies TR switch; (b) Wit l,
sh un t Tlt switch .
ca vit y in tr odu ces n o m ismat ch a nd may be n eglect ed in low-level con sider -
a teons. It will a lso be assumed tha t the junct ion can be represen ted ah
a simple ser ies or sh un t br an ch in g cir cu it ,
If Z, represen t s the t ransmit ter impedance seen a t the TR junct ion ,
then for per fect recept ion it is necessa ry that Z~ = O for the ser ies TR
junct ion or Z, = ~ for a shunt junct ion . The impedance 2., presen ted
hY a transn lit ter a t it s ou tpu t terminals when not opera t ing, is r efer red
to as the cold impedance of the t ransmit ter . Where ther e is no ATR
s~vitch , 2$ is simply the impedance 2. t ransformed down the line from
276
BRANCHED DUPLEXING CIRCUITS [SEC.~~
thet ransmit ter t o the TR junct ion .
If Z.is purely react ive, tha t is, if
t h cold t ransmit ter reflect s complet ely, the phase sh ift between t rans-
mit ter and
TR
junct ion can be adjusted to make -z: = O or CZJas n ces-
sa ry. Forsome t ransmit ters Z.hasan appreciable rea lcomponent wh ich
will dissipa te some of the received signal unless an ATR switch is used;
many others, however , a r e sat isfactory in th is respect .
If t he phase of
Zc is sufficien t ly constan t from one tube to another , it may be possible
to choose the length of the line connect ing t ransmit t er and TR tube so
that Z~ will a lways have the cor r ect phase. This is the most desirable
ar rangement when no ATR switch is used. Unfor tuna tely differences
between tubes lead t o er rors in Z,, and changes in wavelength produce
changes in the phase sh ift between t ransmit ter and TR junct ion .
This
phase shift is given by the so-ca lled
“elect r ica l length” d = %r(l/xr ) of
the connect ing t ransmission line where 1 is it s physica l l ngth . By
making the distance 1 between t ransmit t er and TR junct ion as small as
possible, t he var ia t ion in o due to changes in wavelength can be kept t o a
minimum.
If th phase of Z. var ies too widely among t ransmit t ers, a phase
con tr ol, ca lled a ‘(lin e st ret ch er , ”
may be inser t ed between t ransmit ter
and TR junct ion . Since the impeda ce depends cyclicall on 0 with
per iod T, the line st ret cher must ave a range 0 = or 1 = ~k,. One
device, ca lled a “t rombon e,” wh ich h as been u sed in coa xia l lin es, employs
a sliding U-shaped sect ion of line.
In rect angular waveguide t he wave-
length depends on the inside width a of the waveguide according to the
expression
and o can be changed by varying a.
If a slot is cu t for a su fficien t dist an ce
along the cen ter of each of the wide sides of the waveguide, a can be
ch anged by squeezing th e t wo halves t oget her .
Th k “squ eeze section”
eliminates the need for any sliding con tacts but requ ires a long sect ion
of waveguide, pa r t icu lar ly at long wavelengths. A more compact
wavegu ide line st retcher consists of a sect ion of dielect r ic mater ia l which
is suppor ted by th in rods extending across the wavegu ide normal to the
elect r ic field. Phase may be var ied by moving the dielect r ic from one
side of t he wavegu ide where the field is weak toward the st rong field in
t he cen ter .
If the an tenna system is not per fect ly matched, t he var ia t ion in line
length effect ed by the line st retcher causes a change in the impedance
seen by the t ransmit t er . Th is may resu lt in changes in t ransmit ter
po er and frequency. If th is is object ionable, it can be preven ted by
SEC. 7.4]
Z)UPLEXING LOSS WITHOUT AN A T R TUBE
277
1wing two line st ret ch er s, on e on ea ch side of t he du plexer ga nged t oget her
t o cancel each other .
To determine the loss in the received signa l when the impedance Z,
of the t ransmit ter branch does not have the cor r ect va lue, the case of a
ser ies TR junct ion may be considered. AS can be seen by reference to
Fig. 7.9, the power delivered to the receiver is
To match the receiver to the antenna , Z, must be zero. This gives
P,= y
(3)
(4)
If a is the branch inq-l os jacto~ in voltage, then the loss factor in power is
(5)
Hence, for th e ser ies TR junct ion,
a = II ++ZLI. (6)
The loss in decibels is L = 20 log,, a .
F or the shunt junct ion
a = II +*Ytl,
(7)
where
Y, = ;.
t
Equat ions (6) and (7) show tha t a ser ies TR junction is equ ivalent to a
shunt junction Zj one is sh ifted one-
quarter wavelength along the trans-
m itter line w ith respect to the other.
A simila r theorem for the ATR
switch was discussed in Sec. 4.1.
It is fr equent ly convenien t to
r epr esen t gr aph ica lly t he r ela tion
between a and Y,. As an exam-
ple, a will be determined fo var i-
ous set t ings of the line st retcher
with a shunt TR junct ion, and a
t ransmit ter w ich , when off, has a
voltage standing-wave ra t io of
r , = 3.0. In Fig. 7.10 Y, is
m apped on t he complex pla ne with
G, and B, as coordina tes. The
locus of all va lues of Y, obta ined
I
o
FIG. 7. 10.—Duplexing br an ch in g-loss dia-
gram.
by varying the line st r et cher is the
278
III{A,VC’IIED DUPI,EXI,VG CIRC(:IT S
[SEC. 74
familiar admit tance cir cle of constant standing-wave ra t io. This
type of t ransmission-line char t , in which the rectangular coordina tes
Gand B (or R and X) are used, will be a lleda car tesian char t todis-
t in gu ish it fr om t he r eflect ion -coefficien t Sm it h ch ar t in wh ich t he a dm it -
t an ce or impeda nce compon en ts a re plot ted in cu rvilin ea r coor din at es.
The loci of Y’ = ~Y, and Y“ = 1 +*Y, ar a lso circles. In fact ,
in the theory of funct ions of a complex variable it is shown tha t any
transformat ion rom Yto Y’ of the form
y,=a Y+b
CY +d’
(8)
wherea, b, c,and dare constants, maps acircle into a circle.
It is kn own
as a linear fract iona l t ransformation or as a “circu la r t ransformation. ”
Because of this proper ty it isasimple mat t r to const ruct Y“andt hen
to determine aaccordingto Eq. (7) asthe length of the vector 1 +~Y,.
It appears that the loss is a minimum where the left side of the circle
in tersects the real axis. At this poin t Y~ = 1/r ,, so tha t the minimum
loss is
(9)
This represents the lowest loss obtainable with a line st r etcher . The
worst t ransmit ter is one for which r . = 1 since this makes a. a maxi-
mum. In such a case the loss L is 20 log,, (~) = 3.5 db.
When th e ph ase cha nges int ro-
I
20
duced by the line st retcher are
con sider ed, it is oft en con ven ien t
g
for numer ica l work to use the
.s
3
\
quant ity t?/2r r = l/ A, which ex-
S 10
presses the line length in units of
a wavelength ra ther than to use
e which is expressed in radians,
To=3 1
=20
Th e va lue of l/A. cor responding
/
) ‘
o ~
—
to each Y~ can be read from a
O 0.10 0,20 O.M 0,40 0,50 0.60
_!_—
convent ion al t r ansmission-line
Ag
char t and associa ted with the
FIG.7.11.—Loss vs. t ransmit ter phase with
no ATR switch.
cor responding a by project ing from
Y~ to *Y,, to 1 + 3Y,, and then
measuring off a . The two curves of Fig. 7.11 give the result s for t rans-
mit ters having r= = 3 and 20 respect ively.
They are per i dic in l/hO of
per io 0.50.
Because of the equiva lence of ser ies a d shunt junct ions the curves
of Fig. 7.11 would be the same for a ser ies TR junct ion except tha t the
abscissae are shifted a quar ter wavelength . In this sect ion and in Sec.
SEC. 75]
DUPLEXING LOSS WITH AN ATR SWITCH
279
7.5 the discussion will r efer t o the shunt TR junct ion unless the ser ies
ju nct ion is specifica lly men tion ed.
In most cases the results will be
immedia tely applicable to the ser ies case through the use of the equiva-
lence principle.
The broad region of lowlosses in Fig. 7,11 indica tes the possibility
of using a simplified form of line st ret cher which has only t wo posit ions,
differ in g by on e-qu ar ter wavelen gt h.
Since the loss curve has a cycle
of one-half wavelength, one could a l~vays opera te in tha t half of the
phase range where the 10SSW are smaller . The curve for r= = 20 in
Fig. 711 remains be]ow 1.30 db over the interva l of len th 0.25 which
extends from O to 0.125, and from 0.375 to 0.500. Many t ransmit t ing
tubes have cold impedances which a re a lmost purely react ive. For
these Y, =jl?, =j cot @,andfrom13q. (7)
a ’=ll++j cote[’=l++cot ’e,
The maximum loss over the minimum half of the phase range is rea lized
fore = m/4, which gives a’ = ~, ora loss of 0.97db.
7.5. Duplexing Loss t ithm ATRSwItch.-In theexamina t ion of the
bra nching loss wh en an ATR switch i used, t her e a re fou r differ en t funda -
mental duplex r circuit s t o be consid red.
Th ey r epr esent differ en t
combina t ions of ser ies and shunt TR and ATR junct ions, Any com-
bina t ion of the two kinds may be used if the distance between the
unct ions is pr oper ly ch osen .
These distances, as given in Table 7.1,
a re ba sed on equ iva len t-cir cu it con cept s a nd a re, t her efor e, on ly n om ina l.
The actual distances for best efficiency ar e slight ly differen t and m st be
determined exper imenta lly.
TABLE i’.l.-~AsIc D PLEXEIi CIRCUITS
TR junct ion .4TR junct ion
TR to ATR istance
(nominal)
1’
Shunt . . . .
Series
+A,
Shunt . .
I
Shunt
*ho
Ser es. . Ser ies
~A~
Ser ies . .
Shunt +A,
The equivalent cir cuit for the shunt-TR, ser ies-ATR duplexer is
antenna line, the ATR s itch should cause the t ransmit ter to appear as a
high impedance a t the TR junct ion in order tha t the antenna be matched
to the r eceiver .
Since the ser ies ATR switch itself appears as a high
impedance, it would be cor r ect t o inser t it in the line r ight next to the TR
jun t ion. At microwave fr equencies this is usua lly impossible, and the
280
BRANCHED DUPLEXING CIRCUITS
[SEC. 7.5
ATR switch is placed a t the equiva lent posit ion one-ha lf waveguide
wavelengt h away.
As was poin ted out in Chap. 4 a shunt ATR switch is equiva lent to a
ser ies-connected one if moved down the line a quar ter wavelength .
If the shunt ATR switch s used with he same shunt TR junct ion, the
~.
ATRswitch
Antenna
Fm. 7.12.—Duplexer cir cu it wit h shunt TR
and ser ies ATR swit ches .
dist an ce between t he two becomes
on e-qua rt er wa velengt h. Simila r
considera t ions give the cor r ect
distance in the other two cases.
13eca use of t he equiva lence of
the two types of ATR switch and
the equality of the branching
losses with the two types of TR
junct ion , as shown in Eqs. (6) and
(7), a deta iled analysis will be
ma de on ly of t he shunt -TR, ser ies-
ATR circ it . The results will
then apply with ver y lit t le cha nge
to the other types of duplexer .
In t he fir st cir cu it t o be con sider ed,
the ATR switch will be loca ted
cor rect ly, t ha t is, effect ively n ext
to the TR junct ion . The norma-
lized ATR impedance will be
designa ted bv Z and the t rans-
mit ter impedance, Z. = R. + jX., r efer red t o the ATR junct ion.
Then
the impedance seen a t t he TR junct ion looking toward the t ransmit ter
is Z~ = Z + Z., and the branching-loss factor from Eq. (7) is
~=l+!—
I
Z+ Z,”
For the ATR circuit tuned to resonance, X = O and
(lo)
Befor e con sider in g t he br an ch in g 10SSu nder n orma l con dit ion s, some
ment ion should be made of the influence of the ATR tube on the recovery
t ime of a duplexer . It waa seen in Chap. 5 that the presence of ions in
the TR gap may ser iously a t tenua te signa ls which immedia tely follow
the t ransmit ted pulse. Under cer ta in condit ions the ATR tube may
have a si ilar effect . If the t ransmit ter impedance Z. wer e zer o nd
if the TR tube wer e a lready r ecover ed; the loss would be given according
SEC. 7.5]
D UPLEXING LOS ,Y WITH AN A TR SWITCH
281
toEq. (10) by the factor
a=l+ ~;,
where G during recovery is determined by the conduct ion in the gap.
Wh en Zc differ s fr om zer o, t he a dded impeda nce in ser ies wit h R decr ea ses
the loss so that th is expression gives the upper limit of the loss. The
same expression would be found if the ATR but not the TR tube had
recovered and if G were the conductance of the TR tube. In that case,
h owever , t he expr ession would hold for an y value of Z.. Sin ce G in creases
with Q, the usual TR tube would tend to r ecover more slowly than a low-Q
ATR tube which has large gaps of low conductance.
In consider ing Eq. (10) it is conven ien t to make use of the so-ca lled
“Smith char t” type of t ransmission-line represen ta t ion , which maps the
complex reflect ion coefficien t r ra ther than the impedance Z.
This
quan t ity, which is given by
z–1
‘= Z+l’
(11)
is limited to the in ter ior of the unit circle, ]1’1 = 1. By associa t ing wi h
ea ch poin t r the cor responding Z, con tours of constant R and X can be
const ructed, which form a system
of cu rvilin ea r coor din at es for Z.
If the poin t R r epr esen tin g t he
r eson an t ATR impeda nce is plot ted
on a S th char t , t e area cor re-
sponding to all possible values of
Z, = R + ZC, when Z, is a llowed
to take any physically realizable
value, is found to be a circle like
the smalf circle on the r igh t side of
Fig. 7.13 which was drawn for
R = 5. A glance at a conven t ional
Smith cha rt shows th at Z, is limited
t o t he in ter ior of t his cir cle beca use
R. cannot be nega t ive. In dia-
FI~. 7. 13.—Smith-char t plot for du plexer
with ATR cavity at r esonance.
gr am s su ch a s F ig. 7.13 t he impeda nce coor din at es will be om it ted, except
for the rea l axis which will be drawn horizonta l and will increase from
left t o r igh t . The (R + ZJ -circle in ter sects the real axis at Z, = R
and cc.
On a Smith char t the reciproca l of an impedance Z is represen ted y a
poin t diametr ica lly opposite to Z.
Thus the locus of l/(R + ZJ is
the cir l on the left which crosses the real axis a t O and l/R.
It is now convenien t to t ransform to car tesian coordinates. In so
doing, it is useful to remember that the t ransformat ion from a Smith
282
BRA.VCIIED DUPLEXING CIRCUITS
[sm . 7:
char t t o a car tesia cha r t a lways maps a circle in to a circle.
This is
becaua e t he t ra nsforma tion , givenby
~=l+r
l–r
(12)
hasthe form of Eq. (8). Of cour se this isa lsotrue for thereverse t rans-
format ion of Eq. (11).
Thus the locus of l/(R + Z.) in car tesian coordina tes is a circle
in tersect ing the rea l axis a t Oand l/R asin ~ig. 7.14. Likewise the locus
1-
1
, R+ZC
‘E--?
FIG. 7.14.—Loss diagram for aduplexer with ATR switch at resonance
of +~[1/(11 + Z,)] isa cir cle which crosses the axis a t 1 and at l/2R.
Since the vector whose magnitude is a must fall within this circle, a must
have a value between 1 and 1 + l/2R. That is, for an ATR switch
tuned to resonance the maximum branching 10SSis given by the factor
az= l++@
9
(13)
wher e G is the cavity conductance.
If G = 0.05, which is a reasonable
va lue, the maximum a is 1.025, which means a loss of 0.21 db. With a
ATR cavity of G = 0.05, tuned to resonance and loca ted the proper
distance from the TR unct ion , the branching loss must be between O
and 0.21 db, no mat ter what the t ransmit ter impedance.
F or t he impeda nce t ra nsforma tion s a ss cia ted wit h a loss ca lcu la tion ,
the Smith char t is frequent ly more convenien t than the car tes.ian char t .
It would therefore be helpful to be able to determine a direct ly from a
Sm it h-ch ar t plot of Y,, wit hou t t he n ecessit y for t ra nsformin g t o ca rt esia n
coor din at es. To fa cilita te this, cont ou rs of con sta nt loss, which will sh ow
SEC. 7“5]
DUPLEXING L0,5X WITH AN A TR SWITCH
t he loss cor responding to each va lue of Z,, can be plot ted on the Smith
chart .
These contours can be determined by plot t ing loci of constant a
in car tesian coordina tes of 1 + ~ }-1 and then transforming them back
to the Smith char t for Z,. In the
fir st case, they are mer ely circles
concent r ic with the or igin and of
radius a as shown in Fig. 7.15
wh ich indica t es t h e loss in decibels
for each contour . It is necessa ry
to t ransform only the point s of
in ter sect ion with the rea l axis
since the con our s on the Smith
char t must be circles with cen ters
on the real axis. one in ter sect ion
is a t
1 + +}’, = a,
or
1’, = 2(a – 1). (14)
On the Smith char t , for Z,, this
poin t is a t
~,=l–h
1 + Y,”
(15)
If Eq. (14) is subst itu ted into Eq.
(15), t h en
2ct-3
r l . – ~l. (16)
Likewise the left -hand in t er s ect ion
is a t 1 + *YL = —a, which gives
2a+3
r*=–—
2a + 1“
The center of the circle is a t
and the radius is
I
1
0
I
F IG. 7. 15.—Loss con tou rs on ca rt esia n ch ar t
for 1 + *YL.
4a2 – 3
rO=~@2+r ,J =-–
4a’2 – 1’
4a
— .
p=*(rl–r2)=4a2_1
(17)
(18)
In plot t ing r , distances ar e measured from the cent er of the Smith char t ,
on a scale such tha t the outside cir cle has radius unity. The result ing
contours a re shown in Fig. 7.16. It is convenien t t o draw this diagram
BEA NCHED I) VPLEXILVG CIRCUI 7’S
[SEC. 7.6
on t ransparent paper so tha t it may be la id over a Z~-plot .
In fact ,
a ter such a contour diagram has been const ructed, the car tesian plot
for br an ch in g-loss ca lcu la tion s will r ar ely be u sed.
This same contour cha r t which was der ived for a shunt TR junct ion
may be used for a ser ies junct ion except that , for a ser ies junct ion , it
will have to be applied to a Smith-char t plot of YL ra ther than of Z1.
FXG. 716.-Loss con tours on Smith char t for Zt ,
7.6. Tuning of the A R Switch .-The loss-contour diagram can be
used to study the effect of ATR-switch tuning.
Sin ce t he a dm it ta nce
of the ATR switch consist s of a constant conductance plus a var iable
susceptance, its locus on a Smith char t will be a circula r arc, like the one
labeled Y in Fig. 7.17. The similar a rc on the opposite side of the
diagram gives the impedance Z. If a par t icula r point Z on this a rc is
chosen and Z= is a llowed to assume any value wha tever , it will be found
tha t the poin t , Z~ = Z + Z., will fa ll somewhere within the cir cle tha t
passes through Z and co and has its cen ter on the rea l axis. If the loss
contours, t ken from Fig. 7.16, a re drawn, the range of branching losses
t o be expect ed is found.
For the par t icu la r va lue of Y chosen here, (0.05 – jO. 16), it is seen
tha t the loss can va ry from O to more than 2 db, for differen t t ransmit ter
impedances. Comparison of this result with those just obta ined for an
ATR switch a t resonance shows tha t an amount of detuning sufficient
SEC.76] TUN ING OF THE A TR SWITCH
285
t o give a susceptance of ordy 0.16 will ra ise the branching loss from a
maximum of 0.21 db, to more than 2 db,
Susceptances as la rge as this can easily appear . If, for example, the
va lues G = 0.05, B = 0.16 and QL = 4.0 a re subst ituted in Eq. (4.1),
~=~= B
ho 2(1 + G) L
= 0.02.
Thus, a devia t ion of 2 per cent from the resonant fr equency will permit a
loss of 2 db. Since it is not easy to obtain loaded Q’s much lower tha
/
2.0 db
w/
1’
1.5db /
l.Odb /
FIG.7.17. —LoeE ?dia gr am for ATR swit ch off r es on an ce.
4, it is apparent why it is difficult t o get good ATR-switch act ion over
br oad bands.
The tuning effect can be readily visua lized from Fig. 7.17 since the
effect of detuning is to move Y and Z away from the rea l axis.
This,
in turn, expands the Z~ circle toward the left , where it intersects the con-
t ou rs of h igh er loss.
Mor e specifica llyy, if a t ra nsm it ter wit h a cold volt age st an din g-wa ve
ra t io of r . = 20 is selected, a possible va lue of ZC would be 0.6 + j3.0,
the impedance seen a t a distance of 0/% = 0.45 from an impedance of 20.
This va lue of Z. and the previous ATR conductance of G = 0.05 will
be used in construct ing the locus of Z, = Z + Z, when B is va ried, in
order to find the loss as a funct ion of B (t ha t is, of ATR-swit ch tuning).
Since the locus of Z is a circ e, it follo s tha t Z, will a lso be a circle;
286
BRANCHED DUPLEX IiG CIRCUITS
[SKc. 7“6
for the Z-locus may be t ransformed to rectangular coordina tes, the
constant Z. a ded, and the resu lt ing Z~-locus t r ansformed back to the
Smith char t . Since each of these opera t ions is of the form of Eq. (8),
the resu lt is a circle.
A formal expression or t ransforming the cen ter and radius of a circle
when a constan t isadded canpresumably reobta ined. This tr ansforma-
t ion, however , which is so elementary in car tesian coordinates, proves
to be ra ther awkward on the Smith char t . The following procedure,
t hou gh less elega nt , is pr act ica l.
The value of Zfor some poin t on the
J ?IG. 718,-Diagram for deter minat ion of t uning cur ve.
Z-cir cle is read from the Smith char t , t he constant -Z, added, and the
resu lt ing ZL plot ted again on the Smith char t .
When th ree different
Z, points are plot ted in his l~ay, a cir cle passing through all of th m can
be const ru ted, and this is the Z,-locus,
Llore than th ree poin ts are
usually plot ted, in order to provide a check, and also because the fir st
th ree points might all lie on a small a rc \ rh ich would not provide the
necessary accuracy. After the Z,-poin ts have been plot ted, the circle
can be f und by t r ial and er r or ra ther than by the use of a formal con
struction.
The result is shown in Fig. 7.18.
A value of Z, can be associated ;vith each value of the tuning param-
eter B.
By means of the Smith char t , values of B are marked off on
the Y-cir cle, These” points are then rota t ed 180° to give the Z-plot ,
.4t each o these poin ts, the imaginary component of Z is read, the imagi-
SEC.7“6]
TUNING OF THE A TR SWITCH
287
nary component of Z, added (—3.0 in thk case), and the in ter sect ion of
the result ing reactance line with the Z,-circle found. (In some cases it
may be more accura te to use resistance instead of react ance.) In Fig.
7.18 va lues of B are marked off in ten ths on the Z, circle. It is now a
simple mat ter to r ead off the loss for each point by using the contour
diagram of Fig. 7.16. The resu lt is t he curve labeled 0/2% = 0.45, in
Fig. 7.19. The other curves a re plot ted for the same ATR switch and
t ransmit ter but for differen t phases,
19/2r = l/&, 1 being the distance
‘illfaE5
1.0
B—
30
E
O/2r=0.25
t
20
s
.
“i 10
5
-!0.0
o
10.
B-—
J::;
%==O.OO
.
:0.20 —
~ 0.10
0
-0.5
0 0,5
B—
FIG. 7.19.—Tuning curves for ATRsw’it ch, G = 0.05,7. = 20.
from the ATR switch , toward the transmit ter , to the point where the
t ransmit ter impedance is 20. The curve for 19/27r=0.25 (Z. =0.05)
is found in the same way as the fir st ne.
For O/2r =0(2. = 20.0),
the var ia t ion is so small tha t t he graphica l method is inconvenient . This
is a imple case and it can be ca lcula ted d rect ly. In fact , since G = l/Z.
in this ca se,
()
2+ ;
&=l +-—
()
G
~+~’
G
.
is obta ined by neglect ing small quant it ies in Iiq, (7).
288
BRAN CHED D UPLEXIN G CIRCUITS [SEC.?7
The clifference in scale of the curves of Fig. 7.19 should be noted.
For 8/% = O, the loss is always small, whether or not the ATR swi ch
is tuned to resonance, whereas for .9/27 = 0.25, the loss is small a t
resonance but increases rapidly off reson nce.
For 0/2% = 0.45, the
loss is small a t most tuning posit ions but becomes apprec able over a
small range off resonance. In this region the reactance in Z and 2.
tend to cancel, cor responding to a sor t of resonance between ATR
switch and t ransmit ter . This type of curve is ra ther genera l; the other
t wo symmet rical cu rves r epr esen t specia l cases (Z, is real).
It is evident that an ATR switch may be tuned without causing any
appreciable increase in signal, or the signal may be st rong for near ly all
set t ings of the tuner and tall off sharply over a small range. This
behavior is somet imes cit ed to show that th e ATR switch is unnecessary.
This, of course, is t rue for that par t icular t ransmit ter , but if good opera-
t ion is expected when the t ransmit ter has some widely differen t imped-
ance, the ATR switch , or some equivalen t device, must be used.
7.7. Distance between TR and ATR Switches.—It has been assumed
up to this poin t that the .4TR switch has been loca ted on the t ransmit ter
line at the cor r ect distance from the TR junct ion : effect ively (n /2)h, or
()
+ ~ ~, away, depen din g on t he cir cu it used. Act uallyj t he elect rica l
,
distance changes with frequency, and it is necessary to determine how
t his a ffect s t he br an ch in g loss.
To determine this, Z + 2. is calculated as before Then 2,, instead
of being set equal to Z + Z,, is obtained by t ransforming Z + 2. down
the line an amount equal to the er ror in 19. As before, the contou r
diagram can be applied to find the loss. Since the t ransformat ion for
line length is simply a rot a t ion on the Smith char t , th is can be accom-
plished by rota t ing the con tour diagram with respect to the (Z + Zc)-
plot .
For the ATR switch at resonance, Z + Z. will be a point near the
r ight -hand end of the real axis in Fig. 7“16. If t he distance between the
switches is var ied, t he situat ion is the same as that discussed in Sec.
7.4 where, with no ATR switch, the distance between the TR s itch and
the t ransmit ter was var ied. Hence, in Fig. 7.11 the port io of the
(~, = 20)-curve, in the region of 1 = O or 0.50, is similar to a loss-vs.-fre-
quency plot f r a tunable ATR switch .
If such an .4TR switch is mo nted on a waveguide t ransmit ter line
a cer ta in distance from the TR junct ion, and the ystem is used over a
cer ta in frequency band, it ay b desirable to know the branching loss
at the band edge.
As the distance between the TR and the AT switches
is usually chosen so tha t it is cor rect at the cen ter of the band, the er ror
in th is distance, when the frequency has changed to the edge of the band,
mu st be det ermin ed
SEC.7’7]
DIS TANCE BETWEEN TR AND A TR SWITCHES
289
Th e electr ica l len gth is
(19)
It is necessary to find the cor rect ion AO = e, – 0, where 0, is the length
at the edge of the band, and 6 is tha t a t the center .
Sin ce t he ch an ges
a re small
0, = 0 + O’AA+ fd’’(Ak)z,
where the pr imes indica te differen t ia t ion with respect to A, and Ah is
the change in wavelength from band cen ter to edge. This maybe writ ten
AO = O’AX+ ~&’(Ak )2.
(20)
If the second term is neglected, the fract iona l er ror in t roduced in
AOis
a nd if A@is r epla ced by O’AAthis is a ppr oximat ely
~=~~&
(21)
To find /3,
*, = _ z~l
p A:,
n
or , by using Eq. (4.6)
# = ~1~.
13 ‘
(22)
‘“= -24+9=-z”’*[(+Y-’l)
and
‘= m)-’]%
By the in t roduct ion of the cutoff wavelength A.,
A waveguide of inside width 0.900 in. is commonly used for a band
centered a t A = 3.33 cm. For that case k. = 2 X 0.900 in. = 4.56 cm.,
A/A, = 0.730 and ~ = – 0.43 ~. This value of ~ is a representa t ive one
fo waveguide, since the va lue chosen for ?I/& is usually near the one
given above .
290 BRANCHED DUPLEXING CIRCUITS
[SEC.7’7
For coaxia l lin e, h owever ,
~=–+,
which represents a somewhat la r ger er r or .
It isinterest ingth t~ = O
when A/A. = ~~ = 0.816, a figure close to the 0.730 used above,
Fur a 12 per cent band, Ah/A = 0.06 giving P = 0.026 for the wave-
gui~e constants chosen . Since this is small enough to be neglected, the
o
I~ lG. 7’20.—Los s d ia gr am wit h lin e-lengt h cor r ect ion .
second term in Eq. (20) m y be dropped, and with the aid of Eqs, (19)
and (22), Eq. (20) becomes
()
o= _. 51 ‘AA
6
AA
—=— —————————
AA
()
~,~
(23)
l–x-
.
Again, by the use of k & = ().730,
A9 = –2.140;.
(24)
As an illust ra t ion, if the distance betwee the TR and ATR switches
is &ho,and the bandwidth is 12 per cent , then o = r , and Ai/A = – 0.06,
so that AO = 0.402.
To find the branching loss, R + Zc is plot ted as shown in Fig, 7.13,
Then the cent our diagram of Fig, 7.16 is applied, but with the axis r ota ted
SEC, 7’7]
DIS TA,VCE BETWEEX TR AND ATR SWITCIfES 291
by an angle 2A0 radians with respect to that of the (R + Z.)-plot .
(Angles measured on the Smith char t are 26.) As shown in J ?ig. 7.20,
the loss, for all values of Z., remains less than 0.4 db.
When it is essent ia l t o keep th e er ror in elect r ica l length t o a minimum,
there is some small advantage in choosing 1 so that there is equal er ror
a t each end of the band, ra ther than set t ing 1 = (n,’4’!A,, a t the cen ter
of the band. To do this, let 6’1and 192be the phase lengths at the two
ends of the band, and let OSbe the cor r ect va lue (r im/2). If 01 — 63 is
set equal to % — d~jthen 63 = (6I + OJ /2 is given which means that
+’%+9
(25)
That is, the waveguide wavelengths A,,
and Xo, a re calcu la ted at , each
end of the band, XP, is determined from Eq. (25) and 1 is set equal to
L93A,,.
Actually, 1 is usually determined exper imenta lly. If the measure-
ment is to be made at on ly one wavelength , it should be ma e at that
which cor responds to Ao,.
It is more accura te, ho~vever , to make the
measurements at each end of the band, and find the two values II and 12.
Then , for equal er ror , the actual value of 1 must sa t isfy the condit ion
Ordinar ily this method offer s so lit t le improvement over the previ{ms
meth od th at it is impract ica l.
It should be obser~-ed that , the distance bet lveen the TR and the \ TR
junct ions is important , but that if the TR switch and t lw recei~’er are
matched and the .\ TR s]r itch is tunable, the distance from the TIt s~vitch
to its junct ion and the distance from the ATR sivitch to its junct ion are
un impor tan t so far as the recci~”ed signal is concerned.
For the TR
switch , th is is t rue because 1 matched load altvays looks the same at
any dis tance.
F or the .kTR s\ vitch , it is obviously t rue if the ,lTR switch
is a pure susceptan e. In this case, any change in the distance from the
ATR switch to its junct ion merely changes the susceptmce presen ted at
the junct ion , and this can be cor r ected by tuning the ATR s]vitch .
lf, to bc more cor r ect , it is assumed tha t the ATR admit tance con-
sists of a constan t cmlductancc plus a var iable susceptance, then the
admit tance locus 1“ is t lmt sholrn in Fig. 7,17.
Any chang in the dis-
t nce from the ATR slvitch to its junct ion rota tes this 10C11S lxnlt the
292
BRA NCH17D I) UPLEXI,W7 CIRCUITS
[SEC. 78
or igin . Since G is small, this 10CUSis very near ly concen t r ic w th the
origin.
Hence the rota t ion produces only a small change in G and
the change in B can be cor rect ed by tuning.
7.8. Branching Loss for F ixed-tuned ATR Circuit s.-A fixed-tuned
ATR switch of a cer t a in Q., tuned to a cer t a in wavelength , maybe used
in a duplexer in which the dist ance between TR and ATR junct ions is
adjusted to be cor rect a t some par t icu lar wavelength . Ordina rily both
of these wavelengths will be nea r the cen ter of the band and for the
presen t it will be assumed tha t they a re equal t o the cen ter wavelength ,
AO. The branching loss which may then be expected at some par t icu la r
wavelength—for example, at one end of the band—may be calcula ted. A
genera l approach to th is problem is the determina t ion of the loss for
each value of the t ransmit t er cold impedance, 2..
A rep res en t a t ion
of this solu t ion due to A. L. Samuel 1 consist s of a cen t our diagram trans-
formed from that of Fig. 716 back to the Smith char t for Z.. To
accomplish th is t ransformat ion it is necessary to know the cor rect ion
Ad for the distance between the TR and .4TR junct ions and the ATR
impeda nce Z.
For illust ra t ion , the line length when i = AOwill be assumed to be
o = r . The 10SSwill be ca lcula t ed a t a wavelength which differs from
k~ by an amount such tha t AX\ kO = 0.015. With the same value of
A/A. as as used in the previous sect ion , A6 is given by Eq, 24) so tha t
A(2/kO) = AO/2m = –0.016.
If Q,, = 8.0 and G = 0.05, then
B = –2(1 + G)Q,, ~ = –0.25.
Hence, }’ = 0.05 – jO.25 and Z = 0.75 + j3.8. NTow loss contours
a re plot t ed on the Smith char t for 2. + Z by rota t ing the Z~ diagram of
Fig. 716 by an amount – A(1?Lv) = 0.016. To t ransform any con tour to
the Zt char t a c rcle is const ructed through three or four point s plot t ed
by subt ract ing Z from the values on the (Z + Z,)-plot . The result is
shown n Fig. 7.21.
When such a const ruct ion is made it is helpful t o know that the cen ters
of the circles fall on a st ra ight line.
This follows from the fact tha t the
circles on th or igina l car tesian diagram for 1 + ~Y~ of Fig. 7.15 a re
concent r ic and that a bilinear t ransformat ion always changes con-
cen tr ic cir cles in to coa xia l cir cles. Su ccessive bilinea r t ra nsforma tion s
leave them coaxia l since any number of such t ransformat ions are equiva-
lent to a single one.
Since the high-loss contours a re all crowded into a small region , it
could be said tha t a high loss is ra ther improbable. This, of course,
1Samuel,0p.cit.
SEC.78]
BRA.VCIIING LOSS
293
assumes tha t a ll values of the t ransmit ter r eflect ion coefficien t r . a re
equa lly probable. The probability of the loss exceeding a sta te va lue
a t a given wavelength can be ca lcula ted assuming random phase of r .
or it may be determined for a sta ted wavelength band assuming tha t
phase and wavelength are random.’ The probability of high losses is
usually r at her low. n som e applica tions, u nfor tun at ely, a ny pr oba bility
gr ea ter tha n zer o ma y be u na ccept able.
‘\
/
0,25db
ml
\
\
/
\
/
\
/
\
\
/); =20
\
-—.
F IG. 7.21.—Loss con tou rs for Z.
There is usually an upper limit to rc and it is clea r from Fig, 7.21
tha t t he maximum value of the loss decrea ses with the maximum value
of rCj for the loci of constan t r , a re circles concent r ic with the or igin
whose radii decr ea se with r ,.
Although the set t ing of an upper limit t o r c r educes he maximum
possible loss, th is upper limit may be so high, for some transmit ter s, as
to be of lit t le help. Thus, measurements made on one type of 10-cm
magnet ron used as a radar t ransmit ter gave va lues of r : a round 30 db
and with some tubes it was as high as 50 db. On the ot er hand, va lues
for one type of 3-cm band tube were near 20 db with a maximum of
about 26 db (r c = 20).
The circle for r . = 20, shown in Fig. 7.21 as a broken line, cor r esponds
to a maximum branching loss of 2.5 db ra ther than the 4.5 db which
I H. K, Farr , “ Character ist ics of Fixed Tuned X Band Ant i-TR,” RL Repor t No.
53-May 13, 1944.
294 BRANCHED D17PLEXIRG CIIiCL’I TS
[SEC. 7 .8
would be a t ta ined if there were no rest r ict ion on r ,.
Aft er t h e con st ru c-
t ion of the contour diagram, it is a simple mat ter to plot loss us a t ’unc-
t .ion of t ransmit ter phase, for the maximum expected r ,, I]y reading off
t he loss va lu es ver suh angle a round the r, circle.
‘l%is gives a n in dica tion
of the ~robat ]ilitv of cncounter inz a cer t a in loss when a t ansmit ter of
‘r
2
L
); = 29
1
0
0
0.1
0.2 03
04
0.5
n
u
(u) +
.s
5–
9
:
~
n
4 –
3 –
2 –
1 —
0
I
I I
I
0 01 02
03
0,4
0,5
(b) ~
9
I!’lG. 722 -B~al,ch lng loss vs. t r ansmit t er
phase with ATR cawt~ off I esonanre.
tha t r. is used. l’wo of these
cu rves \ vit l r . = 20 a d ~, re-
spect ively, a re shown in Fig. 722.
The phase is measured from the
poin t of minimum impedance so
tha t the phase l/kv = O cor re-
sponds to 2. = O or 0.05. The
two curves a re a lmost ident ica l
over most of the phase range,
differ ing only in the region of the
maximum.
The st rong dependence of loss
n magnet ron phase indica tes the
desirability of some cont rol over
t his ph ase.
Of cour se, when r , is
igh there is no necessity for an
ATR switch if the phase can be
iven the pr oper va lue; this is just
what is accomplished by the line
st retcher ment ioned in Sec. 7-I.
Never theless, the possibility of
ch oosin g t he best fixed lin e l n gt h
etween t ransmit ter and ATR
tube should not be neglected com-
pletely.
In cases where there is
enough var ia t ion in Z from one
t rmwnit t ing tube to another to
make an ATR switch necessary, it may st ill be possible to choose the line
length so tha t the transmit ter impedance “helps” the ATR switch .
It should be not iced, however , tha t the opt imum distance from the
TR junct ion to the transmit ter will differ by about a quar ter of a wave-
length, depending on whether or not an ATR switch is used. With a
shunt TR switch , for example, the transmit ter should present a h igh
impedance a t a poin t one-ha lf wavelength from the TR junct ion when
no ATR switch is used. A ser ies ATR switch is likewise placed a t this
point to produce a high impedance. The combina t ion of a highATR
reactance and a high t ransmit ter r eactance of opposite sign at the same
point result s, however , in resonance with high branching loss. This is
SW. 78}
?3R A X CH IA’G 1.0S ,?
295
seen from the curves of Fig. 722, w ich exhibit maximum loss at a phase
near l/AQ = 0.25 which cor responds to large Z,.
This point diverges
from 0.25 as the frequency moves toward the band edge.
A quant ity of pract ica l impor tance is the maximum possible loss of a
duplexer when the t ransmit ter may have any impedance whatever . .4
closer examinat ion of the fa tors affect ing this maximum loss should,
herefore, be made, For simplicity the distance between TR and ATR
junct ion s Ivill be a ssumed cor r ect .
Exami ation of Fig, 717 then shows
that the maximum low is realized at the poin t Z, = Z + 2. = R where
th e left edge of t he ZL-cir cle int ersect s th e real axis. Th e cor respon din g
ransmit ter impedance Z, = j~, =
–j~ is purely react ive and just
cancels the .lTR reactance at that point .
The cor r es ponding loss fa ct or
is
11 lG’+IY
az=l+~~ =1+2 G—”
When G is small compared with l?, th is is approximately
1 B’
“=1+2G’
(26)
(27)
which shows that the ATR conductance G has an impor tant influence on
the maximum loss. When G is small, the maximum loss decreases as
G increases.
If a limitat ion is placed on the t ransmit ter standing-wave rat io so
that the cold impedance is not purely react ive, it will be found that the
dissipation in the transmit ter a lso tends to lower the maximum branch-
ing loss. In limit ing the standing-wave rat io, an upper limit is placed
on Irc~. This means that Z~ is confined to a circu lar area smaller than
that in Fig, 7.17 but st ill cen tered on the real axis. As before, the maxi-
mum loss~s at ta ined for real Zt with X = – Xc and
~.=l+; Yf=l+
sow
G
z=~ —
G+jB
‘G2+Bz
If G is small enough , G’ may be neglected
X=–;, R
11
.— .
2R+RC
(28)
B
‘j G2+B2”
compa red wit h B2, s o that
G
=— .
B,
(29)
On the other hand,
~ =rc+j tan+
e
1 + jr , tan @’
296
n RA ,NCIIEII l) (J PLEXIAV CIRC LTIT ,S
[SEC, 7.6
where @ = 27T(1/x~) is the angula r distance from the A’I’R junct ion
to the point where the tr ansm t ter impedance is r .. The rat ionalizat ion
of Z, gives
~c _ rc(l +tan’@)
l+r~tanz~’
(30)
x.=(
1 – r~)tan4
l+r~tanz~”
(31)
Now tan o can be elimina ted betwe n these two expressions. However ,
to keep the a lgebra from becoming unwieldy some a proximat ions will
be made. It will be assumed tha t r . is la rge compared with one, and
tha t R. in 13q. (28) is of such a magnitude as to make some cont r ibut ion
to a but not so la rge as to cause inordina te losses. A va lue of R + R. = 1
gives a loss of 3.5 db; t her efor e Rc is assumed to be of the order of magni-
tude of unity. This is not incompat ible with our assumpti n rega rding
the magnitude of r . since Rt may ha e an va lue between I/r , and rc.
To find the or der of tan o under these assumpt ions, R. is set equal to one,
and Eq. (30) is solved for tan o, which gives tanz @ = l/r .. It is ther e-
for e possible to neglect tanz @ in compar ison with 1 and wr it e
R, =
r.
1 + r: t an z @“
If Eq. (31) is divided by this expression , then
xc –
l–r:
E r . ‘an4 = ‘rctan 4“
The subst itu t ion of this into Eq. (32) gives
R. = “ ,-
()
1+ ~
c
(32)
(33)
Again, t he use of the assumption tha t R, = 1 means that 1 + (XJRC) 2
is of the order of r . and can be replaced therefore by (X./ R.) 2 in E q. (33).
Th e solu tion for R. is t hen
At this point a conductance G, = l/rc may be int roduced. This is the
admit tance seen one-quar ter wavelen@h away from the window r
loop of the tr ansmit ter cavity (not to be confused with G, seen a t the
ATR junct ion). The subst itu t ion of Rc = G,/ B2 and Eq. (29) into Eq.
(28) give5
(34)
SEC.7.8]
BRANCHING LOSS
297
This is an approximate expression for the maximum loss factor when
the t ransmit t er voltage standing-wave rat io remains less than I/G,.
Evident ly the ATR and transmit ter conductance, G and Gl, have a
similar effect on the maximum loss over this in terest ing range.
It is
clear that if r , is to be very large (Gl small) then the conductance of
the ATR switch should not be too small.
If there is a possibility that G, will be so small as to be of lit t le help
in limit ing the maximum loss, G can be adjusted to make a. as small as
possible for some par t icular frequency, for example, a t the edge of the
band. This is done by changing the cavity losses. This opt imum
value of G is 1111as can be found by set t ing the first der iva t ive of a=
equal to zero in Eq. (26) and not ing that the second der ivat ive B2/ G3 is
posit ive. The minimum value of a= at the band edge is then a= = 1 + G
and at the band cen ter a; = 1 + +G.
The ATR switch used as an example in this sect ion has B = –0.25 .
If G = 0.25 is taken , a loss is given at the band edge of 2 db (a. = 1.25)
and a loss, a t the band cen ter , of 1 db. On the other hand, the old value
of G = 0.05 if used in Eq. (26) gives a maximum loss of 4.4 db at the
band edge and 0.2 db at the band cen ter . That is, the maximum loss
at the band edge is reduced from 4.4 to 2 db at the expense of an increase
from 0.2 to 1 db at the band cen ter .
For a bet ter understanding of the rela t ive merits of different values
of G, t ransmit ter phases other than those leading to the maximum loss
must be considered. A curve of loss vs. t ransmit ter phase can be
plot ted by transforming loss con tours to the Zc-plane as was done to
obta in the curves in Fig. 7.22. Since only hat happens for r . = co
however , is importan t , it is unnecessa ry to make such an elaborate
diagram.
The locus of Z + 2. for rc = ~ maybe const ructed and the standard
con tou r diagram of F ig. 7.16 applied t o determ in e t he losses.
Th is locus
is a c r cle t hr ou gh R and m with its cen ter on the real axis.
Points may
be marked off on this circle cor responding to var ious values of the
t ransmit ter phase Z/AOby reading off the value of Xc corresponding to
each phase, adding X and locat ing the in tersect ion of the reactance
contour X + Xc with the (Z + Z~)-circle. The resu lt ing Fig. 7.23
which is drawn for Y = 0.05 – jO.25 is seen to be similar to F ig. 7.18
for the ATR-tun ing curve. In the first figure it is the t ransmit t er
impedance and in the second the ATR impedance, that is var ied.
The applicat ion of the loss-contour diagram gives the loss vs. t rans-
mit ter phase. F igure 7.24a shows the curves drawn for the edge of the
band (B = 0.25); the dashed curve is for G = 0.05, and the solid curve
for G = 0.25. The la t t er value, G = 0.25, makes the maximum loss
at th is frequency as small as possib e. F igure 7.24b gives the same data
298
BRANCHED DUPLEXING CIRCUITS [SEC. 7“8
at the center of the band, aga in for the two values of G = 0.05 and
G = 0.25. F igure 725 is a plot of the maximum loss, as B is varied,
for the same two values of G.
It is clea r that as fa r as the maximum loss is concerned, there is a
considerable improvement in using the larger G. The smaller G gives
much lower loss values, however , for most poin ts not a t the maximum,
The choice of the opt imum G depends on the rela tive impor tance a t tached
to maximum loss and to the loss under other condit ions, The fixed-
0
FIQ.7,23.—Diagraru of Z, for var iable t r an smit ter pha se.
tuned ATR switches in use at present have low values of G which charac-
t er ize copper cavit ies.
Instead of determining the maximum possible loss at each wave-
length as was done for the curve of Fig. 7.25, it might be asked how the
actual loss would va ry as the frequency of a tunable transmit ter was
changed. To answer this quest ion, A. L. Samuel’ assumed tha t the
cold impedance remains constan t as seen a t the output window or ins
of the transmit t ing tube. Because of the change in electr ica l length of
the line between the transmit ter and the ATR tube, the phase of the cold
impedance 2. as seen at the ATR junct ion will increase steadily as the
wavelength decreases. The poin t a t which the loss is read on a curve
] Samuel, op. a’t.
like tha t of F ig. 722 will move to the r igh t .
,it (lie ~ame t ime the cur~,e
it self }vill change because of the change in ATl{ impedance, and the peak
‘ r
(a ) o —
Za----
0.1 0,2
0.3
0.4
0,5
(b) @—
FIG. 724.-Loss vs. t r ansmit ter phase,
(a) at band edge, (b) at band cen ter . In
the solid curves G is chosen to minimize tbe maximum loss at the edge of the band; G = O.O5
in t he da shed cu rvds,
5–
4 –
/’
/’
/’
g3
&,/’
~Q;/
.s
(3,
g
/
AZ
,/
1
/“
..”
----
0
I
I
I
I
J
0
0.05
0.10
0.15
0.20
0,25
B
F IG. 7 .25.—Maximum loss vs. ATR suscep tm ,ce fr om band cen t er t o t h e edge of t h e band.
will increase and move toward the r igh t . For a low-Q ATR cavity and a
transmit t er line of modera te length , the phase of 2. will move faster and
300 BRANCHED DIJ PLEXIXG CIRC1?ITS
[SEC. 79
may even cross the loss peak severa l t imes in the band. The result ing
rurve of branching loss against wavelength will resemble tha t o Fig.
7,26. Where there are severa l peaks the Q of the transmit ter line would
be large compared with tha t of the ATR cavity and the number of peaks
in a wavelength range AA wo ld be given approximately by
where 1 is the distance from the ATR iunct ion to the transmit ter . The
peaks of the curve, of
shown in Fig. 725,
course, fa ll on the maximum loss cu rve of the type
)i—
FIG. 726.-Branching loss for a tunable t ransmit ter .
7.9. Duplexing Loss under Condit ions of Receiver Mismatch.—In
previous sect ions the loss in received signal between the antenna line
and the TR tube has been considered, under the assumption tha t the TR
tube and mixer were cor rect ly matched. This simplifica t ion, which
a llows the branching loss to be ca lcu la ted m or e easily, is just ified in tha t
it permits an insight int o such fa ct or s as ATR a nd tr an sm it ter im peda nces
and the intercomponent line lengths. Never theless, the more genera l
case of a mixer and a TR tube which present some arbit ra ry admit tance
a t the junct ion should be analyzed.
For this purpose it will be convenien t to lump together the mixer ,
the TR tube, an any other componen s beyond the input window of the
TR tube, and refer to them as the receiver . Since par t of the 10SSin
signal between the antenna line and the TR tube or receiver is caused by
r eflect ion fr om the receiver , the defin it ion of branching loss must n ow be
made m or e explicit . For an arbit ra ry r eceiver admit tance, the branching
loss will r efer to the actua l signa l loss minus the loss with an idea l ATR
circu it . The tota l loss in received signa l is simply the sum of the branch-
ing loss and the convent iona lly de ined TR loss.
F igure 7.27 repr esents duplexer with a t ransmit ter branch of admit-
tance Y~ and a shunt TR junct ion .
The admit tance of the receiver as
SEC. ~9]
DUPLEXING LOSS WITH RECEIVER MISMATCH
301
seen at the input window of the TR tube is represen ted by Y,. This
point is effect ively one-quar t er wavelengt h from the junct ion so tha t t he
admit tance s e e n at t h e junct ion is
I/ r = 2..
If the antenna acts as a
matched genera tor , it can be represented
by a current source of interna l conduct -
ance unity. Then the tota l admit tance
across the genera tor is 1 + Z. + Yt , a nd the
genera tor volt age is V = 1/(1 + Z, + Y,)
Antenna
where 1 is the genera tor current .
The
conductance presented by the receiver a t
the junct ion is R,, t he re l par t of I/Y,,
and the power delivered to the receiv r is
p = lvlz~, = d~l’~r
s
11 + z, + Y,!’” ’35)
FIG. 7.27.—Circuit for det er -
The power delivered to a matched load is
minat ion of br anch ing loss with
PO = ~1112and the tota l loss facto ~ is “’’iv” ‘ismatched”
given by
fP=$”=&-ll+zr+Y,l’.
,
(36)
f Y, is set equal to O the value p’ is given for an ideal ATR circuit .
The branching loss is then
l+ r ,.
I the reflect ion coefficien t r , given by Z, = 17, M used then
,
~ = 11 +*( I — r,) Yt l.
(37)
Equat ion (37) applies to a shunt TR junct ion. The corresponding
expression for the ser ies junct ion is a = 11 + ~ (1 — r,)Zt 1, where I’,
st ill r efers to the in ut windo~v of the TR tube,
If t he quant ty
Y; = (1 – r ,)yt (38)
is int roduced, Eq. (37) has the same form as Eq. (7), w-hich gives the
br an ch ing 10SSfor an idea l r eceiver .
Hence if Eq. (38) is wr it ten as
(39)
the branching loss for an unmatched receiver can be determined by
plot t ing Z; on the Smith char t , and using the same loss-contour diagram
of Fig, 7016 as was used for a matched receiver .
302
BRANCHED DUPLEXING CIRCUITS
[SEC. ?9
The const ruct ion of the Zj plot from the Z, plot is easy when r ,
is known. Si ce r pis constant at any one frequency, the t ransformat ion
of Eq. (39) is seen to be circular , since it has the form of Eq. (8). Hence,
if Z~ is a circle, it is only necessary to cnlcula te three or four poin ts
t o fin d t he Z: locu s.
As an illustrat ion it is assumed tha t the receiv r has a reflect ion
coefficient of r , = re?~ where r = 0.50 and 4 = – 45°. As in Sec. 7.8
F IG. 72S.-Br an ch in g-loss dia gr am showing effect of receiver mismatch.
an ATR circuit is assumed for which Y = 0.05 – jO.25, and a
mit t er for which ~. = =. Hence
1
— ..-
I–rr
= 1.19 – jO.64.
The line-length cor rect ion is neglected so that Z, = Z + Z..
F igure 7~8 is a Smith-char t~lot of Z, and Z; for this case. Compar i-
son of the two loci, with the a id of the contour diagram of Fig. 7“16,
shows the effect of the receiver mismatch on the branching loss.
It will
e not iced *hat the Z; locus is part ly outside the area of the usual Smith
char t . This region outside the unit circle Ir ,[ = 1, cor responds to
n ega tive va lu es of R~.
Since Z; is not an actua l impedance but merely a
symbol for the quant ity ZJ (l — I’,), it is not surpr ising tha t it s rea l
pa rt should be negat ive, In order to read losses in this region , t !~e
contours of Fig. 7.16 must be extended beyond the unit circle. It will
SEC. 79]
DUPLEXING LOSS WITH RECEIVER MISMATCH 303
be found tha t in order to cover all the I’,-plane it is necessary to use
va lues of a smaller than unity, cor r esponding to negat ive va lues of the
lossin decibels. Anegat ive branching lossmerely means tha t the actua l
ATR circuit result s in less tota l duplexing loss than the idea l ATR circu it
for which 2, = w. Naturally this is possible only when there is some
r eflect ion loss fr om t he r eceiver .
In the illustra t ion the branching loss
actually falls to —0.2 db at one point .
If the steps taken in const ruct ing the original loss-contour diagram
are followed, it will be seen tha t the process can e extended, without
\-
-9
/’-
FIG. 7.29.—Smith-char t loss-contour diamam for Z,. generalized to include negat ive
v–alues.
any changes, to th more genera l case of 11’~[> 1 and a < 1. The
diagram has been redrawn in Fig. 7.29 to show the genera l form of the
con tou rs for a ll va lu es of loss.
On t he sca le u sed h er e, t he a rea compr isin g
th e con vent ion al Smith cha rt lies inside t he small cir cle on t he r ight-ha nd
side with the rea l in tercepts (O, @).
The numbers on the contours give
the branching loss in decibels.
Much of the area shown outside this
circle would ra rely cor respond to any pract ica l duplexer .
For any
physica l va lue of r , and Y,, however , r{ may have an value in the whole
complex plane except on the rea l axis to the left of – 1.
To understand the geomet ry of Fig. 7.29, a can be elim inat ed between
Eqs. (17) and (18) which give the radius and center (P ,and rJ of a circle
of constant a . This results in p’ = (1 + rJ (3 + rJ . If a new or igin
304
BRANCHED DUPLEXING CIRCUITS
[SEC. 79
2 unit~ to the left of the or igin for r is chosen , and XOis the dist ance
f om the new or igin to the cen t er of the circle, then I’O = xo – 2 and
This shows that two circles whose centers are equidistan t from the new
origin have the same radius and the imaginary axis is a line of sym-
met ry. Let a and a’ be the loss factors cor r esponding to two such
cir cles, a nd L and L’ t he cor re ponding values in decibels. Then if
Eq. (17) is solved for a
4az=3+ro
I + ro’
or
Xo+l
4a2 = —
XII— 1“
Th e nega t ive of ZOmust give a’; t her efore
That is, L’ = – (12 + L), s o that once the circles on one side of the
axis of symmetry are compu ted, those on the ot he side can be found
immediately.
When L’ = L, L = – 6 db—the con tour value for the
a xis of symmet r y.
If ZI and X2 are the in t ercepts of a cir cle on the real axis, t hen
~lzz = (ZO— P)(xO + ~) = Xi — P2 = 1, because of Eq. (40). The rea l
in t ercept s are reciproca l, which is just t he proper ty of the circles of con -
st an t st an din g-wa ve r at io on a n impeda nce ch ar t in ca rt esia n coor din at es.
The loss-contour family on the Smith char t for Z, is seen t o be the same
as the family of “impedance circles”
in car tesian coordina tes, or as the
dou ble family u sed in bipola r coor din at es.
Since the impedance coordina t es on the convent iona l Smith char t
do not ext end ou side the unit circle, t hese must be const ructed when
n ega t ive va lues of Rt a re encoun tered .
The react an ce circles are found
by extendin those a lready presen t , and the resist ance circles can be
found from their rea l in t ercept s a t (R – 1)/(R + 1) and +1.
For an eva luat ion of the ser iousness of the receiver mis atch , a
compar ison of Eq. (37), wr it t en as a = \1 + ~Y~ — ~1’,Y~\ , with Eq.
(7) shows tha t th e cont r ibu t ion of t he receiver mismatch t o t he branching
loss resu lt s from the term –~r,Y,.
It was found in Sec. 7.8 tha t when
the t ransmit t er phase was var ied the maximum loss occu r r ed at the
poin t where Y, was real, provided the TR-to-ATR distance was cor r ect .
Hence the cor r ect ion t erm –~r ,Y, will be of most in terest when Y, is
rea l. For rea l Y~ a nd a fixed value of II’,1, the branching loss is h ighest
SEC. 7.9] DUPLEXING LOSS WITH RECEIVER MISMATCH
305
if t he ph se of the receiver mismatch is such that J ?, is rea l and nega t ive.
Likewise, a posit ive rea l r , will minimize the branching loss.
As an illust ra t ion, a va lue of l’, = 1 resu lts in a loss of 3.5 db if the
receiver is matched. If, however , Y, = 1.5, and Yt = 1, then r , = – 0.20,
increase of 0.6 db in t he branching loss whereas t he reflect ion loss for th is
value of r , is only —20 log (1 — I’:) = 0.18 db. If ~ is taken equal to
0.05, the branching losses for Y- = 1.0 and 1.5 are 0.214 and 0.256 db,
r espect ively, r epr esen tin g an in cr ea se of on ly 0.042 db beca use of r eceiver
mismat h. Thus, the receiver mismatch may in some cases be more
important to the branching loss than to the reflect ion oss.
F igure 7.30 is a diagram, in car tesian coordinates, of Y, and Y;,
which shows how the branching loss var ies if the magnitude of r , is
-2
0
FIQ. 7.30.—Loss’ dia gr am for Y’, wit h con st an t II’,].
held constan t while the ph se changes. If Eq. (7) is writ t en as
12 + Y,l = 2a it is clear that the loss contours are circles of radius
2a centered at (– 2).
Since Y; – Y, = – I’,Y,, Y: must fall somewhere on a circle of radius
lr ,Y,] about Y, as a cen ter . Where r , is real and posit ive, – I’rYt is
direct ed toward the or igin so that this phase of I’, st ill t ends to r duce
the branching loss, even though Y, is not real.
In Chap. 3 phase data were reproduced for the reflect ion coefficien ts
of cer ta in fixed-tuned TR tubes which would enable the determina t ion
of their cont r ibu t ion to the branching loss.
In many cases, however ,
t he phase of the reflect ion coefficien t may not be known, although its
magnitude, or an upper limit of the magnitude, may be known.
Hence,
it is useful to know the maximum change in the branching loss that could
be caused by a I’,, of a cer ta in magnitude but unknown phase,
306
BRA NCHED D UPLEXING CIRCUITS
[SEC. ;9
F igu re 7.30 sh ows t hat
where CM= 11 + +1-~1 is the branching loss for a matched receiver .
Since
the upper limit , in decibels, of the amount by which the actual branch-
ing loss for a receiver o reflect ion coefficien t II’,! can exceed that for a
mat ch ed r eceiver is
(1
1)
20 1W1O 1 + *
An importan t example of receiver mis atch is that encountered in
tuning a TR cavity. With an ideal duplexer the TR cavity is tuned to
FIG. 7.31 .—Gain contour for tunable T R
tube in t he ~~-pla ne.
resonance for maximum signal.
Since this is not generally t rue for
an arbit rary ATR circuit , the
quest ion ar ises as to how much
improvement in signal could be
expect ed by tuning the TR switch
for maximum signal instead of for
resonance.
In this case the over-all loss
fact or p rat her than t he branching
oss is the quant ity of in terest .
The subst itut ion of R, = G,/ / Y ,l 2
n Eq. (36) resu lts in
B2 =
* I1 + Y,(I + Y,)l’.
,
If the TR c vity is matched
through at resonance, then off
resonance Y, = 1 + jllr where B,
can be var ied by tuning. Since G. = 1, @ = 11 + ~[Y, + jB,(l + YJ ] 1,
and if Y; is set equal to
I’t + jlil,(l + Y,),
@ = 11 + ~Y~l so tha t the ordinary contour diagram for Y{ is again
applicable. Of course, th is is not the same Y; as was used for comput ing
the branching loss.
This is illust ra ted in Fig. 7.31 where poin t P r epr esen ts Y, in ca rt esia n
coor din at es, a nd T U and HO the real and imaginary axes, respe t ive y.
SEC. 791
DUPLEXING LOSS WITH RECEIVER MISMATCH 307
The vector jB,(l + Yt) will be at r ight angles to (1 + YJ so tha t Y’,
will fa ll somewhere on the line AI?, which passes through P and is per -
pendicular to the line from P t o (– 1). As in Fig. 730, the contour s of
constan t loss are circles concent r ic about the point ( – 2). Hence, the
va lue of Y[ which result s in the least loss will be repr esented by tha t poin t
Y;. on line All which is closest to (– 2). This poin t , a t the foot of the
perpendicular fr om ( – 2), is labeled M.
The gain in signa l voltage obta ined by tuning the TR cavity from the
matched condit ion to tha t for maximum signal is the ra t io a/Pn, where a
is the loss factor cor responding to Y~, a nd & that for Y:..
Since @ = O,
the ga in is
i = ‘ec “
(41)
and the gain contour s are also d-contours.
Since the locus of a point P which subtends a constan t angle d at
two fixed poin ts E and F is a cir cle t hr ough E and F, t he 0-cont ou rs a re
circles through E and F, similar
to the one shown. This family of
circles can be t ransforme to the
r ,-plane by t ransforming the
points E and F according to
the equa t ion
e
r , = (1 – Y,)/(1 + Y,).
The resu lt ing poi ts a re – 3 and
FIG. 7,32.—Gain-con tour construct ion in
cc, which means that the con-
the I’,-plane.
tours a re a family of st ra igh t
lines through – 3. In the Y,-plane a contour makes the angle CEF
with the rea l axis, and this angle is equal to 19,as can be seen by
moving P around the contour into coincidence with E. Since the t rans-
format ion is conformal, the contours make an angle @with the rea l axis
in the I’~-plane as well. This makes it possible to draw the gain-contour
diagram for a Smith char t , a t once, by the use of Eq. (41). The con-
st ruct ion is indica ted in Fig. 7.32, whi h is drawn for the r~-plane.
Th e
circle centered at the or igin is the boundary of the ordinary Sm th
char t , and the line through (—3), making an angle 0 with the rea l axis,
is a ga in contour . For the maximum gain, sin d = ~, that is, the maxi-
mum improvement to be expected from the use of a tunable TR cavity
to cor rect the branching loss, is 20 logl~ sec sin-’ + = 0.51 db.
Figure 733 shows the “contours in more deta il. Compar ison with
Fig. 7.16 shows tha t the improvement s very small for any ordinary
du plexer , especia lly a t t he maximum loss wh ich occu rs n ea r t ile r ea l axis
As usual, the resu lts of this sect ion, which were obta ined on the basis
308
BRANCHED DUPLEXING CIR UITS
[SEC. V1O
of the shunt TR junct ion , can be applied a t once to the ser ies TR junc-
t ion . The equat ion cor responding to Eq. (36) for the over -a ll loss f ctor
is t hen
B’ = *I1 +2,+2,1’,
,
which differs only in the replacement of Y~by Zt , so tha t exact ly the same
opera t ions a re per formed in the Z~ plane for the ser ies TR circu it as were
ca r r ied out for the shunt TR junct ion in the Y~-plane.
o
0
-m
1
Fm. 7.33.—Gain con tours for tunable TR tubes on a Smith char t ,
7.10. Duplexers with Mu t iple ATR Circuits. -In an ATR circu it
of the type whic has been considered, it is evident from Fig. 7,17 or
from Eqs. (26) or (34) tha t the maximum branching loss increa es
rapidly with the ATR susceptance B. For a given wavelength band,
B at the edge of the band is determined essent ia lly by the loaded Q
of the ATR cavity. Because it is difficult to design a simple ATR cavity
with a sufficien t ly low loaded Q, circu its with more than one resonant
element are often used in an a t tempt to widen the effect ive wavelength
range of the ATR switch .
In Chap. 4 it was poin ted out tha t the improvement of a two-termina l
device by the addit ion of circuit elements connect ed acr oss the terminals
appear s to be precluded by the reactance theorem. This means tha t
there is ava ilable a two-termina l device whos e clmngs in suscep tance
SEC, 7.10]
MULTIPLE A TR CIRCUITS
309
over the band has been made as low as possible, and some improvement
can be obta ined only by using several elements connected in to the t rans-
mit ter line in such a way as to minimize a = 11 + ~Yf[.
Since two elements of admit tance Y give an admit tance ~Y when
connected n ser ies, the use of two tubes reduces the susceptance to half
it s value. If n tubes are used in ser ies, the susceptance is reduced to one
nth of its value. The same effect can be gained by spacing tubes one-
half waveguide wavelength apar t a long the t ransmit ter line provided
that t he effect of line-length var ia t ion can be n eglected.
The use of two tubes, spaced one-quar ter waveguide wavelength
apar t , a lso effects a marked improvement over the use of a single tube.
This is t o be expect ed because, as pr eviously expla ined, t he high branch-
ing losses appear when the transmit ter reactance cancels the large react -
ance of the ATR tube, whereas the effect of adding a second tube one-
qu ar ter wa velen gt h closer t o t he t ra nsm it ter is t o pr esen t a low impeda nce
at the first tube.
The quest ion natura lly ar ises as to whether any spacing other than
ze o or one-quar ter wavelength would give good resu lts. It is not
necessary at presen t to consider
spacings of one-h alf wa velength
or mor e, sin ce t hey a re equ iva len t
to the shor ter ones but with a
grea ter cor rect ion for var ia t ion
due to frequency changes. Actu-
a lly t he on ly sa tisfa ct or y spa cin gs
for broadband work are zero or
on e-qua rt er wavelength , or th eir
equivalen t , because only these
t--- +---+
FIG.7.34.—Equ iva len t cir cu it for t wo ser iea -
coupled ATR tube .
spacings t ill r esult in eq~al losses at the two ends of the band. Any
other spacing gives a lower loss at one end of the band and a h igher
loss at the other , provided that the cavit ies a re tuned to the cen ter of
t he band.
An analysis will be made of the var ia t ion in branching loss for two
ATR tubes as the phase distance 4 = 27rl/Ag between the two ju ct ions
is changed. In Fi . 7.34, 2. is the t ransmit ter impedance as seen at the
first ATR junct ion and Z is the impedance of either ATR tube since
the two are assumed for the present to be ident ical. Also Z* = Z + 2.;
2* is ZI t ransformed down the line a distance ~ to the next ATR junct ion;
Z~ = Z + Z2 and Z, is Z~ transformed back to th TR junct ion . It is
assumed that Z~ = 23 since the effect of an e ror in the TR-ATR distance
can be readily determined by a rota t ion of the loss-con tour diagram.
F igu re 7.35 gives t he Smit h-ch ar t r epr esen ta ti n of t hese imp da nces
for a par t icular value of Z, a t a par t icular frequency. As in some previous
310
BRA NCIIED DUPLEXING CIRCIJ ITS
[SEC, 7.10
illust ra t ions G = 0.05. Since the ATR cavity is assumed to be detuned
to B = – 0.33 on the low-frequency side of resonance, Z = 0.45 + j2.96.
If Zc is a llowed to take any value, Z, is confined to the in ter ior of the
circle, ma ked l“ in Fig. 7.35a, which passes through Z and co. This is
the same circle tha t previously represented Z, for a single ATR cavity
Q
B’
o
0
(a)
(b)
!!
o
(c)
(d)
FIG. 7.35.—Loss diagrams for ATR tubes; (a) Smith char t for ZZ; (b) Z, at low fre-
quencies; (c) Z3 at h igh frequencies; (d) 2s with decrease in 4.
with no line-length er ror s. To obta in Zz the ZI circle is rota t ed about
the or igin by an amount 24 = 4zl/& radians to some posit ion such as
tha t of the circle U. The circles T and V represent Zz for @ = O and
7r/2 respect ively; s is merely a fixed circle which is a iways tangent to Lr
as @is var ied. The boundary circle Q of the Smith char t has the same
property.
SEC. 7“10]
MULTIPLE ATR CIRCUITS
311
The addit ion of the constan t Z transforms this complete ZZ-diagram
to the Za-diagram of Fig. 7.35b. When this is done theli e AB of zero
r ea ct an ce becom es t he ar c A’B’ of reactance X which connect s Z and ~.
The circle Q represen t ing zero resistance goes over in to Q’ represent ing
the res is tance R. Sin ce Q, S, T, and V are or thogonal to the line ABJ the
t ra nsformed cir cles Q’, S’, T’, and V’ are or thogonal to A ‘B’. Since
the circles T, U, and V are tangen t to Q and S, they will remain tangen t
a fter t ransformat ion . Since Z + ~ = ~, Q’, and T’ must pass t hr ou gh
m and must be tangen t to the unit circle W.
When the circles Q’ and S’ have been drawn, it is easy to follow the
behavior of the circle U’, wklch represen ts the range of impedance Z?
for some arbit rary line length & As @increases, U’ moves around in a
clockwise direct ion , a lways remaining tangent to the two fixed circles
Q’ and S’ and assuming the pos t ions T’ and V’ when @ = O and 7r/2.
If it is assumed that the nearer ATR tube is O or ~k, distant from the TR
junct ion and tha t the junct ion is of the shunt type as usual, then Z, = Z3
and the ordina y loss-cent our diagram Fig. 7.16 gives the range of loss
for any posit ion of the circle U’.
The ci cle Q’ is iden t ica l with the
circle T, wh ich r epr esen ts Z~ for a sin gle ATR t ube sin ce bot h pass t hr ou gh
Z and m.
Hence, comparison of U’ and Q’ indica tes the rela t ive
improvement of two ATR tubes over a single tube.
F igure 7“35b represen t s condit ions at th lower end of a frequency
band with the ATR cavit ies resonan t nea the cen ter .
As t he fr equ en cy
is increased from the lower end of the band toward the upper end Z
moves down toward the poin t 20 on the real axis and reaches it a t reson-
ance. The circle Q’, with all the circles inside, collapses in to the small
circle th rough 20 and m.
At st ill h igh er fr equ en cies Z mo es down below
the real axis and at the upper end of the band the condit ions of Fig.
7.35c a re r ea lized .
If the resonant frequencies of the ATR cavit ies a re adjusted for the
same detun ing at each end of the band, as would be done for minimum
loss, Z will be the same at each end except for a change in sign of the
reaxtance and the values at the low and high ends can be designa ted by
Z and Z*. In Fig. 735a the circle T is the same at both ends of the band.
For the moment the change in @ across the band will be neglected and
this means that all of F ig. 7“35a will be iden t ica l a t the two ends of the
band. In Figs. 7“35b and c represen t i g the two ends of the band,
A“B)’ is the image of A’~’ in the real axis since Z* is the image of Z.
Since the circles Q, S, T, and V are symmetr ica l with respect to the axis
All, Q“ will be the image of Q’, S“ of S’, and so for th . In par t icular T“
will cover the same range of losses as T’, an V“ as V’.
On the other hand the circle U, which in general is not symmetr ica l
rela t ive to AB, will t ra nsform t o cir cles U’ and U“ wh ich a re n ot ima ges.
312
BRANCHED D UPLEXING CIRCUITS
[sEC. 7.10
The rela t ive posit ions of U’ and U“ may b visualized by not ing that
U is tangent to Q at a poin t o Q between B and A when moving clockwise
from B t o A. This proper ty must hold for the transformed circles.
It foll ws then tha t any spacing other than zero and one-quar ter guide
wavelength will, in genera l, give unequal losses a t the two ends of the
band, and will give a grea ter maximum loss at one end of the band
than tha t rea liz d by one of the two spacings O or ~x,. 1
The effect of the var ia t ion in @between the two ends of the band will
be considered next . Suppose tha t I#Js set a t either T/2 or r r (1 = *XOor
+Xo) at the band center and tha t @is sufficient ly l near to have the er ror
the same at each end. The change in @merely causes each of the circles
which were at T’ and V’ t o take u one of the posit ions of the var iable
circle U’. On the low-frequency side O, which is measured clockwise
on a Smith char t , becomes smaller and the circles are shifted counter -
clockwise with respect to 2“ and V’ (that is, the point of tangency with
Q is sh ifted in tha t sense).
In Fig. 7 .35d , V’” and T’” have been shifted by an amount
Ad
()
= A ~ = 0.05 and 0.10,
G,
rela t ive t o V’ and T’ respectively.
This cor responds to the fact that
a spacing of one-ha lf wavelength result s in twice the shift expected
from a onequar ter -waveleng h spacing. On the high-frequency end
the shift is equal and opposite so tha t circles represent ing the two ends
of the band on a Zz-char t will be images in the rea l axis AB. Hence the
ZS-diagrams are also images and the argument about the opt imum spac-
ing is the same as before.
It is concluded that even where there is appreciable phase shift
across the band in the distance between ATR junct ions, the best result s
a re obta ined by the use of spacing either one-quar ter guide wavelength
or one-ha lf gui e wavelength at the center of the band. A similar sym-
metry considera t ion applies to changes in the distance between the TR
1To prove this , th e locus is const ru cted of th e poin t on U’ which givesmaximum
lossas @is varied. The point on this locuswherethe lossis a maximumor a minimum
(for b) is a poin t wher e a n envelope of t he cir cles U’ is t angen t to a loss con tou r.
Th ere must be at least four such points :a maximumand minimumof this locus,and a
maximumand min imum of the simila r locus of the poin t on U’ which gives a mini-
mum loss. There a re just two envelopes ,t he cir cles Q’ and S’, and each of theee is
t angen t to a los scon tou r a t on ly two poin t s making just fou r in a ll or one each of the
extremum points enumerated.
Th e two loci of t he maximumpoin t a t t he two ends of t he band a re images. If
L(4) is t he loss a t on e en d, L’(o) t ha t a t t he ot her en d, L a nd L t he va lu es for o = O
and m/2, then L(d) and L’(+) t raversethe samevalues in oppos ite dkect ions and are
equ al a t dJ= Oand /2. F rom t he fa ct t ha t L has only one maximuma nd one mini-
mum and is neverconstant i t followsthat eitherL or L’iegreaterthan oneof L, andL
at all t imes except when @= Oor T/2.
SEC. 7’10]
MULTIPLE ATR CIRCUITS
313
and adjacen t ATR junct ions so that th is spacing shou ld also be set a t
the equ ivalen t one-ha lf gu ide wavelength at t he band cen t er (for shun t
TRandser ies ATR circuits). Fu r thermore theconclusion for t he in ter -
ATR spacing st ill holds when the TR-ATR spacing changes with
frequency.
Compar ison of b and d of Fig. 7.35 shows tha t the fr equency depend-
ence of o causes V’” to be shifted somewhat to the left rela t ive to V’,
with a cor r esponding increase in the maximum loss, wh ile T“” has con -
t ract ed r ela tive
to T’ with a considerable decrease in the maximum loss
(actually a drop from 3.5 to 1.3 db in this par t icular case). Thus, the
quar ter -wavelength spacing is considerably bet ter than the ha lf-wave-
len gt h spa cin g wh en t he fr equ en cy sen sit ivit y of t he spa cin g is n egligible.
But when the phase shift becomes appreciable it tends to increase the
maximum loss in the quar ter -wavelength case and to decrease it for the
ha lf-wa velength sepa ra tion unt il t he la tt er is actually su per ior .
Of course, if the phase shift goes far enough the loss for the half-
wavelength spacing will in cr ea se.
Examinat ion of the tangent point of a
Z~-circle on Q’, which has been marked off in Fig. 7.35d for va lues of
spacing 0.10 apar t , shows, however , that the points tend to bunch around
0.25 where the loss is small. Hence a fa ir ly small decrease in d brings
the T’ circle into this r egion where it remains until @ has dropped to a
very low value. Although quar ter -wavelength and half-wavelength
spacing are g od for a na rrow and a broad band respect ively, zer o spacing
is not to be recommended.
A clearer view of the branching-loss var ia t ion is obtained from the
curves of Fig. 7.36 which plot the branching loss as a funct ion of trans-
mit ter phase with a t ransmit ter of T, = @ for va rious sepa rat ions @of
the two ATR junct ions. 1 The same value of Z was taken as tha t used
1To compu te t hese cu rves t he t angen t cir cles S’ a nd ~ a r e con st ru ct ed. Th e
point of tangencyof the circle U’ is markedoff on Q’for each value of o by transformi-
ng it fr om t he Q-cir cle. Th e Z~cir cle U’ for a ny @can t hen be dr awn a t on ce. For
each such circle,however, it is necesearyt.ama rk off po nts corresponding various
va lues of the t ransmit terphaee 0. This can be done by star t ing with a Z,-diagram
like t h e Z,diagr am of F ig. 7.23 and then transformingindividually the point cor-
respondingto each value of O. To avoid repeat ingthis procedurefor every ~, loci of
con st an t o can be dr awn on the ZAiagram, making it poca ible to dete rmine0, for
each point on”theZ4rcle, from the locus interceptingat that point.
In the cons t ruct ionof these loci it is not iced tha t se 4 var ies; the &poin taon the
U-circleof Fig. 7.35a tra ce out concentriccirclesabout the origin. Hence,the tran s-
format ionof theseloci to the Z~plane yieldsa family of circlecwith centerclying on a
et ra igh t lin e. Th e lin e of cen ter eic det ermin edby t he poin t Z, = Z + 1, wh ich is
t h e t r an sformat ionof t h e cen t er of t h e concen t ric family, and by the cen t e of Q’
wh ich is a member of t he family. By addingR to the interjectionR$ of any O-circle
with the All-axis , the in tersect ion R: wit h t he a re “A1?’k found. With two such
in tersee tioneand the oenter line it ie eaeyto cons t ruct any &circle . The ucual low-
Contourdiagramcan thenbe appliedto any Z@frele to t iudthe 1- for eachvalue of @.
314
BRANCHED DUPLEXING CIRCUITS [SEC. 710
for the diagrams of Fig. 7“35.
The TR-ATR distance was assumed to
be zero. A modera te change in this distance tends to ra ise the genera l
loss level withou t grea t ly changing the for m of the curves.
It is eviden t tha t the best condit ions obta in with b/27T = 1/10 = 0.40.
A modera te decrease in spacing from one-half wavelength is quite
4
2
0
6
4
2
0
6
4
2
0
4
2
0
0 0.10 0.20 0.30 0.40 0.50 $**
F IG. 7 36.—Loss vs. t ra nsm it ter ph ase for
beneficia l whereas a small increase in the separa t ion causes the losses
to r ise and spread out over a la rge par t of the phase range. If the same
va lues of o are read a t the other end of the band (the h igh-frequency
side) a set of curves similar , but in r ever se order , resu lts.
It appears desirable to use half-wavelength spacing at the cen ter of
the band and ar range to have 4 change with fr equency so as to have an
SEC. 710]
MULTIPLE A TR CIRCUITS 315
opt imum value a t the band edge. In this par t icula r example a shift in
~/!Ar of 0.10 between the cen ter and either end of the band would result
in the best loss curve (4/27r = 0.40 in Fig. 7“36) a t each end. If, in Eq.
(24), 8 is set equal to T and AO/27r = –0.10, then AA/k = 0.094. Hence
with half-wavelength spacing and the waveguide constants assumed in
4
2
0
2
0
2
0
2
0
2
0
4
2
0
0
0.10 0,20 0.30
0. 0 0.50 ;!-
two ATR circu it s with var ious spacings .
Eq. (24), a 19 per cen t band would be required to produce the opt imum
phase shift . With the more commonly used bandwidths of five or ten
per cent an ATR spacing of one or two wavelengths is indica ted. The
necessa ry phase shift might also be obta ined with a shor ter spacing by
reducing the waveguide width so as to make X. smaller .
The curve for @/27r = 0.10 is of par t icula r interest . If Z is t rans-
316
BRANCHED D UPLEXING CIRCUITS [SEC. 7.10
formed down the line a distance of 4/27r = 0.10 the result will be very
close to the conjuga te of Z
This condit ion , which ar ses when the
complex conjuga te of Z is equal to the va lue of Zj obta ined with Z. = O,
will be refer r ed to as a “mutua l” resonance between the two ATR tubes.
This condit ion usually exists a t the normal resonant frequency. When
it happens a t a frequency far enough from the center fr equency, however ,
t he losses
usually become high over much f the phase range of Z..
In order to understand th is, r efer ence is aga in made to l?ig. 723
wh ich cor responds to a Z1-plot in the presen t case and which shows most
of the Zc phase poin t s crowded together in the neighborhood of the poin t
Z where o = O. This is because Xc = tan d and ha lf the ange of d
cor responds to va lues of X ~ 1. Since the X-l-con tours of t he Smith
char t a re close in the vicin ity of Z, th is r ange of X. is on ly a shor t in terval
on
the char t . On the Z3-char t a lso, the phase poin t s tend to congrega t e
abou t o = O. It wou ld be expected, t hen , that if th is poin t were in a
region where the losses were h igh , t hey wou ld be so for much of the range
of 0. lV en mutual resonance occurs t he (0 = O)-poin t (ZC = O) gives
ZS = 2R. If th is fr equency differ s very grea t ly from the cen t er fr e-
quency, R is small, the losses are la rge, and the result is a curve like tha t
for 4/2T = 0.10.
For tuna tely this behavior occur s only over a small range of O. This
can be expla ined by applying the same sor t of reasoning to o as was just
used for 0. If va lues of .$ a re marked off on the (O = O)-locus in the
Z2 Smith char t , the point @/27r = 0.10 occur s at a la rge va lue of X,
while the point a t X2 = O is @/27r = 0.30. When this locus is t rans-
formed to the Z,-diagram, the +-points bunch around 4/27r = 0.30 and
are ra ther widely spaced at q$/27r = 0.10. Since the former va lue of @
gives a loss curve with a sharp peak, tha t type of curve will be rea lized
for most va lues of 1$and the curve with the broad maximum will be et
only wh en o/2%r is close t o 0.10.
This mutual resonance will appear if the ATR epara t ion differs
even slight ly from ~~r . It is then quite close to the ind vidual r esonance
poin t and does not cause high losses. Its presence is readily detected,
h owever , if t he st an din g-wa ve r at io is mea su red a s a fu nct ion of fr equ en cy
looking toward Z,, with Z. a matched load. TVhen @is cor ect a simple
resonance curve with a single maximum is obta ined. If the er ror A@
is appreciable, however , the result ing curve will have a dip a t the mutual
resonance poin t , which provides a sensit ive means of determining the
er ror Al in the cavity separa t ion 1.
The point of the dip is given approximately by B = – ~A’qt where
A’@ is the er ror in ~ at that frequency (AO corresponds to the individua l
resonance frequency). This is seen by finding the admit tance Y2 of the
fir st cavity as seen at the second,
SEC. ~11] DOUBLE TUN IN G
317
~,= Y+~tan A’@ “ G+j(B+ tan A’@)
1 +~Y tan A’@ = 1 – Btan A’@+~G tan A’@”
If G, B, and A’@ are all small, Y, = G +~(11 + A’@). When A’~ = –2B,
Y, = G – jB and X = –X2; the condit io for mutual resonance is
therefore sat isfied.
If t he separ at ion AAof t he mutu al and individual r eson an ces is kn own ,
the er ror Al can be found. For A’+ can be thought of as the sum of the
er ror A@ at the individual resonance poin t plus the er ror A“@ due to the
change in frequency from that poin t to the mutual resonance poi t .
That is, Ad = A’+ – A“@, and
A!+ = –2B
z 4QL ~,
while
Since Al = A@ Q/27r ,
?=[:+QL+(3R
(42)
When 1 is too long, the dip in the standing-wave-rat io cu rve will be on
the long-wavelength side of the individual resonance poin t . When two
ca vit ies a re pr oper ly spa ced, bu t n ot t un ed t o exa ct ly t he same fr equ en cy,
a mutual resonance will appear at a point halfway between the two
individual resonance poin ts where BI = —BZ. The st andin g-wave-
ra t io curve will a lso show a dip in th is case. To determine whether
these er ror s are ser ious, it is necessary a t le st in theory, to find the
maximum loss in the usual way as Zc is var ied.
H owever , t he loss cor -
responding to 2. = O would probably be fa ir ly represen ta t ive in this
case, and this :s found by using 23 = 2R = 2G/(G2 + B2).
7.11. Double Tuning for Wideband ATR Circu it s.—In any at tempt
to design wideband ATR circu it s, it is impor tan t to consider the possi-
bility of “staggered” tuning which involves tun ing one of the pair of
ATR cavit ies to resonance near each end of the band. With ha lf-wave-
length spacing, the loss would be negligible at each of the two resonant
frequencies, assuming no er ror in the ATR spacings. Since under these
condit ions the two ATR cavit ies a re ill ser ies, either one will inser t t he
proper high impedance at resonance. When changes in the ATR separa-
t ion due to frequency dependence are considered, the loss is the same
at the resonant frequency of the fir st ATR cavity (the one nearest the TR
ju nct ion ), and is sligh tly h igh er at t he ot her r eson an t fr equ en cy.
At the cen ter frequency, however , t he mutual reson nce appears and
the loss cu rve has a very broad maximum. .4s this occu rs at t he cen ter
318
BRANCHED DUPLEXIN G CIRCUITS
[SEC. 7.12
of the band it is not possible to make b e of the favorable shift in @which
appea rs a t the ends of the band.
This type of circu it does not appear to
offer any advantages for broadband applica t ions, a lthough it is sa t is-
factory where it is aesired to opera te a t on ly two dist inct fr equencies,
for example, for combined radar and beacon r ecept ion .
St aggered tun ing with quar ter -wavelength spacing between ATR
cavit ies does mer it considera t ion .
The losses a re low at each of the two
ATR r esona nt frequencies, but no mutual r esona nce appears a t the cen ter
frequ ncy. If one cavity is tuned to each end of the band, the maximum
loss a t the cen t er frequency is the same as if t he two cavit ies were tuned
to the cen t er fr equency and the loss determined at one end of the band
assuming no er r or in O. T is is t r ue be ause the Z1-circles a re iden t ica l
for a given va lue of Z and for the conjuga te of Z. Wi h the two cavit ies
tuned to frequencies somewhat inside the two ends of the band, the over -
a ll maximum loss is considera bly below tha t for synchronous tuning.
With double tuning the differ nce in susceptance of the two cavi-
t ies is a constant approxima tely independent of fr equency. If th is
difference is made too la rge with quar t er -wavelength spacing, a mutua l
r esonance will appea r at the band edge. As the susceptance differ -
ence is increased, the resonance poin t moves in toward the cen t er of
the band. It appears, t herefore,
tha t t he result s for double tuning
wit h qu ar ter -wa velen gt h spa cin g wou ld be good for moder at e ba ndwidt hs
but would det er iora t e rapidly for very wide bands.
There is some pract ica l disadvantage in using cavit ies tuned to
differen t frequencies. In low-Q circu it s it is nece sary to make the tube
and cavity integra l and fixed-tuned and this means the use of two tube
t ypes if t wo r eson an t fr equ en cies a re desir ed.
The analysis of the double ATR circuit indica tes two possibilit ies.
(1) For very wideband opera t ion , both cavit ies a r e tuned to the cen t er
fr equency and spaced (n/2)ka apar t .
The frequency sensit ivity of the
waveguide between the two cavit ies is adjusted to give opt imum elec-
t r ica l length a t the band edge. (2) For modera te bandwidth the cavit ies
a re spaced one-quar ter wavelength apar t and stagger -tuned. The
resonant frequencies a re adjusted to g ve the lowest loss over the band.
7.12. ATR Circu it s with More than TWG %vitches.-where a circuit
using two ATR cavit ies fa ils t o cover the fr equency band proper ly the
use of addit ional cavit ies may reduce the branching lo s st ill fu r ther .
If, for inst ance, on e ha s n ident ica l ca vit ies wit h h alf-wa velen gt h spa c ng
and impedance Z, the resu ltan t impedance, assuming all distances a re
cor r ect , is Z, = nZ + 2. and the maximum loss is obta ined by set t ing
Z, = nR. By the addit ion of more tubes this loss could be made as
small as desir ed if t he cor rect spacing over t he band could be mainta ined.
The situat ion is not quite so simple when the var ia t ion in the phase
SEC. 7“12] A TR CIRCUITS WITH MORE THAN TWO SWITCHES
319
length of the spacing is taken in to account , F igure 7.37 shows plot s
of Z~ for differen t numbers of ATR tub s. By the ext nsion of the nota -
t ion of Fig. 7.34, Zl, Za, Zb . . .
r epresen t the va lues of Z~ for 1, 2, 3,
. . .
ATR cavit ies. As usual each cir cle is drawn to represen t the range
of Z. when Z. is a llowed any value.
For each tube Z was taken to be
0.20 + j2.00, which represen ted a cavity with a conductance of G = 0.05
detuned far enough to permit a maximum branching loss of about 11 db
when used lone. The successive cavit ies a r e spaced a distance
FIG, 737.-Impedance plot s So, succes>i~ely added ATR cavit ies.
l/ A, = 0.40 apar t which makes a llo~vance for a drop from half-wave-
length spacing at t he band cen ter
The construct ion ~vas made in the usual manner by rota t ing one
circle a distance of 0,40 and then adding Z to a few point s to get the next
circle. If the cor r ect TR distance is assllmed, the maximum loss for
1, 2, 3 tubes is 11 db, 3.5 db, 1.00 dbj 0,40 db, 0.30 db, 0.27 db,
0.27 db . . . .
The impedances Z,, Z,, Zs . . .
approach a limit ing va lue Zl which
may be found easily if the tubes and spacings a re all ident ica l.
It is
mer ely the itera t ive or character ist ic impedance of t he st ructur e.
The
st ru ct ur e ca n be divided in to idcn tir al symmet rica l elemen ts by bisect in g
each ATR cavity,
Then each element is a t ransmission line of length
@ = 2d& in ser ies \ vith ~Z at each end,
The cha ra ct er ist ic impedance
320
BRANCHED DUPLEXING CIRCUITS
[SEC. 712
is t hen -, whe e Zw and Z= are the open-circu it and shoficircu it
impedances of t he elemen t. The impedance of an open-en d t ransmission
line is –j cot @ so that Z- = &Z – j cot $. When one end of the ele-
ment is shor t -circu it ed the line is t ermina ted by iZ.
By the use of the
st an dar d t ran smission -lin e form ula , t he im peda nce Z,. is
Since the imped nce seen from just in fron t of the first ATR cavity is of
interest
d
Zl=~Z+t iZmZmc=~Z+ l+~–jZ cot&
This shows that Z, can become infinite only when @ = mr. Hence
ha lf-wavelength spacing is to be prefer red. Cont ra ry t o the situat ion
for only two tubes, t he depa r ture from one-ha lf wavelength over the
band should be kept as small as possible.
For quar ter -wavelength spacing ZI reduces to *Z +
r
1 + : which
is t he expr ession for t he con tin ued fr act ion
1
‘+Z+ 1
z+ 1
obtained by adding the elemen ts in one a t a t ime.
If two st r uct u res of iden tica l elemen ts wh ich h ave qu a rt er -wavelengt h
and half-wavelength spacings, respect ively, a t t he cen ter of a band are
compared, it appears ha t the loss at the ends of the band is less for the
half-wavelength separa t ion . Unlike the case of only two ATR tubes,
thk is t rue whether or not d changes with frequency. It has already
been seen that this is t rue when o is constan t .
Figu re 737 illu st ra tes t he h alf-wa velen gt h ca se at t he low-fr equ en cy
end of the band where the spacing has dropped to .40 wavelength ,
t is seen that Z~ has moved around from Z in the direct ion of lower losse.
A considera t ion of the successive poin s Z. on the Smith char t will show
that this is normal, whereas in the quar t er -wavelength case Zt tends
t o sh ift in t he opposit e dir ect ion .
The pr inciples of double uning can a lso be car r ied over to more than
one pa ir of ATR tubes. Thus with an even number of .4TR cavit ies
SEC. 7. 12] ATR CIRCUITS WITH MORE THAN TWO SWITCHES
321
uniformly spaced every other cavity cou ld be tuned to one frequency
near one end of the band and the remainder to another freque cy near
the other end. If enough cavit ies a re used to approximate the limit ing
impedance then , uniike the situat ion for on ly two tubes, the ha lf-wave-
length spacing with double tuning compares favorably with the quar ter-
wavelength spacing.
It will be remembered tha t the half-wavelength spacing with double
tuning was unsa t isfactory for two tubes because the curve of loss vs.
t ansmit t er phase had a very broad maximum at the cen ter of the
band. With addit ional pairs th is will st ill be t rue bu t it will be of no
impor tance, for the maximum can be made as small as desired.
Th e
impedance of two tubes at th t ransmit ter phase which gives maximum
loss at the cen ter of the band is Z + Z* = 2R. For n pairs it is 2nR,
and this increases rapidly with n, causing the loss to approach zero and
giving Z1 = CO. Near the ends of the band the loss will a lso be low
since one of the fir st two tubes will be resonant .
For quar ter -wavelength spacing with double tun ing the maximum
loss at the band cen ter cannot be made to approach zero since Z1 will
be complex.
Near the band ends it will a lso be infer ior to ha lf-wave-
len gt h spa cin g beca use of t he effect ju st discu ssed for syn ch ronou s t un in g.
Th es r esu lt s on t he br an ch in g loss for du plexer s wh ich u se a su fficien t
number of ATR cavit ies t approach the limit ing impedance indicate
that the ha lf-wavelength spacing is sa t isfactory for both synchronous
and double tuning and that the depar tu re from one-ha lf wavelength
should be made as small as possible o er the band.
The discussion of mult iple ATR circuits on the basis of the limit ing
impedance Z1 appears a lit t le academic since, in pract ice, n can never
approach infinity. However , the actual impedance usually approaches
ZI ra ther rapidly, and the limit ing condit ions ay afford a simple
although approximate picture of the behavior of a small number of
elements. For any specific case the actual loss can be determined
graphically.
A ra ther severe limita t ion is placed on the number of tubes by the
arc loss. Since this is appreciable for Iow-Q tubes, the loss at high level
increases with any a t tempt to decrease the loss at low level by adding
more tubes. In addit ion the proble of minimizing the reflect ion at
high level becomes more ser ious as elements a re added. This reflect ion
is usually impor tan t from the point of view of efficien t t ransmit ter
oper at ion and would be smallest wit h qua rter -wavelength spacing wh er e
cancella tion wou ld occu r .
F in allY, t he var ia t ion with frequency of the TR-to-Al’R distance
may in t roduce an appreciable loss even with Z~ = ~.
There does not
appear to be any way to cancel th is effect a t both ends of the band by
322 BRANCHED DVPLEXING CIRCUITS
[SEC. 713
means of specia l ATR cir cu it s.
H owever , an er ror in this distan e which
causes considerable loss with poor ATR circu it s may be inappreciable
wh en t he cir cu it s a re efficien t.
7.13. Branching Loss with the Available ATR Tubes —As a mat ter of
8 -
n
V6
.E
z
34
2 -
0-
0 1
2 3
100+
IhQ. 73S.-Maximum ranching loss for a
duplexer with one ATR tube.
pract ical in terest , cu rves are re-
produced in Figs. 7.38, 7.39 and
7.40 which show the maximum
br an ch in g loss t o be expect ed fr om
duplexer s using ATR tubes with
the measured values of G and Q.
given
in Table 4.4 of Chap. 4.
The curves for the 3-cm band
were ca lcula ted assuming a wave-
length band cen t er ed at 3.33 cm
and wavegu ide of inside width
0.900 in. The curves for the 10-
cm band a sumed a cen ter wave-
length of 10.7 cm and wavegu ide
2.840 in . wide. The TR tube and receiver were assumed to be matched.
The loss va lue r ead from a cu ve is the maximum loss that cou ld occur
for any t ransmit t er impedance at a wavelength differ ing b Ak from the
14 I
‘0123456-0 123456
100 * 100 +
FIG. 7.39. —.Maximum brancbing loss for a
FIG. 7.40,—Maximum branching loss for
3-cm-band uplcxer wit h two ATR tubes.
a 10-cm -ba nd du plexer wit h t wo ATR t ubes.
cen ter of the band. It is also the maximum loss anywhere over a cor -
r ect ly cen ter ed band of width 2Ak.
Th e var ia t ion with wavelength of th e elect r ical distance between TR
and ATR junct ions was neglected in calculat i g the r~u-ves of Fig. 738
SEC. 714] BRANCHING LOS ’S FOR A GENERAL T-JUNCTION
323
for a single ATR tube. The effect is small and separa t ions of both one-
ha lf wa velen gt h a nd on e wa velen gt h h ave been u sed in differ en t du plexer s.
For this simple case the maximum loss in decib ls a t any wavelength is
found from Eq. (26) to be
[
( )1
2
L=2010g,0 l+~G+~ +
The fact tha t the losses a re lo~ver in the 3-cm than in the 10-cm band is
caused by the higher G of the 3-cm-band tube which more than makes up
for it s h igher Q.
The curves labeled “*x, spacing
“ in Figs, 7.39, 740 a re applicable
to a duplexer with two .4TR cavit ies separa ted by one-ha lf wavelength,
the nearer one being a lso one-ha lf wavelength from the TR junct ion.
In the curves marked
“ zero spacing” no cor r ect ion was made for the
va ria tion in elect rica l length of t hese t wo dist ances.
It is seen tha t the
improvement a fforded by the phase shift in the ATR spacing more than
offset s the added loss due to the phase shift of the TR-to-.4TR distance.
The use of two ATR tubes apparen t ly provides a band about twice
as wide as tha t for one tube. Actua lly the improvement might be made
grea ter . The ha lf-wa elength .lTR spacing represen ts that genera lly
used at presen t , but it probably does not give the opt imum frequency
depen den ce of t his impor ta nt elect rica l len gt h.
7.14. Branching Loss for a Genera l T-junct ion.-I~p to this point the
discussion has been based on the simplest ser ies- or shunt-branch ing
circu it representa t ion of the T-junct ion . An actua l waveguidc T-junc-
t ion used for connect ing receiver , t ransmit ter , and antenna lines is in
genera l more complica ted than this, and can be represen t ed only by
the three-termina l-pa ir network of Fig. 71. In pr inciple, six complex
quant it ies can be determine by exper iment , for example, the elements
of t he impeda nce ma tr ix, Ivhich will complet ely ch ar act er ize t he T-jun c-
t ion a t one fr equency. If t he t ransmit ter , receiver , an antenna imped-
ances, 21, Zfi, and Z~, a rc known he tota l loss in r eceived signa l a t the
jun ct ion ca n be found.
If a rm ( I ) goes to the antenna , a rm (2) to the t ransmit ter , and arm
(3) to the receiver , and if E , is t he antenna genera tor voltage,
I?l = EO – 112, = Z,,l, + Z1212 + Z1313,
~, = –1,2, = 22,11 + 2 ,,1 , + Z,Ja ,
E, = –13Z.q = 2,,11 + Z,,I, + 23313.
To find the loss it is merely nwessary to solve the system of equa t ions
for 1s,
(2,1 + 2,)1, + .2,,12 + z13~3 = Eo,
}
2,11, + (z,, + 2,)1, + 22313 = o,
Z3,1,+ Z3,1,+ (233+ ZR)13= o.
(43)
324
BRANCHED DUPLEXING CIRCUITS
[SEC. 714
Foraprope ly matched system, lJ = ~EO, andtheloss inany other case
Eo
‘s 20 10g10m, “
!
It is not possible LOsay much about t he loss for a genera l T-junct ion .
However , for the dependence on Z,, the loss con tour s on the Smith char t
will st ill be th e familiar bipolar family of circles.
This is evident since
Z, occurs in only one term of the Eqs. (43), and the solut ion can be writ ten
in the form
~3=a+bZt
— EO.
c + dzt
The loss factor is then
f?=~=lc+dzt”
2a+bZ,
(44)
If
C + dZt
z,=—
a + bZi’
the loss contour s in the Z1-plane will be the concen t r ic family of circles
2fI = lZl~. Since the tr ansformation of Eq. (44) is circu lar the con tour s
in the Z~- or r~-plane will be a bipolar family.
j Xa
jXa
(1)
j X~
\ (2)
F IO. 7.41.—The equiva lent cir cu it of
‘al 20” Y-junct ion in the H-plane,
As an illustrat ion, the contour diagram for an H-plane (shunt )
waveguide T-junct ion of the symmetr ical 120° type will be const ru ct ed
with the use of the circuit constan ts for waveguide 0.400 in. by 0.900 in.
ID at a wavelength of 3.20 cm in free space and it will be assumed that
the antenna and receiver are matched. The equivalent circu it for the
junct io is show in Fig. 7.41 with the reference planes given by the
broken lines in the sketch to the r ight . The values of the consta ts are
x. = 1.46,
X, = –0.65,
n ormalized with r espect t o t he wa vegu ide impedan ce.
SEC. 7“14]
BRANCHING LOSS FOR A GENERAL T-J UA’CTION
325
To facilit a te compar ison with the idea l shunt junct ion , Z, will be
r efer r ed to a poin t on the t ransmit ter arm where an open cir cuit would
be placed to produce a match be-
tween the other two arms. This
will ensure tha t , a t least for la rge
en ou gh va lu es of ZL, t he beh avior
of the ideal and the actua l junc-
t ion will be about the same.
Since the refer ence point for Z,
will be a t a cer ta in distance from
t he t ermin als (2) of t he equ iva len t
cir cuit , ZI will be ca lled t he t ran s-
m it ter impeda nce r efer red t o t hose
termina ls. The diagram for Z,
Tr ill then be const ruct ed from
which tha t for Z~may be obta ined
by a simple r ot at ion .
Let Z2 equa l the tota l imped-
ance across the terminals of jXb
looking out arm (2) which will be
con sider ed t he tr ansmit ter arm.
z, = ~b(zc + z,)
z. + z* + z,’
:m
ntenna
Recewer
a
+-, +
‘D
z, 4
z,
Transmitter
FIG. 7.42. —Duplexer circuit using the
Y-ju llct ion of F ig, 741.
and the loss between arms (1) and (2) can be found by using the circu it
of F ig. 7-42. In fact ,
E,
z*
z = (1 + 2.)(1 + z. + 222)”
When the junct i n is matched, El = *Eo; for other cases the branch-
ing loss is given by the factor
P=; :=11+ Z.I”l+; (1+ ZO)Y2.
If
Y3=(1+Z.)Y2=
(Z. + z, +_ZJ(l + ZJ,
Zb(z,+ z.)
and
rn=ll+z.l=<l+” x:= 1.77,
then
6 = mll ++Y31,
which is just m t imes the usual loss factor for a simple shunt
with t ransmit ter admit tance Y3. If Eq. (45) is solved for 21,
(45)
(46)
junction
326
lI1tA.VCHliD L)UPLEXING CIRCUITS
1
z,=—
Y,
– z..
‘— – Yb
l+Z.
[SEC. 714
(-L7)
It is now possible t o begin ~~ith thestanchud loss diagram drawn for
l’s, mult iply the va lue of each contour by m, and t en t ransform the
whole family from the Ys-plane to the Z,-plane by means of Eq. (47).
From there it can be t ransformed to th~ rl-plane (Smith char t ) by the
usual Eq. (11). The diagram may lw rota ted to bring the zero-loss
FIG. 7.43.—Loss diagram for the junct ion of Fig. 7.41 plot t ed on Smith char t Io, Z,.
poi t a round to the infinite-impedance poin t and the result is shown in
Fig. 7.43, the loss-contour diagram on the Smith char t for Z,.
In making the t ransformation of Eq. (17) between ZI and l’~ or
between )7, and YS, the work can be simplified by making use of cer ta in
proper t ies of genera l circula r t ransformat ions. Since a bipolar family
of circles is completely determined by its two foci, it is necessary only
to t ransform these two points. The foci a re the poin ts A and B of Fig.
7 29 a bou t wh ich t he cir cles con ver ge for ext reme va lu es of t he pa ramet er .
The family given by Eq. (46) is the concentr ic system of circles of Fig.
7 15 with the foci –2 and =.
Compar ison of igs, 7.43 and 7.16 shows the difference between a
par t icular waveguide T-junct ion and an ideal shunt-branching circu it .
s,.:,. 7,141
IIIM,VCIIINC L(X’S FOR A G13,VERAL T-J [;A’ CTION
327
The most importan t aspect is the sh ift of the infin it e-loss poin t around
closer to the zero-loss poin t with consequen t increase in loss in the upper
half of the Smith char t . In previous sect ions, ATR circu its have been
considered which resu lt ed in values of Z~ such that posit ive and negat ive
reactance are equa lly probable.
Because of the lack of symmet ry of
F ig, 7.43, it migh t be well to adopt an lTR circuit which wmdd favor
the nega t ive reactance wher the losses are smallcx, This cou ld be
done by tun ing the ATR cavity to a slight ly lo]vcr frequency m, instead
of choosing the TR-to-ATR distance so as to give zero loss ~vith the ATR
switch at resonance, it cou ld be made slight ly longer .
In any rasc, t he
amount of cor rect ion would depend on the expect ed range of the Zt
values and on the par t icu lar junct ion used, since the con tour diagram
wou ld pr esumably be differ en t for ea ch ju nct ion .
Th quest ion ar ises as to what can be done to an actual jlmct ion to
make it look like a simple shunt (or ser ies) circu it .
This circu it is con -
sider ed idea l beca use of its symmet rical loss ch aract er ist ics.
It is not
difficu lt t o prove tha t nothing is accomplished by inser t ing any sor t of
t ransform~r in any one arm of the junct ion . Such a t ransf rmer would
have to be matched to the line, and it would, t herefore, change noth ing
in either the receiver or an tenna arms which are assumed to be connect ed
to a matched load and matched genera tor . It can be shown that in the
t ransmit ter arm it would on ly change the line length , for a four -t erminal
network can be matched to the line on ly if it , is symmetr ical, and it then
acts merely as a length of t ransmission line.
The on ly changes that will benefit the junct ion must involve all th ree
arms, since no unmatched device can be inser t ed in only one or two arms.
It would appear tha t the T-junct ion would be considerably improved
if it were possible to adjust the rela t ive posit ions of maxi um and mini-
mum loss on t he Smit h ch ar t so t hat t hey occu rr ed diamet rically opposit e,
that is, one-quar ter wavelength apar t as in the ideal shunt circu it ra ther
than in the distor t ed posit ions of Fig, 7.43.
If th is is accomplished, the quest ion ar ises as to whether any fur ther
improvement can be rea lized; that is, could t he junct ion be manipulated
to sq eeze the loss contours over to the left side of the Smith char t so
that the losses would be low in the opera t ing region . The answer to this
quest ion is n o.
If a short circu it is placed in arm (3) and the t ransmission between
arms (1) and (2) is measured, the two adjacent posit ions of the shor t
circu it which resu lt in zer o and in complet e t ransmission may be loca ted.
A lossless T-junct ion with 120° symmetry is iden t ical with a simple
shunt junct ion if these two posit ions are one-quar ter wavelength apar t .
Its proper t ies a re, t herefore, complet ely det ermined and no fur ther
improvement is possible. The reason can be pictured quite simply.
328
BRANCIIED DUPLEXING CIRCUITS
[SEC. 7.14
In the impedance mat r ix all the diagonal terms are equal, and all the
nondiagona l terms are equa l because of symmetry.
There are, thus,
on ly two independen t terms and as they are both imaginary, two rea l
constan t s suffice to descr ibe the junct ion .
Now if 1 is the distance
between the two posit ions of the shor t circu it which give zero or com plete
t r ansm ission , 1is a fu nct ion of th ese t wo con sta nt s an d sp cifyin g 1 = ~AO
places a condit ion on them w ich allows one to be elimina ted. The
remaining constan t depends on the posit ion of the r eference poin t for
measur ing impedance. By proper choice of the reference point th is
constan t may be made equal t o that of a simple shunt circu it .
Thk indicates the possibilit y of making a waveguide T-junct ion
accura tely equi a len t to a simple shunt circu it by varying some one
dimension which does not dest r y the symmet ry. The elect r ica l meas-
uremen t involves on ly an elemen ta ry exper iment with a plunger . To
the au thor ’s knowledge th is exper iment has not been at tempted.
It can be shown in the same way that any lossless junct ion is equiva-
len t to a shunt junct ion if it is possible to match between any two arms
by a shor t circu it in the th ird, and if the two shor t -circu it posit ions for
zero and complete t ransmission are one-quar ter wave ength apar t .
The genera l n etwor k with th ree pairs of termina ls has a th ree-r ow imped-
ance mat r ix with nine elements. Since the nondiagonal elements a r e
equal in pairs, t her e a re six in depen den t con sta nt s.
The requ irement of
matching places two condit ions, and the choice of r efer ence planes,
th r ee more. The proper ty of one-quar ter -wavelength shift for cu toff
makes a tota l of six condit ions which fixes all the constan t s.
It will be not iced that no dist inct ion is made between shunt and ser ies
jun ct ion s, as t hey a re equ ivalen t if t he r efer en ce plan es a re n ot specified.
In fac , the sca t t er ing mat r ices for simple shunt and ser ies branch ing
cir cu it s a r e
Series
Shunt
! -i -!1 1:-: -!1
If each reference plane for the ser ies junct ion is sh ift ed one-quar ter
wavelength , the sign of every matr ix element will be r eversed, and hen
all the nondi gonal elements can be made posit ive by reversing the
termina ls on arm (l). The resu lt is iden t ica l with the matr ix for the
shun t junct ion .
CHAPTER 8
PRACTICAL BRANCHED DUPLEXERS
AND BALANCED DUPLEXERS
BY AROLD K. F.4RR AND ARROLL W. ZABEL
The fir st par t of this chapter is devoted to a review of examples of
branched duplexers which have been used and to some of the observed
r esu lt s oft his u se. Th ese examples a redivided in to twocla sses-coa xia l-
line duplexers and waveguide duplexers. The coaxia l-line duplexers
have been used a t 10 cm and at longer wavelengths; waveguide duplexers
have been used in high-power insta lla t ions a t 10 cm and at all power
levels a t sh or t r wa velen gt hs.
Few coaxia l duplexers have used ATR
swit ch es wh er ea s most wa vegu ide du plexer s h ave in clu ded t hem ,
In the
secon d pa rt of t he ch apt er , ba la nced du plexer s a re descr ibed.
BRANCHED DUPLEXERS
BY HAROLD K. FARR
8.1. The lectr ica l Design of a Duplexer .—In select ing a switch it is
necessary to choose between the fixed-tuned and the tunable types.
Systems developed since the fixed-tuned tubes became available have
u sed t hese t ubes a lmost exclu sively.
It is imp r tan t to keep the number
of differen t adjustments in a radar system as low as possible. This not
only facilit a tes main tenance and tuneup but reduces the possibility of
incor rect adjustments. To at ta in th is object ive, it may be necessa ry
t o make some con cession s in per formance.
It has been seen tha t the limitat ions in fixed-tuned ATR tubes may
lead to some loss. However , the usual tunable ATR cavity which has a
much higher Q may also cause losses due to tempera t r e detuning or
t ra nsm it ter -fr equ en cy r ift .
Fur thermore, the recept ion of signals a t
more than one frequency, which occurs when beacon recept ion is com-
bined with rada r , may be ext remely inefficient . There seems to be no
deter iora tion in per form ance using fixed-tuned TR tubes since t he r ecep-
t on loss usually compares favorably with the cor responding tunable
tubes. If a nar row r-f filter happens to be desirable, as for image rej ec-
t on , then , of cour se, a tunable TR tube may be prefer red.
The ‘mechanica l simplicity of the fixed-tuned ATR tubes makes
them cheaper than the or responding tunable circuit s. However , when
329
330
BRA,VCHED AND BALANCED L)CI’PLEXERS
[SEC. 81
length of life is t aken into account , the cost of the fixed-tuned TR tubes
will be comparable with the tunable ones.
Aft er the switches have been select d, the junct ion for the TR s~vitch
is the next considera t ion. .1 junct ion \ r ith 120° symmetry has the best
elect r ica l pr oper ties, but for n ar ron-ba nd a pplicat ions ot her kinds ~r hieh
offer mechanical advantages may be used.
If a 120° junct ion is chosen
and if the lo~vest possible r ecept ion loss is desired over a wide band of
fr equencies, t he necessa ry a ltera t ion should be made to ensure tha t t he
junct ion is equiva lent to an ideal shunt or ser ies circuit as expla ined in
Sec. 71. It would probably be impract ical t o a t tempt this with any
junct ion ot her than the 120° junct ion ,
If the complete 120° symmetry is not used, ther e should, if possible,
be symmetry of the t ransmit ter and antenna arms with respect t o the
other a rm since the proper t ransmit ter match i most impor tant .
If the
two arms used for re ept ion (or t ransmission) lack symmetry with
r espect t o the third, they should be checked for reflect ion loss with a
plunger in the third arm.
The ATR junct ion has been discussed in Chap. 4. At low power
level t he only impor tant aspect is it s effect on the Q. At high power
level t he problem is the same for both TR and ATR ju ct ions. The
distance from the window to the waveguide wall must be adjusted to
give a good match for t r ansmit ter power . In pr inciple, th is is done a t
high power level so tha t t he switch will be broken down. In pract ice,
it is much simpler to make such m asurements a t low power level, and
to simula te the condit ions of high power level by shor t -cir cuit ing the
e lect rodes or detun ing sufficien t ly.
F or low-Q t ubes wit h la rge win dows,
it is necessa ry to cover the inside of the window with Wood’s metal or
wit h some ot her con du ct ive coa tin g.
It is mor e accura te in on e r espect to make this sor t of standing-wave-
ra t io test a t low power level.
Because of the fin te fir ing t ime of the ar c,
the standing wa e measured a t high power will be an average of that
befor e a nd a ft er fir ing a lt hou gh t he sta nding-wa ve r at io of in ter est is th at
measured after fir ing. If the de ect ing element reads average power , the
‘‘ a pparen t” standing-wave ra t io in power a t high power level is
where W is t he tota l energy per pulse r eceived by the probe, and W? and
W. are it s maximum and minimum values as the probe is moved in the
slot . If it is assumed, for example, tha t t he line is matched when the
t ube is fir ed,
I
I
s],{. 8’11
EI,I<(’7’l:fC.4 I , l ) I ?,$ ’IGN
331
where TI and TZ are the lengths of the por t ions of the pu lse before and
after fir ing, PI= and PI. a re the maximum and minimum power s in the
standing wave before fir ing, and P~ is the power after fir in .
If it is
assumed that the j nct ion reflect s completely before fir ing, PI. = O and
PI= = (V1,)2 = (2 Vz) 2 = 4P2 where VIZ and VZ a re the volt ages cor -
responding to the power s P,. and Pz , if un ity impedance is assumed,
Finally,
TI
‘2=1+4Z”
If, for instance, the fir ing t ime is one ten th of the remainder of the pulse,
then rz = 1.4, whereas the actual standing-wave ra t io a fter fi ng is 1,0.
This effect is not ordinar ily not iceable for long pulses u t may be so for
pu lse lengths of 0.1 psec or less.
If the junct ion is to beused overa band of frequencies grea ter than
1 or 2 per cen t , it will probably be necessa ry to mount the cavity \ vith
t he win dow flush wit h t he \ vallof t he t r ansm it ter lin e a lth ough , for n ar row
bands, it can be set back one-half wavelength .
High-Q cavit ies a re often ir is-coupled to the nar ro~v side of a wave-
gu ide simply by cu t t ing a small hole in the waveguide wall. At h igh
power level the hole usually appears as a capacit ive susceptauce of small
magnitude. This can be canceled by adding a small t ransverse st r ip
of metal on the opposite side, as for the induct ive matching ir is, or the
mismatch may be small en ou gh t o be n eglect ed.
If TR and ATR cavit ies
which have the same mismatch are mounted one-quar ter wavelength
apar t , the susceptances will cancel a lmost completely. Unfor tuna tely
the ATR cavity usually has a much la rger window than any high-Q TR
cavity. A voltage standing-wave ra io of 1.15 has been observed for
such a combina t ion .
The window of a 1ow-CJ cavity is dist inct from the waveguide wall
and may, ther efor e, be moved in unt il the h igh-level match is ach ieved.
Specifica t ions for th e voltage standing-wave ra t io of fixed-tuned tubes
are given in Table 4.4 of Chap. 4. Some of the 10-cm-band tubes cou ld
doubt less be improved by changes in the mount .
Where a pre-TR switch is used, the TR cavity must be mounted
with the input w ndow an odd number of quar ter wavelengths from the
input window of the pre-TR tube.
In t he 10-cm du plexer s this dista nce
is usually th r ee quar ter s of a wavelength . This a r rangement places
the inpu t window of the pre-TR tube at a poin t of maximum voltage
when the TR tube is fired.
The distance between TR and ATR junct ions must be adjusted for
best signal recept ion . For simple ir is coupling to the main waveguide,
th is distance is often very close to the nominal one-quar ter or one-half
332
BRAiVCH17D AND IIALA NCIID I) l~PLIEillRS
[SEC. 81
wavelength. Therefore, it ma be assumed that it is this distance and
the complete duplexer merely checked as ment ioned below. For the sim-
ple t ypes of wa vegu ide jun ct ion s wh er e t he equiva lent -cir cuit con st ants
are known, the cor r ect ion t o the nominal spacing can be ca lcula ted with-
out r ecourse to exper iment but such ca lcula t ions are valid only when the
cavity and other components are kept a t a distance from the junct ion
of a t lea st a qu ar ter wa velen gt h.
The exper imenta l determina t ion of the cor rect spacing is made in t wo
steps: a measurement on the ATR switch a lone, and one on the TR
junct ion a lone. With the .4TR switch tuned to resonance, the posit ion
of the minimum poin t of the standing-wave pat tern is found rela t ive
to the ATR junct ion. Then by means of an adjustable shor t-circu it ing
plunger in the t ransmit ter a rm, tha t posit ion of the minimum point
rela t ive t o the TR junct ion which gives the best match for r eceived signal
is determined. As expla ined in Sec. 7.7, this determin t ion of the TR-
to-ATR distance is best done at a fr equency cor responding to the wave-
guide wavelength given by Eq. (7.25). This is near , but not necessar ily
at , the cen ter of the band.
The measurement of the posit ion of he standing-wave pat tern rela -
t ive to the ATR junct ion is the determina t ion of the distance of plane
A of Fig. 4.1 from the center of the junct ion . This cor rect ion is small
and may be negligible. To make this test , it is necessary to add a tuning
adjustment to the cavity, if none is present , and to check for resonance
by mea su rin g R with a plunger as descr ibed in Sec. 4.2. A small er ror
in cavity tuning would inva lida e the phase measurement .
To help
eliminate phase er ror s which arise if the ATR window is not proper ly
centered, the measurement should be repea ted after the cavity has been
removed from the mo nt , tu rned 180°, and replaced. The two readings
can then be averaged.
After the TR and the ATR circuit s have been combined, the TR-tc-
ATR dist an c sh ou ld be ch ecked a ga in by mea su rin g t he volt age st an din g-
wave ra t io looklng in from the antenna end. Because of the difficulty
of making accura te phase mea urements in t ese test s, the distance may
be found to be in er r or a t this point . To cor rect it , the plunger posit ion
hich gives the same impedance a t the antenna arm as tha t given by
the ATR switch is determined. A measurement of the change in plunger
posit ion from this point to the point of best match gives the er ror in the
TR-t o-ATR dist an ce.
If more than one ATR switch is used, the separat ion between cavit iea
must be determined at the s me frequency used for the TR-to-ATR
distance. The data a re given by the measurement a lready made on the
ATR switch. By using these da ta , the cor rect separa t ion is the nominal
distance plus twice the cor rect ion given by the distance of the reference
SEC. 82] MECHANICAL DES IGN
333
plane from the cen ter of the tube, the cor r ect ion being counted once for
each of the two tubes. For a ser ies mount the cor r ect separat ion maybe
sligh t ly grea ter than the nominal one-quar ter or one-half wavelength , as
indica ted by an induct ive susceptance B. in F ig. 4“10a. For a shunt
mount , the cor r ect ion has the opposit sign .
When the two ATR switches have been combined with ha lf-wavelength
spacing, their sepa ra t ion may be checked by the mutual-r esonance
method of Sec. 7.10. The er r or in spacing is th en given by Eq. (7.42).
This sensit ive check is not applicable to quar t er -wavelength spacing,
but for hat spacing the separa t ion is probably less cr it ica l. When
making this test , it is impor tan t to have both cavit ies tuned exact ly to
resonance at the frequency for wh ich the spacing is to be one-ha lf wave-
length . Each cavity can be tuned separa tely by using the plunger
method if the other cavity is replaced by a shor t -circu ited dummy.
In actual ope a t ion it is best for a fixed-tuned cavity to be set a t a
frequency wh ich will give equal susceptance at the two e~ds of the band.
As this may not be exact ly the same as the frequency at wh ich the line
lengths a re adjusted, there may be a slight mutua l resonance at some
frequency if two ATR cavit ies are used. As this effect will, very
probably, be small, it is bet ter to tolera te it in order to have the min i-
mum loss at band edge.
8.2. Mech anica l Design Problems.—A mechanica l problem of con-
siderable impor tance is that of the method to be used for at tach ing
the TR and the ATR switches to the main wavegu ide or other com-
ponen ts. This problem was consider ed in Chap. 4 in connect ion wi h
the ATR switch , and some of the methods discussed there have been
applied t o TR cir cu it s.
One of the m st conven ien t methods is tha t o
the choke-flange coupling used for making ordinary waveguide con-
nect ions. The 1B26 TR tube at 1.25 cm, and the 1B24 and the fixed-
tuned TR tube a t 3 cm, connect t o a standard choke coupling with the
window in the plane of the flange to permit mount ing flush with th e wave-
gu ide wall. The choke-flange connector s used at 3 cm on the cavit ies
for th e 724 tubes wer e mounted abou t one-quar ter wavelength from the
windows which wer e placed one-ha lf wavele gth fr om the main
waveguide.
Ther e is some difficu lty in bu ilding a wavegu ide junct ion with a flush
choke coupling. Because of in ter fer nce between the choke and the
wa vegu ide, it is vir t ually impossible t o do th is in a ser ies ju nct ion.
In a
shunt junct ion it can be accomplished by eliminat ing th e par t of the ch oke
occupied by the waveguide and leaving two arc-shaped open ings on
eit her side of t he wa vegu ide.
The lB2~ TR tube at 3 cm has been mounted on a simple 90° T-junc-
t ion using split chokes in th is manner . For tuna tely, because of the
334
BRANCHED AND BALANCED DUPLEXERS
[SEC. 82
peculiar fields at the junct ion , it was possible to obtain a good high-
level match with the input flange of the tube mounted 0.040 in. back
from the inside wall of the waveguide, a circumstance which great ly
facilit at ed t he con st ru ct ion of t he mo n t.
.4 duplexer designed at the Bell Telephone Labora tor ies made use
of a 1B2-1 TR tube and an ATR tube of similar const ruct ion , both
mounted on simple 120° H-plane junct ions using split chokes. 1
In th is
way t he main ~vaveguide made a 60° bend at each junct ion but in opposit e
direct ions and, consequent ly, th e antenna and th e t ransmit ter arms were
parallel. The same choke const ruct ion was applied to the vest igia l 120°
junct ion of Fig. 78.
At low power level the split chokes are sat isfactory since the match
is not cr it ical. At h igh power level, because of the distor ted fields in
-
t he junct ion , a good contact may be required between the flanges of the
tube and the mount on the 120° junct ion . Th 90° junct ion seems less
cr it ica l in th is respect , bu t breakdown across the choke gap will occu r
at power s wh er e t he 120° ju nct ion is sa tisfact ory.
The high-Q cavit ies used at 10 cm are often at t ached permanent ly
t o the main waveguide since t he tubes may be replaced without , removing
the cavit ies. Similar ly, an ir is-coupled mixer may be permanent ly
a t tached to such a TR cavity.
illost of the fixed-tuned 10-cm tubes
use the coiled-spr ing contact descr ibed in Chap. 4. In loop-coupled
circu it s the input and output loops often plug into a keyed hole.
In many system which must opera t e at high alt tudes or which
handle high power , t he r-f lines are filled with gas (usually air ) under
pressure.
For such a pressur ized system special precaut ions are neces-
sa ry in order t o make all join t s air t ight .
P ressu rizin g a duplexer u su ally
means sealing off the cavit ies from the main wa eguide.
Of cou rse,
on ly the components that car ry the t ransmit ter power need be pres-
surized.
This eliminates not on ly the output circu it of the TR switch ,
bu t even the in ter ior of the cavity since the cavity is on ly weakly coupled
t o t he main line during transmission .
Naturally the par t of the cavity
that contains the specia l gas for the r -f discharge must be sea led off
fr om t he a tmosph er e.
One way to pressur ize a cavity is to enclose it completely and to
provide special pressur ized fit t ings for the output termina l, t he keep-
alive con nect ion , and t he t un in g con tr ols.
F igure 8.1 shows an example
of this t echnique as applied to the 721A cavity used on ~-in . coaxial
line. The removable par t s of the cover are sealed with rubber gaskets.
The 3-cm ATR tubes, 1B35 and 1B37, must be mounte in a special
holder , Fig. 4.20, which encloses the tube except for one end. These
I A, B. Crawford, “X Band Duplex C rcuit for 1B24 Type TR and ATR Tubes, ”
BTL Report No. MM-44-16@92, Apr . 22, 1944.
SEC. 8.2]
MECHANICAL DES IGN
335
tubes have been pressur ized by adding an out er flange on the holder to
take a cover that goes over the exposed end of the tube and by a rubber
gasket that seals th e cover .
Tubes that have a glass window sea led in the ir is of the cavity
may be pressur ized by sealing the cavity to the waveguide with a rubber
gasket . The cavity window is then par t of the pressur ized system. At
3 cm the fixed-tun d TR tube and the tunable 1B24 tube are made to
fit the standard UG-40/U waveguide connector which is provided with a
groove for a rubber gasket .
At 10 cm the fixed-tuned TR and ATR
tubes have a fla t flange which compresses a fl rubber gasket . The
1B38 pre-TR tube car r ies no flange but is mounted n a housing which
has a join t with a fla t flange and gasket . Since the pre-TR tube itself
is not sealed to the housing, t e ou tpu t wavegu ide and TR cavity must
s till be p res su r ized .
Cavit ies that a r e ir is-coupled to waveguide or to coaxia l line have
been sea led by cement ing polyglas across the input window. In 10-cm
waveguide duplexers a sheet about & in. th ick is sealed to the inside
s r face of the wav guide by means of P liobond cement .
A problem analogous to pressur izat ion is that of the eliminat ion of
the r -f leakag . Where high transmit ter power s a re u ed, r -f energy
which radia tes from join t s in the t ransmission line may cause ser ious
in ter fer en ce wit h ot her cir cu it s, pa rt icu la rly t he a ut omat ic-fr equ en cy-
con t r ol circuit wh ose funct ion ing is most cr it ica l dur ing transmission.
336
BR.4NCHED AND BALANC’ED DUPLEXERAS
[S E ,: 83
Of course, any method of connect ing microwave t ransmission lines in-
volves efficien t chokes or uniform contact t o ensu e a match.
Even
when th is is done, however , t here may be appreciable leakage which
n ecessit at es a ddit ion al sh ieldin g. Wh er e pressu riza tion is n ot r equ ired,
metal gaskets may be used in the grooves in tended for rubber pressur iz-
ing gasket s. These askets have been made by compressing th in shavings
of monel metal in a mold of th same shape as the gasket .
8.3. Duplexers in Coaxial Line. -Coaxia l duplexers based on the
broadband T-junct ion descr ibed in Sec. 7“1 have been widely used for
10-cm-band radar systems in &in . diameter line. F igure 8“2 shows such
a duplexer with a 721A TR tube. The antenna connect ion is at t he upper
left , and the magnet ron t ransmit t ing tube is connect ed dir ct ly to the
side arm in the upper cen ter . The dist ance from the junct ion to the
magnet ron cavity is kept as small as po sible to minimize the var ia t ion
in the cold impedance seen at the junct ion .
F igu re 8.1 is a pressur ized
duplexer for &in . line. The loop-coupled mixer appears at t he top of
t h e p ict u r e.
The effect of cold impedance on received signal for a duplexer of this
type was studied by R. V. Pound and Rose Berger for 10.7-cm magn~
t rons. 1 They found that the cold impedance of these tubes was suffi-
cien tly uniform t o permit set t ing a manufactur ing specificat ion limit ing
the st anding-wave ra t io to values grea t er than 20 db and the phase
var ia t ion to + 5 mm beyond tha t which is due to wavelength changes.
The maximum signal loss from improper cold impedance t o be expect ed
1 R. V. P ou nd and Rose Berger , “ Preplumbing of Tees for G-Ban d,” R.L Repor t
238, NOV.3 , 1942.
SEC. 83] COAXIAL DUPLEXERS
337
anywhere within the 7 per cen t band was then 0.8 db, of which 0.4 db
was caused by t he finite standing-wave ra t io of th e magnet ron .
F igu r 83 illu st ra tes a du plexer in &in . coa xia l lin e u sin g Ir is-cou pled
cavit ies and 721A tubes. A circu it of th is t ype was designed at Radiat ion
FIG.S.3.—Coaxialduplexerwith iris-coupledcavit ies.
Labora tory and represen t s one of t he few coaxial applicat ions of an ATR
switch . An ir is-coupled TR cavity at 10 cm was also designed at the
Bell Telephone Labora tor ies .’
1J. P. Schafer,“SCR-545 Stan dardLoop Outpu t TR Boxes,” BTL MM-43-160-28
March 18, 1943,
338
BRANCHED AND BALANCED DUPLEXER,5
[SEC,8.3
Figure 8.4 shows a small low-powered assembly of r -f t ransmit t ing
and receiving components for a 10-cm system using tubes of the light-
house type for t ransmit ter and loca l oscilla tor . The TR cavitY with a
1B27 tube isseennear the cen ter of thepictu re andthetype Nantenna
fit t ing project s upward a t t he r ight cen ter . J ust to the left of this, the
FIQ.
s
.4.–
-Ligt
ring
COIT rots,
side arm of the T-junct ion leads up to the input loop a t the r ight side
of the bot tom of the TR cavity.
The cont rol of the t ransmit ter cold impedance presen ted a specia l
problem in this system since the t ransmit ter cavity was coupled to the
line by means of an adjustable probe. To get maximum power from the
t ransmit ter it was necessa r y t o compensa te for the var ia t ion among tubes
SEC. 84]
A DOUBLE-TUNED D UPLEXER
339
and cavit ies by an adjustment of th is kind. This adjustment , however ,
had a marked effect on the cold impedance, and it was usually necessary
to decouple the probe to a po n t at which the t r ansmit ted power was
somewhat below the maximum in order to get a sa t isfactory match for
t h e r eceived sign al.
At a la ter stage of developmen t a study was made of the dependence
of the t r ansmit ted power and the phase of the cold impedance on the
depth and diameter of the probe for a numb r of t r ansmit ter tubes and
wavelengths.’ A junct ion distance and a probe design which would
m in im ize t h e over -a ll loss of t ra ns-
mit ted and received signal wer e
chosen . It was concluded tha t
the eliminat ion of the probe ad-
justment by th is design would
permit a loss tota ling not more
than a few decibels for the usual
t ubes a nd ca vit ies.
8.4. A Double-t un ed Duplexer .
The uplexer of Fig. 8.5 was
designed for 1050 Me/see and
differ s r at her r adically fr om t hose
used at shor t er wavelengths.
Th is device, wh ich wa s developed
at Naval Research Labora tory,
provides for coupling the t rans-
mit ter , an tenna, mixer , and local
oscilla tor d i.r e c t 1y to the TR
cavity. z For compar ison , Fig.
8.6 is a schemat ic r epr esen ta t ion
of a more conven t iona l radar sys-
tem. The t ransformers represen t
coupling loops or ir ises in the
cavit ies of t r an sm it ter , TR swit ch ,
a nd loca l oscilla tor . At h igh power
(a )
(b)
FIG. 8.5.—Duplexer for 1050 h tcisec.
level the TR cavity in t roduces a shor t circu it in loop LZ so tha t the t rans-
mit ter is connected direct ly to the antenna .
If the t r ansmit ter cavity is
sufficien t ly detuned when the elect ron beam is turned off, a shor t cir cu it
i in t r odu ced acr oss loop L1 at low power level, and t he antenna is cou pled
direct ly to the TR cavity. Since the received signal differs from the
reson an t fr equency of t he local oscilla tor by th e in termedia te fr equ en cy
1R. E . Ta ylor , ‘‘ TR Dist an ce a ad F ixed P robe P ossibilit ies for t he LHTR Unit ,”
RL Report No. 5>12/27(44.
2M. Cla rk , “The DoubleTuned R, F . Sys tem:The TR Box,” NRL Repor t CI tG-
56, Dec. 19, 1944.
340
BRANCHED AND BALANCED DUPLEXERS
[SW 84
Transmitter TR cavity
Local oscillator
~TmT@
kritenna
Mixer
FIG. 8.6.—Radar r -f sys tem.
of t he r eceiver , t h eloop Li a ppea rs a s a shor t cir cu it t ot hesign al’’’h ich is
s
matched into the mix r . Likewise
L, is a short circu it for the !ocal-
oscilla tor power which also goes
in to the mixer .
In the presen t duplexer the
t ransmit ter and TR cavit ies were
LL.1
w
TR tu~
FXG. 8,7.4r0as sect ion of the duplexer
for 1050 Me/see .
placed close together so that loops
L, and LZ could be replaced by a
sin gle loop coupled t o bot h ca vit ies.
Similarly Li and L, were reduced
to one loop. In Fig. 8.5a the type
N coaxial fit t ing at the r igh t is the
antenna connect ion , and tha t a t t he
left is the mixer lead. The TR
cavity consist s of the cent ra l por -
t ion of the la rge sect ion of rectan-
gular tubing which forms the body
of the duplexer , and the open ends
of the tubing are the t ransmit t er
and the loca l-oscilla tor connect ions .
Th e cavit ies of t hese oscilla tors a re
a t tached direct ly to the duplexer
with the t ransmit t er on the r ight
and the local oscilla tor on the left .
F igu re 8.5b is a view looking in
from the t ransmit ter end at the
a nt enna couplin g loop.
The TR cavity is actually a
double-tuned circu it with a pass
band about 2.5 per cen t wide at 3
db, The par t it ion shown in Fig. 8.7 extending par t way across the cen ter
SEC. 8’51
WA VEG UIDE D UPLEXERS
341
of the duplexer divides it in to two cavit ies with a common i s.
Th er e is
a post down the cen ter of each cavity and a small gap between the post
and the cavity wall. The cavity voltage is developed across this gap
which , on the t ransmit t er side, is formed by the elect rodes of the TR
tube.
Two tuning r ings which move along the two cen ter posts of the cavi-
t ies can br ing any frequency from 950 to 1150 Me/see within the pass
band. These r ings are made of silver-pla ted ceramic mater ia l suppor ted
by a ce amic br idge. The tuning is linear with the displacement of the
tun ing slug and requires about Z-in . t ravel t o cover the band of 200
Me/see. The two cavit ies must have the same character ist ics to obta in
the proper bandwidth . This is accomplished by means of an adjustment
on the gap in the r igh t-hand cavity to match var ia t ions in TR tubes.
7
6
.0
‘5
.=
%4
~
53
.-
~2
1
0
1816141210864202 46810’12141618
Frequency in Me/see
FIG. S.8.—Ba ndpa ss ch ar act er ist ics of t he dou ble-t unwl TR cir cu it .
F@n-e 8 .8 shows plot s of the t ransmission character ist ics of the TR
circuit with the cen ter of the pass band set a t 050 and 1150 Me/see.
The curve for 950 Me/see is similar to that for 1150 Me/see.
The a t tenuat ion through the TR c vity of the th ird harmonic of
the t ransmit ter frequency was so slight (about 1 db) that a specia l th lrd-
harmonic filt er was added between the TR cavity and the mixer to pre
ven t cr yst al bu rn ou t.’
8.6. Wa veguide Du plexer s.—F igu re 8.9 sh ows a wa vegu ide du plexer
for the wavelength range 8.1 to 8.8 cm with shunt-coupled TR and ATR
cavit ies for the tunable 1B27 tube. Since the cavit ies a re placed only
one-quar ter wavelength apar t , space limita t ions make i necessary to
mount them on opposite sides of the waveguide.
T e two coaxia l
fit t ings project ing toward the camera are the connect ions on the rn ixer
which is ir is-coupled to the TR cavity.
The large solenoid opera tes
the crysta l ga te which protect s the crysta l when the keep-alive cu r ren t
1R. Novick, “The Dou bl Tu ned R-F System: Th e Mixer ,” NRL Repor t CRG-57
Dec. 23, 1944.
342
BRANCHED AND BALANCED DUPLEXERS
[SEC. 8.5
is tu rned off. he left end of the -waveguide goes, of course, to the
antenna , and the r igh t end goes to the t ransmit t er .
Fro. 810. -Duplexer s for 10.7 cm.
The upper duplexer of F ig. 8.10 is used in the band from 10.3 to 11.1
cm with a ser ies-coupled pre-TR switch and tunable 1B27 TR and A R
t ubes, t he la tt er sh un t-cou pled.
The TR and ATR junct ions are one-
SEC, 65] WA VEGUIDE D UPLEXERS
343
half wavelength apar t . The ir is-coupled mixer is mounted on the TR
cavity and the crysta l-ga te solenoid t the r ight of the cavity.
The
shor t waveguide a t the top, which
makes an acute angle to the trans-
mission line, is a direct iona l
coupler for checking system per -
formance. The system is pressur -
‘:m
ized with polyglas at the windows .:
of the TR and the ATR cavit ies S .
.,-
.
.
and with a rubber gasket a t t e
flange on the pr e-TR housing.
The lower duplexer of Fig.
8.10, wh ich is a lso design ed for t he
1 .7-cm band, has the same TR
and pre-TR circuit but uses two ~
JL12
0.5
10.7
10.9
11,1
L in cm
FIQ. S. 11 .—Ma ximum r ecept ion 10SS for
10.7-cm band duplexer . The point s
fix d-t uned ser ies-c u pled ATR
ar e experiment alvalues, and the curve is
t he ca lcu la ted br an ch in g loss.
t ubes sepa ra ted by on e-h alf wa ve-
344
RANCHED AND BALANCED DUPLEXERS
[SEC. 8.5
by assuming a I-dbloss for the TR cir cuit plus the maximum possible
branching loss by using the measured values of G and Q~ given i Table
4.4 for the 10.7-cm band ATR tube.
The actua l va lues of G nd Q. for
the tubes used wer not available an may have been somewhat differen t
judging by the low values for the exper imenta l losses. The asymmetr ica l
FIG. 8.13.—A 3-cm duplexer for fixed ATR and tunable TR tubes.
FIG. 814.-Narrow-band fixed-tuned duplexer f r 3 cm.
dist r ibut ion of the exper imenta l point s is probably caused by some er ror
in the separa t ion of the ATR cavit ies or in their tuning.
F igure 8.12 is an ea r ly 3-cm duplexer and mixer assembly. The
tunable cavit ies with 724B tubes ar e mounted one-ha lf wa velength fr om
t he main wa vegu ide on ser ies T-ju nct ions on e-qua rt er wa velengt h a pa rt .
They a re connected to the waveguide through choke-flange couplings
with knur led nuts and aligning pins.
The mixe is tuned by the plunger
a nd tu ning scr ews.
. more recen t 3-cm duplexer is shown in Fig. 813, The rectangula r
SEC. %5]
WA VEGUIDE D UPLEXERS
345
box on the left is the mount for the fixed-tuned 1B35 AT tube, The
tunable 1B24 TR tube is a t t ached to the flange moun ed at the cen ter of
the waveguide to form a shunt junct ion of the vest igia l 1200-Y type
shown in Fig. 7.8. The large-diameter groove in thk flange holds a
pressed meta l gasket which preven ts r -f leakage. The flange to the r igh t
of thk one connect s t o a small a t tenua t ing waveguide which is used to
couple u t one or two milliwat ts of the t ransmit ter power to opera te the
au toma t ic-fr equency-con t rol cir cu it s for t he r eceiver .
The sma ll cylinder
Fm. 8. 15.— Wide ban d fixed-t un ed du plexer for 3-cm .
above th e flange is the connect ion to a direct iona l coupler . F or mechani-
cal simplicity the separa t ion between TR and ATR junct ions is made one
wavelength ra ther than one-ha lf wavelength . This is permissible since
he duplexer is designed to be used o er a band only 2.6 per cen t wide.
The duplexer of F ig. 8.14 is designed for the same band and has the
same ATR circu it bu t uses a fixed-tuned TR tube shown mounted ne-
half wavelen gt h fr om t he main wa vegu ide on a ser ies T-ju nct ion m atch ed
with an induct ive ir is in the TR arm.
The externa l appearance of the
ATR mount is slight ly differen t from the preceding model, but it has the
same in ter ior and fits the same tube.
Th e du plexer of Fig. 8.15 u ses th e same tu bes as t he r ecedin g du plexer
but can be opera ted over the much broader band of 12 per cen t from 3.13
to 3.53 cm, This is made possible by mount ing the TR tube flush with
346 BRANCHED AND B LANCED DUPLEXERS
[SEC. 8.5
the main waveguide wall on a vest igia l 1200 Y-junct ion an using two
ATR tubes one-half wave ength apar t w th the first tube one-half wave-
length from the TR junct ion .
Transmitter
For the lower half of the band
K
from 3.13 to 3,33 cm, 1B35 ATR
tubes are used, and for the upper
half from 3.33 to 3.53 cm, 1B37
t ubes a re used.
The duplexer shown in Fig.
8.16 is an a t tempt to place the
ATR tube close to the TR junc-
t ion to avoid the adverse effect s
Rece,ver
of the var ia t ion with wavelengt h
FIG. 816.-Duplexer wi h TR and ATR
of the dist ance between TR and
tubes at the same junct ion .
ATR tubes.’ The advantage of
th is const ruct ion seems to be par t ly offset by the increased Q. of the
ATR cavity as shown in Table 4.3 of Chap. 4.
F igure 8.17 is a view of a duplexer for 1.25-cm wavelength with the
1B26 tunable TR tube in fron t . The wavegu ide connect io ju t to the
FIG. S .17.—.4 1,25 cm dup lexe r,
left o the TR tube carr ies the r -f power for au tomat ic frequency con-
t rol. Another view of the same duplexer in Fig. 8.18 shows the mixer
a t tached just above the duplexer .
The two coaxial fit t ings of the Bh’
type are the i-f lea s rom the two crystals, t he left one for automat ic
1Samuel, Cranda ll, and Clark ,
“Final Repor t on roa d-Ban d TR and ATR
SEO.&6] TWO-CHANNEL D UPLEXERS
347
frequency cont rol and the r ight one for the radar signal. The 1B36
fixed-tuned ATR tube plugs into the lower par t of the duplexer where it
is secured by the la rge knur led nut . The TR and the ATR tubes are
bot h ser ies-mou nt ed a nd spa ced on e-qu ar ter wa velen gt h a pa rt .
8.6. Two-chdnnel Duplexers.—In cer ta in systems it may be desir -
a ble t o r eceive simult an eou sly two sign a s, for example, r ada r a nd bea con ,
on two separa te receivers tuned to differen t frequencies. A convenien t
method of isola t ing the two channels is the use of two high-Q cavit ies,
on e for ea ch ch an nel.
The assembly shown in Fig. 8“19 uses two tunable T; cavit ies with a
single pre-TR switch .’ Since in this instance the signals cliffered in
F IG. 8.18.—.4 1 25-cm du plexer a nd m ixer ,
fr equency by about 6 per cen t , the window of the radar TR cavity
appeared as a shor t circu it to the beacon signal and vice versa . The
addit ion al TR ca vit y, t her efor e, in tr odu ced n o complica tion in mat ch in g
the line to the receiver a t either frequency. A tunable ATR switch was
used at the radar frequency but no e w s used for the beacon signal.
The branching 10SSof the beacon signal was minimized by a favorable
t ra nsmit ter cold impedance.
The necessity for shar ing the pre-TR tube should be not iced. Since
the window of a TR cavity mounted behind a preTR tube is th ree
quar ter s of a wavelength from the main waveguide, it present s a high
impedance at the main waveguide wall when tuned off resonance. If
each TR cavity were mounted with its own pre-TR tube at a diilferent
poin t on the t ransmit ter line, the one nearer the antenna would inter rupt
the signal dest ined for the fur ther one.
11,. D. Smullin , “ Mod ifica tion of CPS-6 Duplexer t o Allow Simult an eou s Bea con
a nd Ra da r Recept ion ,” RL Repor t No. 53-4/16/46,
348
BRANCHED AND BALANCED DUPLEXERS
[SEC.
FIG. 819.-Two-channel duplexer for 10cm with apre-TR tube.
-.
.
,.44 ,. ,.1
FIQ. 8, 0.—Duplexer for twochannels using two ATR tubes.
SEC. 87]
AN ATTENUATOR SWITCH
349
Figure 820 illust ra tes another fmm of two-channel duplexer . It
comprises an ATR switch for each channel, and since no pre-TR tube is
necessa ry, t wo TR ca vit ies ar e mount ed dir ect ly on t he main wa veguide.
8.7. An At tenua tor Switch . -In some radar systems the t ransmit t ed
power is a tt enua ted at t imes in or der t o confuse nemy list ening st at ions.
This a t t enuat i n , which might be as high a 20 or 30 db, would normally
be in tr odu ced between t ra nsm it ter a nd du plexer wh er e it wou ld n ot a ffect
the received signal. In some set s, however , it has proved more con-
venient t o install the at t enua tor between duplexer and antenna and to
add an ATR switching devic to allow at tenuat ion only dur ing
transmission.
Since it may be necessa ry for the at t enua tor t o absorb virtually all
of t he t ransmit ter power , it is preferable to diver t this unused Dower into
another line which can be termi-
nated in a specia l load capable of
high power dissipa t ion. The power
enter ing the t ransmit ter arm of Fig.
8.21 divides a t the junct ion between
the antenna arm and the arm lead-
ing to a dissipa t ive load. If the
extensions of the plungers in the
two stub arms differ by one-quar t er
wavelength and if the two output
arms a re ma ched, the impedance
seen from the t ransmit ter arm will
be a match.
By moving the plun-
gers syn chronously, t he t ransmit ter
.
: Xg
To antenna
receiver
I :r<;. 821 .—At t enua t or swit ch
power may be divided between antenna and load in any desired ra t io.
The switch, which is fired dur ing t ransmission, has no effect on the
p lunger act ion .
The least power will reach the antenna arm when the plunger in the
left -hand stub arm inser t s a high impedance in the line. At that t ime
t he r eceived signal wou ld a lso be la rgely r eflect ed if t her e wer e n o swit ch .
Th e swit ch , h owever , en su res a low impeda nce for ever y plu nger posit ion ,
When
all the t ransmit t ed power is being delivered to the antenna , the received
signal suffers no loss at t he junct ion, lVhen maximum transmit t er
power is being diver ted to the load, the r ight -hand stu arm present s a
low impedance. The received signal a t t he junct ion is then presen ted
with a match in both the receiver and in the load arms.
The power
divides equally bet ween t he t wo arms and, including reflect ions fr om t he
termina t ing impedance Z. = 2, the tota l signal loss s 3.5 db,
[SEC. 8+3
50
BRANCHED AND BALANCED DUPLEXERS
By an examina ion of the t ransmission rat io
P _l +x:
g–
2+ + x;
expressed in terms of the react ance X. of the r igh t -hand stub, it may be
confirmed that t he received signal loss always lies bet ween O and 3.5 db.
If it is necessary, this loss an be obviat ed by a second swit ch on t he r igh t -
h and st ub.
BALANCEDDUPLEXBRS
BY CAIULOLL. ZABEi,
It becomes difficu lt t o use the branched-duplexer t echnique when a
very flexible, broadband duplexing unit is desired, or when a c-w power
source is used instead of a pulsed power source.
For these uses the
developmen t of a va riet y of magic T’s has made possible a n ew t echn iqu e.
Arm
FIQ. S.22.—A ma gic T.
8.8. Proper t ies of a Magic T.
The general proper t ies of a magic
T are most easily descr ibed by con-
si er in g t he symmet rica l combin a-
t ion of an E-plane T and an
H-plane T (Fig. 8.22). This de-
vice is complet ely symmet ric a bou t
a plane which bisect s the E-plane
and the H-plane T’s. If genera tors
and loads are placed on the var ious
arms in such a way that the sym-
met ry of t he device is n ot dist ur bed,
then the elect r ic field in the wave-
guide must be either even or odd
about the symmetry plane, or it
must be a linear combinat ion of the
even and odd fields. The sym-
met ry of an elect r ic field at a dis-
tance x from this symmet ry plane is des r ibed by the equat ions
E(x) = E(–x),
if the field is even , or
E(z ) = –E(–z )
if t he field is odd Let us consider , for example, a genera tor on arm (4)
and matched loads on the other three arms.
The symmetry has not
been distu rbed. Since the elect r ic. field in arm (4) is even about the
symmetry plane, t he elect r ic field must be dist r ibu ted with an even
symmet ry t hrou gh ou t t he en tir e st ru ct ur e.
Thus a t any instant o t ime
SEC. 88] PROPERTIES OF A MAGIC T
351
the phase of a wave in arm (1) a t a dktance d from the symmetry plane
must have the same phase as a wave in arm (2) a t the same distance d
from the symmetry plane. Arm (3), however , will not propaga te a
mode which is even about the symmetry plane, and therefore no ower
will be coupled into this arm. In genera l there will be a reflected wave
in arm (4), but this can be eliminated by in t roducing a matching device
which is symmetr ica l about the symmetry plane, The device usually
e ployed is a post placed in the bot tom of guide (1 )–(2) project ing up
in to arm (3). With this device in place, one-half the genera tor power
will couple to arm (1) and one-ha lf t o arm (2).
N“ext consider a genera tor on arm (3) with matched loads on the
r emain in g t hr ee a rm s.
Here again the symmetry is preserved but now,
since the field in arm (3) is odd about the symmetry plane, t he elect r ic
field in the en t ir e st ructur e must be odd about the symmetry plane.
h-o power will be coupled into arm (4) because the only mode tha t a rm
(4) will propaga te has an even dist r ibut ion of the elect r ic field about the
symme ry plane. However , the phase, a t any instant of t ime, of the
\ vave in arm (1) a t a distance d fro the symmetry plane will be out of
phase with a wave in arm (2) at the same distance d fr om t he symmet ry
plane. Any reflected wave in arm (3) may be elimina ted by in t roducing
a matching device symmetr ica lly about the symmetry plane; this is
usually an induct ive ir is. Here again all the ge era tor power divides
equally between arm (1) and arm (2).
The result of placing two coheren t genera tors on the device may now
I)e considered: one on arm (3), t he other on arm (4), and matched loads
on arms (1) and (2). Under these condit ions, a lso, t he symmetry is
not distu rbed. Since arm (3) is independent of arm (4) the amplitudes
and the phases of the two waves may be var ied independent ly. In par t ic-
adjusted unt il t he wave coupled from arm (3) to arm (1) is in phase with
the wave coupled from arm (4) to a m (1).
Arm 3
This adjustment makes the ]vaves in arm
(2) just out of phase, and hence no power
will be coupled to a rm (2). Thus, ~vith
due regard to phase and amplitude, potver Arm 1
0
Wavegwde
Arm 2
Junction
incident at arm (3) and arm (4) couples
only to arm (1). By rever sing the dir ect ion
of t ime, ther efor e, power inciden t in a rm (1)
Arm4
couples on ly to a rm (3) and arm (4), and not
FIG,
S.23.—.1 lmdess pa ssive
to a rm (2). The amplitudes of the waves
four-terminal-pair network,
in arm (3) and arm (4) a re equal and ther e is a par t icula r phase rela t ion-
ship between the two waves. The above argument may be repea ted,
but this t ime the phases of the waves in arms (3) and (4) a re adjusted
352
BRANCHED AND BALANCED DUPLEXERS
[SEC. 8.9
so that the two waves coupled to arm (2) are in phase while the two wave
in a m (1) are 180° out of phase. By reversing t ime it is se n that power
inci en t in arm (2) is divided between arm (3) and arm (4), but the
rela t ive phase of on of the waves differs from the former case by just
180°.
By matching arm (3) and arm (4), arm (1) and arm (2) have also been
matched and the coupling between arm (1) and arm (2) has been elimi-
na ted. In fact , a four-terminal-pair lossless st ructure, Fig. 823, has
been made which has the proper ty that power inciden t on any terminal
pair divides equally between the two adj scen t terminal pairs with no
reflect ed power and no coupling to the opposit e terminal pair .
There re many physical st ructures in waveguide and in coaxial
line which have the proper t ies of a magic T. The magic T descr ibed
above has been widely used because of t he simplicity of it s const ruct ion .
Par t icular applicat ions of magic T’s oft en r equ ir e ot her t ypes.
8.9. Linear Balanced Duplexer .—The use of a c-w genera tor in a
system imposes more st r ingent condit ions on the duplexer than are
imposed by a system that involves the use of a pulsed genera tor . A
device is r equir ed which keeps t he gen er at or or t ransmit ter discon nect ed
from th e receiver at all t imes, and yet allows maximum coupling bet ween
the t ransmit ter and the antenna, and maximum coupling from the
antenna to the receiver . ~fore precisely, the product of the two coupling
coefficien ts must be a maximum.
Con siderat ion of th is problem shows th at it is impossible t o con st ru ct
a lossless th ree-termina l-pair net wor k which will sat isfy t hese require-
ments.
It is desired that the coupling between terminals (I) and (2)
be zero, Fig. 8.24. If a wave is incident on term nals (l), t here will
be , in general, a reflected wave at termi-
m2
E~
nals (1) and a t ransmit ted wave from
z<
terminals (3). Similar ly if a voltage is
o
inciden t on terminals (2), there wil be
Arm 1
a reflected wave on terminals (2) and a
Transmitter
~~c~i~er transmitted wave on te m i n a 1s (3).
However , when the direct ion of t ime in
F IG. 824.-A lossless pa ssive t h ree-
both cases is r eversed, t he self-cont radic-
ierminal-pair network.
tory resu lt is obta ined that either the
coupling between terminals (3) and (l), r the coupling between terminals
(3) and (2), must be zero. In other words, there is zero coupling, either
between the t ransmit ter and the an tenna or between the an tenna and the
receiver.
It ca n be shown , h owever , t ha t t h er e does exist a Iossless fou r-t ermin al-
pair network which sat isfies the requirements sta t ed and that such a net -
work is the magic T. Figure 825 indicates the use of a magic T as a
SEC. $39] LINEAR BALANCED DUPLEXER
353
duplexer dur ing t ransmission and recept ion. It is impor tant t o rea lize
tha t t his is t he best possible solut ion using a lossless four-t erm inal-pa ir
network and that th is solut ion necessit a t es a 3-db loss of t ransmit t ed
power and a 3-db loss of received
power . Thus a tota l loss of 6 db is
the min mum at tenua t ion possible
when this type of duplexing is used.
It is apparent tha t th is device can
be u sed in m icr owave communica tion
in a manner l ent irely ana logous t o t he
hybr id coil in low-fr quency com-
munication.
Severa l magic T’s may
be combined into a complica ted
duplexin g st ru ct ur e in volvin g sever al
t ra nsm ission lin es or a nt en na s.
Thes e t a temen t s a r e ea sily p roved.
Arm 3
Antenna or
transmission line
Arm, JL
——-—-+
rm 2
Transmitter —
Receiver
11 r
rm 4
Matched load
FIG. 8.25.—A magic T as a linear
ba lanced duu lexer .
With mat r ix not a t ion and with reference to Fig. 8.24, the most genera l
t hree-t ermina l-pa ir device ma y be r epr esen ted as
~]=~: :: ;;]~],
where a , is the incident complex amplitude in a rm (i) and b, is the
scat tered complex amplitude in a rm (i). Amplitudes b; and ai a re so
normalized tha t their absolute va lues squared represent t he incident and
sca t t er ed power s.
If the device is
two condit ions
If t hese two fact s
linear and lossless, t hen its ma t r ix must sa t isfy the
S,j = S,,:
SS*= 1.
a re used and the sca t t er ing matr ix is rewr it t en to
include the first r equirement s of a ba lanced duplexer , t hen
[1
s,, o
S13
s= o 8.22S23
s,, s,, S 3
Since SS* = [, this means tha t S13S~S = O. Thus either S,, or S23
must be zero. But S13 is the coupling from genera tor to an tenna which
must not vanish , and S23 is the couP ling from antenna to receiver which
a lso must not vanish . It must then be concluded that there does not
I W. A. Tyr rell,
1’Bridge Circuits for LIicrowaves,’)
BTL MM-43-16C-23, F eb 12,
1942,
354
BRANCHED AND BALANCED DUPLEXERS [SEC. 8.9
exist a thre~termina l-pa ir , linear , lossless network tha t will sa t isf y the
r equ ir em en ts of a linear du plexer .
Let us now ask if there exist s a linear , lossless, four -termina l-pa ir
network which may be used. It is desired tha t Sl, be zero, and tha t
IS,,I 21S,,12 be a maximum. Each termina t ion ma be removed and
replaced with a lumped impedance and a matched termina t ion with-
out dest roying any of its proper t ies. That is, S12 will st ill be zero and
IS131ISZSI2 will st ill be the maximum. Now, however , i?J IIand S2, must
be zero. If this were not t rue the genera tor could be mismatched and
i$l~ in cr ea sed wit hou t ch an gin g S29.
Bu t IS,3121SZ312s a lr ea dy a maxi-
mum, therefore SI ~ must be zero.
Simila r ly S2,Zmust be zero. Now
the sca tter ing mat r ix is
[1
00
LS13 S14
s = ]13 ;2, ;;: ~: .
~14 s24 5’34s44
Since SS * = I,
1s131’ 1s141’ 1,
1s,,1’ 1s241’ 1,
1s,31’+ 1s,31’+ Ih’,,1’+ IS3,12= 1,
Isl,l’ + 1s2,1’+ 1s34/2 ]s441’= 1.
If the fir st two equa t ions are added,
IS,,12 + IL$,412+ l&,12 + l&12 = 2.
From the second two equa t ions
l~,, z + IS2,1’ + ~S,41’ + l.!,,)’ + l~,,j’ + \ &4j2 + Z&12 = 2.
Thus
1~,,1’ + ]Ag,,l’ + 21S34]’ = O,
and, since each term must , be posit ive, each term must vanish.
From
(1)
(2)
Eqs. (2), this means tha t
1s,31’ + [s231’ = 1,
IS’,*I’ + /s,41’ = 1.
If these equat ions ar e subst ituted in 13q. (1),
IS131= 1s 4[,
and
1s141= ]s231.
If the fir st of Eqs. (3) is squared
Is,,l’ls,,l’ = +(1 – Isl,l’ -
(3)
[s2314).
SEC. 8’ 10]
NONLINEAR BALAArCl?D DUPLEXER
355
E l~,~ljl~,~lzis a maximum, the der iva t ive with r espect t o Sjsmust be
zer o, or
,
21s,3[3– 1+(1 _’~:j312F =0,
and
I,s,,l’ = ;.
Ifth isresult issubst itu ted in13qs. (l) and(3)
This device is, however , the magic T. Therefore it has been proved
t ha t t he best possible four -t ermina l-pa ir , lossless, linea r n et wor k for use
as a linear duplexer is t he magic T.
Fur thermore, the maximum value
of 1~1,1IS*’ I2 is ~. The maximum amount of useful power iS thus 6 db
below the genera tor power , and the minimum amount of loss in such a
device is 6 db.
8.10. Nonlinear Balanced Duplexer .—If it is possi le to acid non-
linear elements to a duplexer , much bet ter use of the magic T may be
made. Let us consider , fir st , the possibilit ies when a pulsed magnet ron
is used as the power source, and TR gas witches a re used as the nonlinear
elements.
It will be assumed tha t the waveguide type of magic T dis-
cussed in Sec. 8.8 is used.
Consider fir st an ar rangement of two magic T’s as indicated in Fig.
8.26. Power incident in arm (4)
TR switches
will divide between arms (1) and
(2) in an even fashion: a t a given
&
1 ~-7
distance from arm (4), the voitage
1’
in arm (1) will be in phase with the
L—J
voltage in arm (2). If t he upper 4
3
H
19
4’
3’
pa th to the second T has the same
4
r -
elect r ica l length as the lower pa th ,
1,
t he two waves will a r r ive in arms
2
2
L-J
(l’) and (2’) in phase. These two
FIG. 8.26,—A lm lm l{ed lna gir-T du plr .xr r
waves will thus couple only to arm (4’).
Similar ly, power incident in
arm (3) will a r r ive in rms (l’) and (2’) ou t of phase, and thus collp]e
only to arm (3’).
If a pulsed t ransmit ter is placed on arm (4) and a TR switch is inser ted
in the upper pa th at a distanced from the fir st magic l’, the TR switch }vill
fi e, reflect ing most of the power back to arm (1). The leakage power
will be incident in m-m (l’). A second TR s}vitch , ident ica l ~r ith the
fir st , may be placed in the lower path in var ious posit ions. If it is placed
a t t he distance d + &/4 from the fir st magic T, then the tota l path of
356
BRANCHED AND BALANCED DUPLEXERS
[$EC. $-10
the power from the T to the lower TR switch and back to the T will
be a half-wavelen th longer than the similar path to the upper TR switch .
The reflected wave in arm (1) wiIl then be 180° ou t of phase with the
reflected wave in arm (2). Now the transmit ter power will couple
only to arm (3), and the transmit ter will see a matched load. The
leakage power from the lower TR switch will ar r ive in arm (2’) in phase
with the leakage power in arm (l’) from the upper TR switch , and,
therefore, the leakage power will all couple to arm (4’). A low-power
signal ar r iving in arm (3 ) will not fir e the TR swit ch es a nd, t her efor e,
will couple only to arm (3’).
Severa l observat ions may be made about the opera t ion of such a
duplexer . Fir st , the antenna is completely disconnected from the t rans-
mit ter when the TR tubes are not fir ing. Regardless of its impedance,
there will be no loss of signal to the t ransmit ter . Since no ATR tubes
a re required, it might be possible to make a device matched over a
broader frequency band than is possible by the branched-duplexer
technique,
Second, all the leakage power wil be dissipa ted in the matched load
in arm (4’) whi e no leakage power is coupled to the receiver on arm (3’).
In order for th is to be t rue, both the rela t ive phase and the amplitudes of
the waves in arms (l’) and (2’) must be identica l. Thus, not only must
the elect r ica l length of the t ransmission lines or waveguides in the upper
path be the same as in the lower path , but the phase shift in the two TR
switches must be the same. In order for the device to be used over a
band f frequencies, the Q of the two TR switches must be identica l.
Since the amplitudes of the two waves must be equal, the amplitudes of
the leakage powers from the two TR switches must be the same through-
ou t the en t ir e magnetron pulse.
This is difficult to a complis . The
gas discharges in the two TR tubes must star t at the same time and in
the same manner . In pract ice some leakage power en ters arm (3’) to the
r eceiver . The leakage power from ach TR tube must be low enough
to protect the receiver . The amount of decoupling of the leakage power
to the receiver must not be relied upon too heavily.
The bandwidth of th is device is cont rolled by the impedance seen
by the t ransmit ter and by the Q of the TR switch . The Q of the TR
switch determines t e bandwidth in exact ly the same manner as it deter -
mines the bandwidth for the branched duplexer s.
The s tanding-wave
ra t io seen by the magnet ron is determined by the difference in path to the
upper and to the lower TR switch .
Wh en th e differen ce is exact ly on e-
quar ter gu ide wavelength , there is no reflec ed wave. As the wavelength
is changed, the difference in path length is a ltered and a ref ected wave is
produced. Moreover , the m-agic T it~elf has a fin ite band over which it is
well ma tched
SEC. 8.11] R ING-C RGUI1’ I) UI’LEXllR
357
8.11. Ring-circuit Duplexer .—There a re sever al balanced duplexer s
that opera te on the genera l pr inciples discussed in Sec. 8.10, but which
differ physically. The power-handling capacity as well as t he maximum
bandwidt h va r ies con sider a bly.
They a lso differ in the type of magic
T used. The balanced dupleser tha t uses a combina t ion of E-plane
and H-plane T’s is limited to po~ver levels of less than 150 kw, a t 3 cm,
for arcing occurs a t about tha t po~~er level around the matching post .
It has a bandwidth of about 12 per cent .
A magic T descr ibed as a r ing circuit has been par t icula r ly successful
for maki~g a good balanced d~lplexer .
A r ing circuit consist s of a loop or r ing,
Fig, 827, of wavegu ide to ]vh ich four
wavegu ides a re joined to form four E-
plane T’s. The elect r ic vector is p~ra llel
to the plane of the paper , The mean
circumference of the loop is one find one-
ha lf gu ide ~vavelengths, The distance
between arms (1) and (3), (3) and (2),
and (2) and (4) is a qua r ter of a gu ide
~vavelength a long the mean circumfer -
ence. The charact er ist ic imDedance of
3A,,
I:lG 827. -Diagran1 of a
r ir ru it nla giv T.
rirlg-
the loop is 1/{2 t imes tha t of the four a rms.
If t he E-plane T is considered to bc a pure ser ies junct ion with no
junct ion effect s, t he proper t ies of t he r ing circuit may be obta ined by
the same genera l met hod used in Sec. 88.. The r ing circuit is symmet r ica l
about a plane between arms (2) and (3). As before, fields tha t a re even
and odd about the symmet ry plane are considered.
These two solu t ion s
may be combined to give a genera l solut ion.
First , if t he elect ric field
is odd about t e symmet ry plane, the elect r ic field must be zero at t he
plane of symmet ry. A sheet of meta l maybe placed along the symmet ry
pla ne wit hou t dist ur bin g t he fields.
Only o e half of the r ing circuit is now considered. The impedance
matr ix of this device is obta ined in the ordinary ay from the linear
equ at ion s of a two-t ermin al-pa ir n etwor k,
V, = ZI,I, + zls~s,
V3= 21,11+ Z3313.
The impedance seen a t the reference plane of a rm (1), when there is no
cur ren t a t arm (3), is 211.
In the lower sect ion there is, then, t he
impedance of a sh or t circuit , t ransform ed one-eight h wa velengt h ar ound
the loop, plus the impedance of an open circuit on arm (3), and the sum
transformed one-four t h wavelength to arm (1). This result s in zero
impedance from the lower sect ion a t arm (1). From the upper sect ion
358 BRANCHED AND BALANCED DUP EXERS
lSEC. 811
t her e s t he im pedan ce of a sh or t cir cu it t r an sform ed t hr ee-eigh th s wa ve-
length or –j/~. Thus
’11 = $2”
Si ilar ly, t heo her mat r ix elements a r found with the resu lt
Elect/icwatl ‘
(d)
‘i+ , ?;
Magnetic wall )
w
o
J ! - - @
“’L-jfi
242
c)
FIG. 8.28.—Diagram t o illust r ate t he calcula t ion of t he scat ter ing matr ix of a r ing-cir cu it
m agic T.
For the even case the sheet of metal must be replaced with a magnet ic
wall wh ich mainta ins an open circu it a t t he symmetr y plan e.
In this case
z
H
*-&.
even
=1’
++2 -+2
In both cases the resu lt of squar ing the matr ix is just – 1,
ZL, = –1,
Z:,m = _[.
The scat t er ing matr ix S is
s = (z – 1)(Z + l)-’,
or
s = (z’ – 2Z + 1)(Z’ – l)-’.
SEC. 811 ] lUfiGW RCLT IT I) UI’LEXEIZ
IfZ2 = –[, then
S=z.
Hence, in the even case Z,, = S,1 = +j/@, and
359
th is is the reflect ion
coefficien t in arm (I). The complex wave coupled to arm (3) is
Z13 = S13 = j/@
The sca t t ered waves in each arm for the two cases
tube
f
it
1.193’”
FIG. S.29,—Dimensions for a r ing circu it a t 3.33 cm.
a re known , as indica ted in Fig. 8.28a and b. Th e even and odd solu t ions
may be added in any way. For example, the two solu t ions shown in Fig
8.28a and b may be added with the resu lt , F ig, 8.28c, that a wave of
amplitude 2 is incident in arm (1) which couples a wave of amplitude
<2 to arms (3) and (4). No
wave is coupled to arm (2) nor is
there a reflected wave in arm (1).
By sym etry, it is seen that an
amplitude of 2 inciden t in arm (4)
will couple a wave of amplitude
{2 to arms (1) and (2) with no
reflected wave or coupled wave
to arm (3). From the same im-
pedance matr ix, the resu lt of a
wave inciden t in arms (3) or (2)
can be found (Fig. 8.28d, e, and f).
The Dower incident in any arm
1.4 -
1.3
Q
&ml -
Arm2
g 1.2
>
1.1
1.0
3.1 3.2
3.3 3.4 3.5
Wavelengthin cm
FIQ. 8.30.—Standing-wave ra t io of r ing.
cir cu it magic T.
divid& equally between th~ two adjacen t arms with no coupling to the
opposit e arm and n o r eflect ed power .
Thus, the r ing circu it is a magic T.
It is obvious that the r ing cir cu it is somewhat fr equency-sensit ive
since its opera t ion depends upon cor rect line lengths. The voltage
360 BRA NCHI?D AND BALA NC’ED D [7PL17XI?RS
[SEC. 8.1 I
standing-wave ra t io a t arm (1) and arm (2), with matched loads on the
remaining arms, plot ted against wavelength is shown in Fig. 8.30 for a
r ing circuit const ructed according to Fig. 829. F igure 8.31 is a plot
o~
1,0 ~
3.1 3.2
3.3 3.4
3.5
3.1 3.2 3.3 3.4 3.5
Wavelength in cm
Wavelength m cm
FIG. 8.31.—Cr oss cou pling between a rms
FIC. 8.32.—Standing-wave ra t io pr esen ted
(1) and (2). to he magnet ron hy r ing-circu it duplexer .
of the ra t io, expressed in decibel , of power inciden t in arm (1) to power
coupled to arm (2).
A non linea r ba lanced duplexer may be constructed with r ing circu its.
As before, ca re must be taken in placing the TR switches if the maximum
FIG. 8.33.—Rkg-cir cu it duplexe r
I__.. . .
milled from aluminum. The top ha lf has been
r emoved t o sh ow t h e det ails.
Th e two h alves a re split a lon g t he cen ter of the wide side
of t he wavegwde.
bandwidth is desired. As th frequency is changed, the standing-wave
ra t io presented to the t ransmit ter will change, not only from a change in
the character ist ics of the ring circuit , but also from a change in the
elect r ica l posit ions of the TR switches. In the r ing-circuit duplexer ,
SEC. 812]
PRACTICAL MAGIC T’S
361
these two effect s are near ly equal.
If the TR swit hes are placed at
the cor r ect distance from the r ing circuit , the effec s can be made to
cancel each other . On the drawing of the r ing-circuit balanced duplexer
shown in Fig. 8. 9 the posit ions of the TR tubes are indicated.
The TR
switches are the broadband type 1B63. F igure 8.33 is a photograph
of a r in g-cir cu it ba lan ced du plexer milled fr om aluminum.
The volt age
standing-wave rat io presen ted to the t ransmit ter as a funct ion of wave-
length is plot t ed in Fig. 832. The duplexer can be used up to peak
power levels of 350 kw at l-psec pulse length and a pldse recur rence
frequency of 500 per sec if the corners inside the E-plane T’s are slight ly
rounded.
8.12. Pract ica l Magic T’s.—In the discussion of the magic T which
consists of a combination of E-plane and H-plane T’s, Fig. 8.22, the
procedure that was followed in the matching of the junct ion was inher-
en t ly importan t in der iving the magic-T proper t ies, To obta in the
desired resu lt , it is necessary to match the two arms that lie in the
symmet ry pla ne.
It is clear , how-
ever , that had the arms which are
on each sid of the symmetry plane
been matched, there \ rould have
been no reason to expect that the
resu lt ing const ruct ion would be a
magic T. The coupling between
opposite arms would not have been
zero, and the two arms in the plane
of symmetry would not have bum
matched. In the first case, four
in dependen t a dju stmen ts a re made,
the amplitude and the phase of a
~Ic. S34. -Posit ion of post and ir is
r eflect ion coefficien t in ea ch of t he
for ma tching a magic T in ~-in . by l-in ,
t wo arms in t he plane of symmetry.
waveguide.
In the second case, only two adjustments a re made, since the result ing
device must remain symmetr ica l. For this type of symmetry, four
in depen den t par amet er s in t he t wo arms a re necessar y.
These arms are
in the plane of symmetry.
These four adjustment may be made in a var iety of ways all of which
depen d upon t he shape of t he device and t he desir ed bandwidth and power -
handling capacity. As seen by Fig. 834 the H-plane arm is matched
by adjust ing the length and the posit ion of a cylindr ical post placed
inside the junct ion while he E-plane arm is matched by the size and
posit ion of an asymmetr ical induct ive ir is. The post is 0.125 in. n
diameter and 0.650 in. high. The ir is is 0.032 in . th ick. This method of
matching resu lts in a magic T that is less frequency-sensit ive than a
362
BRANCHED AND BALANCED DUPLEXERS
[SEC. 812
magic T in which both arms are matched by sing lumped constan ts such
s ca pacit ive or in du ct ive ir ises.
The 10-cm-band magic T is similar ly
matched, as shown in Fig. 835. The post is 0.375 in . in diameter a d
is 1,750 in . h igh . The ir is is 0.032 in. th ick.
Th e 1.25-cm-band magic T
has the post replaced with a metal fin , Fig. 8.36. The ir ises are 0.020 in .
FIG. 8.35.—Position
of post and ir is for matc}~ing a magic T in 1~-in ,
by 3-in . waveguide.
S.36.—Posit ion of post and ir is for matching a magic T in ~-in .
by A-in . waveguide.
th ick. The frequency sensit ivit ies of the t hree magic T’s are shown in
Figs. 8.37, 8,38, 8.39. The curves show the st anding-wave ra t io VS.
wavelength in each arm for magic T’s before an t i a fter the match ing
devices a r e a dded.
It is seen that the standing-wave rat ios for the unmatched magic T
are h igh . By changing the dimensions of the var ious arms, these
standing-wave rat ios may be lowered considerably and the final match
SEC. 8. 12] PRACTICAL MA GIG 7“,T
363
4.0
\
\
E‘-arm
\
\
~ (unr latched)
\
\
3.5 —
–L,.
\
\’
\
\
\\ \
\
J.’.
\
3.0 —-- ., ---
I
I
2.0
1,5
-.
1.0. (
unmatct ed)
8.0 8.5
9.0
9.5
10.0 10.5
11.0 11.5 12.0
Wavelength in cm
FIG. 8.37.—Effects of a post and ir is for match ing a magic T in 1}-in . & 3-in . wavegu ide.
4.0
3.5
H-arrr
(unmatched)
---
- --J_, _
——.
1-
—-— ———- ____
——_. -———
3.0
1
~ 2.5
E.a rm
2
(unma:chedj
‘.
~.
‘ -L\-
___
2.0
--
-—_. ____ - ____
E-arm
1.5
d
Side arm
E-arm
Side arm
----
H-armJ
—-— ____
1.0 L— —
3.10 3.15
3.20
3.2 3,30
3.35 3.40
3.45 3.50
Wavelength in cm
Fm. 8.38.—Effects of a poet and ir is for mat hlng a magicT in i-in . by l-in . wavegu ide.
%4
BRANCHED AND BALANCED llUPLl?XERS
[SEC. 812
more easily at ta ined. Such a magic T has been const ruct ed’ at the
Telecommunicat ions Research Establishment in Engla d. If the
E-plane arm is considered t o be a pure ser ies connect ion with no junct ion
effect s, a match in this arm could be at ta ined by m king the charac-
ter ist ic i pedance of the symmetr ical arms one half the character ist ic
impedance of the E-plane T. Quar ter -wavelength t ransformers or a
t apered guid~ may then be used to return to a guide of standard size.
It is convenien t then , to have the H-plane arm also of the reduced
dimensionsat the junct ion . Over a band of wavelengths from 3,05cm
‘7-----:---
‘n;:
1:
,0
~-.
-_
E-arm
----
/“‘
---
(unma~hed)
-- ---
/
---
-----
-— ___ ____
~ 2.5 ,:/
$
/1
1’
2.0 ;
/
Sbdearm
E-arm
_ $mmatchad) > /
1.5 -
---- .-- —— - ______
Side a;;
~ ~
- ~ ‘
H-arm
—
~
1.0
1.21
1.22
1.23
1.24
1.25 1.26
1.28
1.29
Wavelength in cm
Fm. 8.39.—Effect s of a post and ir is for matching a magic T in ~-in . by ~-in . waveguide.
to
3.30 cm, an unmatched magic T const ruct ed of guides having inside
dimensions 0.9 in . by 0.4 in . and 0.9 in . by 0.2 in. had a volt age standing-
wave ra t io in the E-plane arm of about 1.16, in the H-plane arm of 3.3,
and in the side arm of 1.61. If these figures are compared with the curves
in Fig. 8.38, it is apparen t that the match of the ser ies arm is great ] y
improved, with no effect on the shunt arm and without too drast ic an
effect on the side arms Final matching was accomplished by matching
the ser ies arm with a large post and then ma cKlng the shunt arm with a
small post , Fig. S’40. The result ing curve of voltage standing-wave rat io
vs. wavelength for t he magic T, which includes the quar ter -wavelength
t ransformers, is shown in Fig. 8.41 for an exper imental model.
1Private communicat ionfrom P. R. Tunnicliffe ,TRE, Jan. 16, 1946.
SEC. &121
PRACTICAL MAGIC T’S
365
Considerable ca re must a lso be t aken in matching the r ing-circuit
magic T. In the discussion in Sec. 8.11 it was assumed tha t the junct ion
effect s of t he E-plane T could be neglect ed. It is seen from the fre-
F IG. 8.40.—Modified m agic T.
quency-sensit ivit y curves, Figs. 8.30 and 831, that this assurr rpt ion was
allowable for the 3.3-cm band for the l~in. by +-in. waveguide.
N1easure-
ments made on a r ing-cir cuit magic T for the 10.O-cm to 11.2-cm band
using 3-in . by lj-in , wavegu ide
show curv s very similar t o Figs.
8.30 and 8.31. However , \ rhen
plungers were put in firms (3) and
(4) no posit ion o the plunger
cou ld be fou nd }vh ich Lvou ld give
a low standing-wave ra t io in tkm
remaining arms. Apparen t ly the
simple ser ies-cir cu it a ssumpt ion
cannot be used here, By chang-
ing the size of t he cen t er post ,
Fig. 829, from 1.972 in., which is
1.50,
1.40
1
H. arm
/
Wavelen@hi~ cm
llu . 8.41. —l’requency sensit ivity of tho
m odified m agic T,
t he ca lcula ted va lue for 3-in. by l&in. wa vegu ide, t o 2.100 in,, t he plu nger
posit ion can bc found and a curve similar t o Fig. 832 is obta ined. How-
ever , t he standing-~r :ive ra t ios when the shor t cirmlits a re replaced by
matched loads a re high and the cross a tenuat ion is much lower .
366
BRANCHED AND BALANCED DUPLEXERS
[SEC. 812
Some of these difficu lt ies ar ise from the failu re of the assumpt ion
that the junct ion effect s a re unimpor tant , and some from the very close
spacing of the E-plane T’s. With theequivalen t circu it of the E-plane T
a va ila ble, t he ju nct ion effect s m ay be in clu ded in t he design .
The second
difficu lty may be removed by adding cor r ect line lengths between the
var ious rms. Although he argument sta ted in Sec. 8.11 is not applica-
ble hen sufficien t symmet ry is lacking, it can be shown tha t th e magic-T
proper t ies are reta ined if any number of guide wavelengths are inser ted
between any of the arms provided that the tota l number of half wave-
lengths added to the en t ire r ing is even .
If th is ru le is followed a grea t
many alterat ions on the simple r ing circu it can be made.
For a wavelength of 3.3 cm and a waveguide size of 1 in. by ~ in. by
0.050 in. wall, neither of these considerat ions is of impor tance. At a
wavelength of 1.25 cm and a gui e size of ~ in. by ~ in. by 0.040 in. wall,
it is easily seen tha t the arms must be spaced so closely that they run
in to each other . Here obviously it is necessary to apply the ru le just
sta ted. Each addit ion of length increases the frequency sen it ivity
considerably, an d t her efor e t he addit ion of lin e lengt hs sh ould be a voided
if possible. It i not cer ta in if t he junct ion effect s must be considered.
To t he a ut hor’s kn owledge, n o r ing circuit s based on t hese consider at ion s
have been con st r u ct ed .
The a ltera t ion of the line length between the arms is not the only
t ransformat ion that can be made on the r ing-circu it magic T. From
t he discussion in Sec. 811, t he sca t ter ing mat r ix of t he r ing-circu it magic
T is seen to be
[1
0011
0 –1
s=j+:_l () ;“
1100
The solu t ion for Z in Eq. (4) is
z = (1 + S)(1 – s)-’
or
z = (1 + 2s +s )(1 – s’)-’,
Since S’= –I, Z=S
[1
0011
0 –1
z=j+; _l o :“
1100
If a t ransformer with a turn rat io of n : 1 is placed on one arm of the magic
T, the impedance mat r ix of the new st ructu re is found by mult iplying
the cor responding row and column by n or by v“Z where Z is the rela t ive
SEC. 8’12]
PRACTICAL MAGIC T’S
367
character ist ic impedance of th e new transmission line compared with t he
old line. If t ransformers are put on each arm, the new impedance
mat r ix will t hen be
Z. = MZM,
where
‘=l:r:.i!”
As an example, let Z, = Z, = 1, 2, = Z1 = 2. Then the product MZM
results in
[1
0011
0 –1
Z.=j~_lo~.
1100
This mat r ix may be considered as the sum of four mat r ic s. Three of
t h ese mat rices a re on e-qu ar ter -wavelengt h lin es a nd on e is a t hr ee-qu ar ter -
wavelength line, a ll of a charact er ist ic impedance of 1,
‘n=’F:i:l+’!:::l+ ””
Thus, t here is a new magic T which is shown in Fig. 8.42. ith oth r
choices of the 2,’s a grea t many
var ia t ions ar e possible,
FIG. 842.-A t ra n formed r in g-cir cu it
F IG. 8 43.-A r igh t-a ngle r in g-cir cu it m agic
magic T.
T.
These considera t ions are also applicable to a magic T of another type.
This is called the r igh t -angle r ing circu it .
This r ing circuit consists of
four one-quar ter -wavelength lines, two with a character ist ic impedance of
1, and two with a character ist ic impedance of 42, wh ich connect fou r
368
BRANCHED AND BALANCED I) UPLEXERS [S EC. 8.12
t erminal pair s, l ig. 843. Byapply ng hemethod used on the ordinary
r ing circu it , t he sca t ter ing mat r ix and the impedance mat r ix may be
found,
and
OOlj
OOjl
1
ljoo’
jloo
1
0 *’
Oflo
Z=j 1
0%/’ 201
The same ru le for adding line lengths between the var ious arms a plies
here. and new st ructures mav be found by adding t ransfo mers to the
=1
4
Yo=lJ7-
(a)
(b)
F IG. S44.-Coa xial r in g-cir cu it m agic T’s.
arms as is done for the ordinary r ing circu it . It will be observed from
the sca t ter ing mat r ix, however , tha t the volt age coupled from arm (1)
to arm (4), or from arm (2) t o arm (3), is now 90” ou t of phase with the
wave coupled from arm (1) to arm (3), or from arm (2) t o arm (4).
If a ba lanced duplexer were made with a r ing circu t of this type, the TR
switches would h ave t o be placed at equal distances from th e r in g circu it s.
Th e con st ru ct ion of ma gic T’s is n ot limit ed t o r ect an gu la r wa vegu ide.
A var iety of magic T’s maybe made from coaxial lines and from combina-
t ions of wavegu ide and coaxial line. The discussion presen ted in Sec.
8.8 was based on the ser ies and parallel natu res of t he ~-plane T and the
H-plane T, Fig. 8.22. It is easy to repeat the symmet ry arguments with
the ~-plane T replaced with a coaxial probe, or the H-plane T replaced
with a coaxia l loop, or both subst itu t ions made at once.
As has been
SEC. 8.13] CIRCULAR -POLARZZA T ZON D UPLEXER
369
poin t ed out , matching must be accomplished in the ser ies and in the
pa r allel a rms.
Coaxial lines may be used in both types of r ing-circu it const ruct ions
as indicated in Fig. 8.44. The coaxia l T shown is a parallel circu it and,
therefore, admit tances are easier to handle. The scat ter ing and admit-
tance mat r ices may be found as in the ser ies cases. Although severa l
coaxial r ing circuit s of t he t ype sh own in Fig. 8.44b have been cons t ruct ed ,
n o per forma nce dat a a re available.
8.13. Circu lar -polar iza t ion Duplexer .—A third var ia t ion in the
design of a balanced duplexer uses magic T’s which involve a round
wavegu ide. As an example of such a magic T, consider the construct ion
indicated in Fig. 8.45. The two symmetr ica l arms of the magic T, arms
&Arm 3
0’-7
4
;
Arm 2
+—
( Arm 4
-r_
.-
Arm 4
,
A
FIG. s.45.—A magic T u sin g r ou nd w-awgu idc.
(1) and (2), a re the two perpendicu la r polar izat ions in the round wave-
as in Sec. 8.8. For the ordinary magic T of Fig. 822, in order to obtain
a matched magic T, the match ing must be accomplished in arms (3) and
(4). Arm (4) can be matched to arms (1) and (2) by using a quar ter -
wavelength t ransf rmer between the rectangular and the cylindr ical
gu ides. The t ransformer shown in Fig. 8.46 is approximately a quar ter -
~vavelength lo g, and its impedance is approximately cor rect for a t ransi-
t ion betw-eer . t r ansmission lines of differen t character ist ic impedances.
End effect s and the change in cross sect ion a lter both the length and the
Z“ of the t ransformer . At 1.25 cm the choi e of dimensions of the rec-
tangular and the cylindr ical gu ide is such that a match can be obta ined
in arm 3) by simply adjust ing the distance between arms (3) and (4).
At 3,3 cm a match ing ir is is necessary.
The advantage of using a magic T with round guide in a duplexer
be omes apparen t i t he magnet ron and antenna are visualized as placed
37’0
BRANCHED AND BALANCED DUPLEXERS
[SEC, 8.13
on arms (-l) and (3), for then the two TR switches are in the same guide.
The t~vo swit ches can , in fact , be made in to a single tube. The difference
in the elect r ical pa th length from the magic T o the TR switch for the
two arms, arm (1) and arm (2), must be a quart er of a guide wavelength ,
as in the previous duplexers.
N’ow, however , the physical dist ance
between the magic T and the TR switch is the same for the two arms
since they are in one waveguide.
The guide wavelengths in arms (])
/
0.701”
l r
0.170”
~ q ~0.420”
6*
0.157”
,1
II
,1
,, II
J
II ,1
0.196” ~ I ‘
0.350”
,)1 j
\ w
~’-– -–– J
+
\
;0332,, “w ‘--=: =--- -
,,
1’
~
FT~, 8.46. —Din~r)l sion> o
f 1,25-cn l-ba rld cir cu la r n ,a gic T.
-qq~
0.215”
0,215”
LJ3LI
,,—,
J3’~
,
,
4,
,,
—~
UL.---J:
r
Magic T
+ Ag
TR
+ A9
Magic T
plate
switch
plate
B1(,, &48.-L)iagr an1 of cir cu la r -pola r iza t lu ll {IUI J IVr r
r esu lt in a {~ll:~r t,er -~ a ~’clen gt lldiffer en ce in elect rica l pa th len gt h. III
ot h er words, if X; and k: are the vavelengtbs in arms (1) and (2) respec-
t ively, t en
?r
1 = z= 2- z=,
A; – A:
where 1 is the length of the sect ion of the cylindr ical gu ide in Ivh ich thv
guide wavelengths differ .
The change in gu ide wavelengths may IN
SEC. 8“13]
CIRCULAR-POLARIZATION DUPLEXER
371
>
accomplished by using an ellipt ica l sect ion of gu ide, by inser t ng a fin
in to a circu la r gu ide, by using lumped constant s such as a number of
capacit ive posts, or by using a dielect r ic slab in circu la r gu ide.
The
second method is illu st r a ted in Fig. 8.47. The stepped const ruct ion on
each end of the fin is a quar ter -
wa velen gt h t ra nsformer t o m at ch
in to an d ou t of t he pha se-sh ift ing
section.
The waves in arm (1) and arm
(2) m-e thus in phase with each
oth er when they n ter the sect ion
of gu ide conta in ing the fin , and
are 90° ou t of phase with ea rh
other as they leave the sect ion .
Before en ter ing the sect ion con-
t ain in g t he fin , t he combin ed wa ve
will thus be a linea r ly polar ized
wave whose elect r ic vector is
eit her pa ra llel t o or per pen dicu la r
to the symmet ry plane of the
magic T. After leaving the fin ,
the combined w ve is either a
Resonantwindows
Resonantwindow
Resonantcross
F IG. S .49.—Tlt s~vit[h .
r igh t-h an d or a left -h an d cir clda rly pola rized wave.
Th e sect ion of wave-
gu ide con ta in ing the fin is thus the microwa ve equ iva len t to the quar t er -
wa velen gt h pla te u sed a t opt ica l fr equ en cies.
2.01
1.22 1.24 1.26 1,28
Wavelengthin cm
F IQ. S51).-B:111d~vi,it ll of TI { swit ch of F ig. 8.4!)
Th e cir cukw-pola r iza t ion d llplexer will, t h er efor e, con sist of two magir
T’s in cylin clr ir al gllidej t }vo qu ar ter -wa velen gt h pla tes, a nd a TR swit ch
in cylindr ica l gu ide, Fig. 8,48.
The opemt ion on both 10]v and h igh
power is iden tica l t o t ha t of t he ba la nced d~lplexer s pr evim lsly descr ibed.
The TR switch must t ransmit t~vo perpendicu lar pola iza t ions, for
example, the waves in arms (I) aIMl (2). Fkure 849 indi~ak a possible
construction.
The or ien ta t ion of the resonan t cross is not impor tant
since a circu la r ly polar ized \ Va \ ’eis symmetr ic abollt the direct ion of
372
BRANCHED AND BALANCED DUPLEXER8
[SEC. 8.14
propagat ion . F igure 8.50 sh ows t he voltage standing-wave rat io wh ich
the TR switch presen ts to the quar t er -wave p ate. lt is seen that over
the frequency band shown the maximum loss is 0.5 db. F igu re 851 is
1.5
h
Magnetron
s
03
Signal
>
1.0
1.22
1.24
1,26
1.28
Wavelengthin cm
FIQ, 8.51 ,—Standing-wave rat io as seen by tbe magnetron and signal
t he over -a ll volt age standing-wave rat io of the duplexer as seen by the
magnet ron and the an tenna of an exper imenta l circu lar -polar iza t ion
duplexer shown in Fig. 852.
When the leakage pulse is observed on a fast oscilloscope, the energy
appears to be almost en t irely in the spike. The tota l energy t ransmit ted
I~l<;, S52. -Duplexes for 1.’25 cm eI llr lloyiIlg
vi!rulu L,ola lizat lon.
by the TIt swi ch for example,
the amount of energy per pu lse
en ter ing the matched absorber in
arm (4), is 9 ergs. The energy
per pu lse absorbed by the rrystal
is 0.06 erg. The decrease in leak-
age energy accomplished by the
magic T and the quar ter -]vave-
measu rement was made on ly at
the cen ter of the 1,25-cm band.
The maximum amount of prover
ivh ich the dl~plexer will t ransmit
at a tmospher ic pressure is 87 kw
at 0.3 psec pu lse width , 55o pps
r epet it ion fr equ en cy.
8.14. Turnst ile Duplexer .—A
balanc d duplexer that employs a
circular ly pola r ized wave but does
not use a quar ter -wavelength pla te
can be const ructecl with a six-terminal-pa ir ne~w-ork called “ the tu rn-
st ile, ”
Fig. 853. I,et us co sider th ree exper i en t s per formed with
matched terminat ions on 5 arms, and ]vith a matched genera tor on the
remain ing arm of the tu rnst ile.
814]
TURNS TILE DUPLEA’ER
373
1. With thegenera tor on arm (6), Fig. 8.54a jin thecylinclr ica l guide,
make an adjustmen t of two parameter s, such as a post diameter and
length indica ted in l’ig. 8.55, unt il
there isno reflected wave. Since the
4+
<
device is symmetr ica l abou t a plane
th rough arms (3), (4), and the cylin -
~1-ot
dr ica l guide, no power will be coupled
to arms (3) and (4). The elect r ic
field of the wave in arm (6) is odd
about the plane of symmetry. Such
a field will not propagate in arms (3)
‘% ~
and (4).
The waves in arms (1) and
(2) are equal in amplitude and are
180° out of phase with each other .
If unit power is inciden t in arm (6),
J
Arm
the voltages in arms (1) and (2)
+
2
may be char cter ized by + I/@
Arm6
and – 11~.
2. F rom Exper imen t (1) it must
Arm Arm
4 3
be concluded that if unit power is
T
Arm5
inciden t in arms (1) and (2), Fig, 854b,
such that their r espect ive voltages are
Arm
1
180° out of phase, no power \ vill be
coupled to arms (3), (4), and (5) while
(b)
the amplitude of the wave in arm (6)
FIQ. 8.53.—A tur n st ile ju nr t ion ,
will be W. There will be no reflected wave in either arm (1) or arm (2).
3. If a genera tor is placed on arm (1) only, Fig. 8.54c, there will
be, in genera l, a reflected wave and a wave which is coupled to each
-v+
F=-&&’jjjKo:Ajg!d
l + r mv + t r mr
~
+1
a+l
+1
+fi
(a)
(b) (c) (d)
FIO. 8.54.—Diagram to illust ra te the matching of a turnst ile junct ion, In (a) the
directionof th e incidentwaveis into the paper;in (b ), (c), and (d) the waves emerge from
the plane of the paper .
of the remaining arms except arm (5). From the symmet ry of the turn-
st ile the power coupled to arms (3) an (4) will be equal and the waves in
phaae with each other . When unit power is incident in arm (l), the
374
BRANCHED AND BALANCED DUPLEXERS [s~c. 814
amplitude of the wave coupled to arm (6) will be @2 as indica ted by
Experiment (2). Compar ing Ilxper imen ts (2) and (3), it is obse ved
tha t for consistency it is necessa ry tha t the reflected vave in arm (1)
be equa l to the transmit ted wave in a rm (2), a = B. If now by a second
adjustment a = 0, then /3 = 0, and necessar ily, 8 = ~.
This is a device
I#F
.350’
E
o.lw”~
0=
0,065” h
+1~
b
0
0
‘m
1;
*
: :’,
-.7 -+, -J
~1.,.l r ‘-
--l_ -L. _’ -L___
‘:
0
0
FIG. S.55.—Dimensions for a matched
turnst ile iunct i n at 1.25 cm.
whose proper t ies re indica ted in
Fig, 8.54d. If a wave is inciden t in
any one of the re tangula r wave-
gu ides wh n the rema in ing guides
a r e t erm in at ed in t h eir ch ar a ct er ist ic
impedan es, one-ha lf the incident
power will couple t o on e pola riza tion
in the cylindr ica l guide, and one-
four th the power will couple to each
of the adjacent r ectangu lar gu ides.
o
1
i[=~
$@
%2-7
.
II ,,
d
I
d++
1
FI~. 8.56.—Turnst ile with
shor t circuit s on two arms.
No power will be r eflect ed, and no power will be coupled either to the
opposite rectangu lar arm or to the perpendicular polar iza t ion in the
cylindr ica l guide
For duplexing purposes a shor t cir cu it is placed in arm (3) and one
in arm (4), F ig. 856. If the shor t circu it s are placed so tha t one of them
is one-quar ter guide wavelength fa r ther from the plane of symmetry
than the other , the two reflect ed waves will a r r ive at the cylindr ica l
wavegu ide 180° out of phase with r espect to each other .
This condit ion
is equi alen t to Exper iment (2).
Th e t wo waves, t her efor e, will cou ple
to arm (5) in the cylindr ica l gu ide and no power will be coupled either to
arm (1) or t o arm (2). The resultan t wave in the cylindr ica l gu ide will
depend upon the rela t ive phases of the two perpendicular ly polar ized
waves in arms (5) and (6).
If the pogit ions of the two shor t circu it s are
a dju st ed, main ta in in g t he on e-qu ar ter u ide wavelen gt h r ela tive displa ce-
ment , the phase of the wave in arm ( ) may be var ied withou t changing
SEC. 8’ 14]
lUlLY8TILE LiCPLEXEli
375
the match of the modified turnst i e or the coupling from arm (1) to arm
(2). In par t icular the phase ~ay be made just 90° clifferen t from the
wave in arm (6). The resu ltan t wave will then be circu lar ly polar ized.
Cr it ica l dimensions are shown in Fig. 855 for th 1.25-cm band.
It is clear tha t the modified turnst ile accomplishes everyth ing that
the round agic T and the quar tm-~vavekmgth pla te accomplished in
t h e pr eviou s duplcxer .
Two su h turnst iles and a TR s~vit h for round
F1~, S.57.—BeJa nced dupl xer employing t u rn st ile ju nct ion s.
q \//
LQ2
1.24
1.26
1.28
Wavelength in cm
F IQ. 8.58. —F requ6llcy sen sit ivit y of t ur nst ile du plexer a t h igh power s,
gu ide, Fig. 8.57, form a balanced duplexer which funct ions in a manner
ident ical with the circu lar -polar iz t ion duplexer of Sec. 8.13. The
frequency sensit ivity at h igh power le el is shown in Fig. 858. At low
power level the modified turnst ile has a voltage standing-wave rat io of
less than 1.1 over the band of wavelengths from 1.22 to 1.28 cm. The
over -a ll fr equency sensit ivity of the turnst ile duplexer is, therefore,
approximately that of the TR switch, as shown in Fig. 8.50 of Sec. 8.13.
CHAPTER 9
MEASUREMENT TECHNIQUES
llY H. A. LEITER
The measurements of the r -f proper t ies of TR and ATR tubes and
of complet e du plexer s usua lly in volve on ly st an da rd t ech niqu es common
t o a ll m icr owa ve mea su remen ts.
The emphasis, however , is not neces-
sar ily the same, and in many cases it is desirable to develop more or
less specia lized test equipment and procedures. one of the most impor-
tant reasons for the development of specia lized test equipment is the
n ecessit y for m ass-pr odu ct ion t est in g of t he t ubes by r ela tively u nt ra in ed
personnel.
h ’Meas rements on TR tubes and duplexers may be classified under
t h ree h ea din gs: (1) low-level r -f mea su remen ts, (2) h igh -level r -f mes,su re-
ments, and (3) d-c measurements.
The low-!evel r -f measurements on
TR t ubes in clu de t un in g, in ser tion loss, Qoj QL2, cou plin g, a nd keep-a live
inter act ion . The measurements on ATR tubes include tuning, QOand
QLZ,a nd cou plin g. Du plexer low-level m ea su remen ts a re con cer ned ~vit h
tuning, maximum and minimum inser t ion loss for var ious magnet ron
impedances, and bandwidth . High-level r -f measurements must be
made of a rc l ss, a rc lea ka ge power , spike lea ka ge en er gy, dir ect -couplin g
a t tenua t ion, harmonic leakage power , h igh-level standing-wave ra t io,
a nd r ecover y-t ime ch ar act er ist ics.
D-c measurements a re concerned
wit h t h e keep-a live cha ra ct er ist ics.
They include minimum fir ing volt -
a ge, fir ing t ime, oscilla tion s, a nd volt -amper e cha ra ct er ist ics.
For the genera l background and a fuller descr ipt ion of microwave
t est equipment and t ransmission-line components the r ea der is r efer r ed
to the following volumes of this ser ies:
“ Micr owave Tr an sm ission
Circuit s” Vol. 9 and “ Technique of Microwave Measurements” Vol. 11.
9.1. Basic Low-level Tes Equipment .-The fundamental test setup
for low-level mea urements from which almo t all others a r e der ived,
con sist s of a n r -f sign al sou rce, suit able level-set tin g a nd pa ddin g a tt en u-
a tors, a power monitor and wavemeter , a slot ted sect ion or standing-
wave detector , and the object under test which may or may not be
followed in the transmission line by a second, slo\ ted sect ion and a
matched load or power measur ing device.
With such a setup, the
impedance (magnitude and phase of the standing-wave set up by the
test object ), loaded and unloaded Q, inser t ion loss, tuning, and other
376
SEC. 9.1]
BAS IC LOE7-LEVflL TES T EQUIPMENT
377
proper t ies can be measured. The measurements maybe made in coaxial
or waveguide t ransmission lines depending upon the object under t est
and t he par t icu la r frequency band.
In the 10-cm (3000 bIc/see) band,
waveguide and coaxial lines find almost equal use.
At 3 cm and below,
almost all measurements are made in waveguide. In fact , almost the
only coaxial lines used are flexible dielect r ic-film cables. Although
it is dangerous to genera lize, it is probably t rue that wave uide t est
benches are more flexible and accurat e than those made of coaxial lines.
It is easier to make matched var iable a t tenua tors, matched loads, and
good slot ted sect ions in waveguide, ch iefly because there is no center
conductor to suppor t . At wavelengths grea ter than 10 cm, waveguide
finds lit t le use because of it s grea t bu lk. A typical 10-cm bench using
Ii in. by 3 in. waveguide which includes two slot ted sect ions, two at tenu-
ators, and a matched load may be 5 ft long and weigh 30 lbs.
Sign al sou rces most common ly u sed a re klyst ron s or pa ra llel-elemen t
t r iodes of the “ligh thouse” const ruct ion . Reflex klyst rons, because
they are much more easily tuned, have replaced two-cavity klyst rons.
With presen t detect ing and measur ing techniques a power level of 50
to 100 mw from the tube is ample for most measurements. These power
levels may be obtained with the 21<28 and 2K41 klyst rons in the 10-cm
band, and with the 2K39 tube at 3 cm. The 2K39 and 2K41 tubes have
in tegral cavit ies and opera te at beam poten t ia ls of 200 and 600 volt s,
respect ively, with reflector voltages about —200 volt s with respect to
the ca thode. The 2K41 tube may be turned over a range from about
8.8 cm o 14 cm, but only about a 10 per cen t tun ing range can be obtained
on the main tun ing knob. T e 2K39 tube may be tuned over a 1 per
cent band from 3.1 to 3.5 cm by the tuning cont rol. With 1500 to 2000
volt s between anode and ca thode, the output power of these tubes may
be pushed to 0.5 to 1 wat t .
The 2K28 tube is a cell-type tube that is used with an externa l cavity.
It operat es at lower voltages than the 2K41 tube and produces 100 mw
at a beam voltage of 300 volt s.
This, however , is a lmost its maximum
output power . The tube may be tuned from about 8.5 to 12 cm in a
simple waveguide cavity with two shor t -circu it ing plungers. The
2K25 tube is a low-power tube in the 3-cm b nd. The outpu t power is
about 30 mw at 300 volt s. The 2K25 and 2K28 tubes, because thev are
easily tuned and require smaller power supplies, are usually used in
preference to the 2K39 and 2K41 tubes if the lower u tput @wer is
suficient.
The C43 (ligh thouse tube) t r iode is most useful above about 15 cm
wavelength . It t oo operat es on about 200 to 300 volt s. It suffers from
the fact that it haa no elect ron ic tuning as the reflex klyst rons have;
but it requires a simpler power supply.
378
[sEC. 9.1
he r -f power from each of these tubes is coupled out th rough some
form of coaxial line. All except the 2K25 tube are coupled to the
main line by a flexible coaxial cable. The 2K25 tube is arranged to
mount direct ly on the wavegu ide (1 by ~ in. by 0.050 in. wall) with no
in termedia te fit t ings. The use of flexible cable has many advantages;
but it must be rec ll@ that the fit t ings used t o join these cables together
(type N fit t ings) may in t roduce standing waves of as much as 1.5 or 2 in
voltage. Therefor ej wh ere it can be avoided, measurements should n ever
be made t hrough such connectors.
ossy cables are used whenever possible between the r-f genera tor
and t he ot her test equ ipment , in order t o isolate the oscilla tor from effect s
of mismatch in the unit under test .
Transit ions from cable t o coaxia l
line usually involve a type N r-f connector and a tapered sect ion , or
sect ion of line containing step t ransforme s, to afford a match from the
cable in to the air-filled coaxia l line. Transit ions from coax al line or
flexible cable to waveguide are of several t ypes. The most common
var iety has a probe approximately one-quar ter wavelength long, but
other devices, such as “door knobs”
and crossba r-su ppor ted probes,
serve equally well and are often less suscept ible to mechanical distor-
t ion t han t he simple on e-qu ar ter-wa velen gt h probe.
The slot t ed sect ion is one of the most importan t it ems of test -bench
equipment . It must be very carefully const ructed if accura te work is
to be done. If any dimension var ies from the value specified, the elec-
t r ical measurements are affect ed in some manner . Inner dimensions of
slot ted sect ion s in gu ide must be a ccu rat e.
This is t rue also of the outer
conductor of coaxial slot ted sect ions, with the fur ther requirement that
the inner conductor must be accurat e in size and very closely coaxia l
with the outer conductor . It is the presence of the inner conductor
which makes coaxial slot ted lines so much more difficu lt t o const ruct
than the waveguide slot ted sect ions. In a sect ion of either type the slot
should be as nar row as possible and accurat ely parallel t o the axis of the
line. The th ickness of the wall in which the slot is cu t must be held to
close limits, so that the project ion of the probe in to the guide will be
uniform along the slot ted sect ion .
A gradual var ia t ion in th ickness
causes the s nsit ivity of the device to vary from one end to the other .
The same act ion would ccur if t he inner conductor of a coaxial sect ion
were not accurat ely cen tered. The length of the slot should be grea t er
than a iull wavelength . A full wavelength would ensure that two volt -
age minima and one maximum, or one minimum and two maxima, could
always be obtained were it not for th e fact that Cend effect s 7’cause values
near the ends of slot s to be unreliable.
The pickup pro e should be made of fair ly small wire and should be
inser t ed int o th e transmission line as shor t a distance as possible, in order
SEC. 91!
BAS IC LOW-LEVEL TES T EQUIPMENT
~,;,g
tha t it shall not cause a standing wave. Tunable probes a re best because
the grea t er sensit ivityy permit s less inser t ion. The r-f volt age picked
up by the probe is either rect ified by a detector mounted in the probe and
a pplied t o a ga lva nomet er s or amplifier , or is a pplied dir ect ly t o a spect rum
ana lyzer which conta ins a superheterodyne receiver .
A probe of the
second type, which does not conta in a detector , is somet imes called an
“r-f probe,” because it can be used to pick up r-f power which will be
delivered t o another inst rument by means of a flexible cable.
The choice of t e inst rument used to indica te the magnitude of the
power picked up by the probe depends on the kind of measurements t o
be made and on whether or not the r-f oscilla tor is modula ted. If the
r -f oscilla to is squ ar e-wave modu la ted, a n amplifier is u su ally employed.
Most amplifiers used for this purpose have tunable select ive circuit s
incorpora ted in them and, therefore, they amplify only at some desired
frequency. This is very useful for eliminat ing effect s of power-supply
r ipple, or other in t er fer ences .
The amplifier is t uned t o t ha t modula t ion
frequency used with the r-f oscilla tor . Since the oscilla tor is modula ted
with a square w ve, t he rect ified r -f pulse has considerable harmonic
content.
If the amplifier is tuned to amplify at one of these harmonics,
an appreciable er ror may be int roduced, since most of t he harmonic com-
ponent is in the rising and falling edges of t he pulse, where the r-f fre-
quency may be quite different from the frequency obta ined over the fla t
top of the pulse. If he modula t ing voltage does not swing the reflector of
t he oscilla tor t o a n onoscilla ting volt age dur ing ha lf of t he cycle of t he r ec-
tangular pulse, er ra t ic result s may also be expect ed, because it is likely
that the frequencies obta ined in the two ha lves of a cycle will be con-
siderably different . The presence of two or more frequencies may be
ch ecked by in sert ing an a bsor pt ion wa vemet er in to t he cir cu it a nd obser v-
ing the “dips in power level as the wavemeter is tuned over the band.
It is somet imes very convenient to apply the output voltage of a cryst l
to an oscilloscope, so that t he envelope of the modula ted r -f signal may
be observed. Power for this monitor ing crysta l may be taken out of the
line by means of a probe similar t o the one used in the standing-wave
measurement , or by means of a direct iona l coupler .
Wh en t he r -f oscilla tor is unmodula ted, a ga lva nomet er s m aybe u sed t o
register the crysta l cur rent . The crysta l curren t is very near ly propor -
t iona l to the power picked up by the probe. Consequent ly,
‘swR=k=&iwi2
where the E’s a re field-st rength values along t he guide, t he P’s are the
cor responding values of power into the crysta l, and the Z’s a re the cor -
r esponding cr yst a l cu rr en ts.
380
M17AIS UR EMEN T TZ!CHN IQUE,5
[SW. 9.1
‘l’he equa t ion rela t ing crysta l cur ren t to the applied voltage is, more
accurately,
I = E“
where m expresses the lJ J Vof the det ector , that is, if m = 2, t h e det ect or
is said to have a square law. }l-ith th is nota t icm,
()
I jm
VSWR = ~ .
m,.
The crysta l is very near ly a square-law device,
t e va lue of m should be obtained ex~erimentally.
bu t for precise work
This may be con-
sidered a calibrat ion of the crysta l and it is necessary to ca libra te, as a
unit , t hecrysta l with its associat ed equipment , such asaga lvanometer or
an amplifier , since ou tput impedance has some effect on the crysta l la~v,
and since the amplifier it self may not be quite linear .
If t he range of
crysta l cur ren t s in use is la rge, it will be n ecessary t o obtain a cont inu ous
ca librat ion cu rve, bu t the cryst a l may be ca librated a t on ly one poin t if
the var ia t ion in cur ren t is not very la rge. For voltage st anding-wave
ra t ios less than th ree, calibrat ion at a single poin t is usually sufficien t
since the var ia t ion in crysta l law with crysta l cur ren t is a slow funct ion .
Calibrat ion of a cryst a l is usually done by shor t -circu it ing a line with a
metal plug and compar ing th e va lues of cryst al cu rr en t vs. probe posit ion
with t heoret ica l va lues of field st rength which may be ca lcu la ted.
In a
shor t -circu ited lossless line, t he field st ren gt h at any poin t may be calcu-
la t ed from t he rela t ion
~ = sin 2yl
h.
The va lue of m, the crysta l-law parameter , can be determined by making
a measu remen t at any distance 1 from a min imum, since
When a spect rum analyzer is used, the r -f power is applied direct ly
from t he probe t o a ca librat ed cut off a t t enu ator built in to t he inst rument .
When st and ng-wave ra t ios are measu red with th is appara tus, t he probe
is set a t t he posit ion of a voltage minimum and the heigh t of the pip
noted. The probe is then moved to a maximum posit ion and the signal
is adju sted, by means of the calibra ted at t enuator , to the same heigh t
as when the probe was set a t a min imum in the standing-wave pat t ern .
SEC. 9’1] BAS IC LOW-LEVEL TES T EQ~J IPMENT
381
Spectr um analyzers a re very seful for measur ing standing-wave ra t ios
grea ter than two. The calibra ted at tenuators can be adjusted to give
accuracies of +0.2 db if ca re is taken , and if the dr ive mechanism is care-
fully built . The sensit ive receiver in the analyzer a llows measurement
of standing-wave rat ios as h igh as 40 db (100-to-l voltage ra t io).
Ma tch ed lin e t ermin at ion s, m at ch ed pa ds, an d mat ch ed va ria ble a tt en -
uat rs should have volta e standing-wave ra t ios less than 1.05 for rough
work and less than 1.02 for a ccu r at e mea su r emen t s.
Units usable over a
broad band of frequencies can be built t o fuliill the requ irements sta ted
above. Matched pads are par t icula r ly importan t when direct measure-
F1a.9. 1.—A typical test bench for use at wavelengths nea r 3 cm.
ments of inser t ion loss a re to be made. Sect ion 9.2 will discuss th is
further.
Squ ar e-wave modu la tor s a re u su ally conden ser -coupled t o t he r eflect or
circu it of the reflex klyst ron tube and requ ire on ly about a 50-volt square
wave t o th row the tube in and out of oscilla t ion .
Th e squ ar e wa ve sh ou ld
r ise sharply and be as fla t as possible on top in order to make the fre-
quency modulat ion small. Exper ience has shown that a symmetr ica l
square wave, in which the durat ion of the posit ive half of the wave is
equal t o that of nega t ive half of the wave, gives the best resu lts.
Wavemeters a re of two types: the coaxia l type which is most often
used at 10 cm, and the cavity type which is used most frequen t ly at 3 cm.
They may be coupl d to the source of r -f pow r in such a manner as to
cause a dlp in power when they are at resonance (absorpt ion type) or
they may be used as t ransmission meters. The absorpt ion type is more
popu lar sin ce t he m onitor in g device also indica tes wh et her t he r -f sou rce
382
MEAS UREMENT TECHNIQUES
[SEC. 9“2
is in oscilla t ion .
Measurements of high-Q devices call for gr e t er accu-
r acy than can easily be obtained with or dinary wavemeter s.
Mea ns for
obtain ing the required accuracy ar e discussed in Sec. 9.3.
A typical test bench for use at wavelengths near 3 cm is shown in
Fig. 91. The oscilla tor is at the left , then there is a direct ional coupler
for monitor ing the power , an a t tenuator , a direct ional coupler with a
transmission waverneter and a crysta l holder , a second at tenuator , the
standing-wave detect w-, a broadband TR tube (1B63), and a matched
load terminat ing the waveguide line. The power supply for the oscilla-
tor and a square-wave modu~ator are conta ined in the box on the left
behind the waveguide. On the lower r ight is a spect rum analyzer , and
a bove it an au dio amplifier .
R.f
FIG. 92.-Determinat ion of inser t ion loss of 1B24 R tube,
9.2. In ser tion -loss Mea su remen t.—In ser tion loss L is defined as
Pi
L = 10 10g10n
(1)
where Pi is t he im:ide t po er awl is t he power deliver ed to a matched
load by a matched genera tor ; P1 is t he power deliver ed to a matched l ad,
by the same matched genera tor , a ft er the unit for which the loss is t o be
Inser t ion loss is made up of two
component s—reflect ion loss and dissipat ive loss.
Reflect ion loss is
caused by an impedance mismatch which reflect s par t of the inciden t
power back toward the genera tor .
Dissipa t ive 105s takes place with in
the element and is Z’R loss. Dissipa t ive loss is usua lly det ermined by
subt ract ing the r eflect ion loss from the tota l inser t ion loss.
Inser t ion loss is det ermined direct l bv measur ing the power deIiver ed
by a matched genera tor t o a“matched load and then measur ing the power
SEC. 92]
IN SERTION -LO&S MEASUREMENT
383
delivered to the matched load with the un it to be measured in the circu it .
A m atch ed calibr at ed at ten ua tor is ver y u seful in th is m ea su rem en t, sin ce
it eliminates the necessity for an accura te power -measur ing device.
With the unit t o be measured inser ted between the matched genera tor
and the matched a t tenua tor (F ig. 9.2), the power level in to the match d
load should be set a t some conven ien t value. The unit eing measured
is then removed from the circu it and the at tenua t ion increased unt il the
power level retu rns to its former value.
The difference between the
a tt en ua tor r ea din gs r epr esen ts t he in ser tion loss.
In gen er al, t he pla t in-
ized-glass type of a t tenuator , in either coaxia l line or waveguide (see
Fig. 93), is pr efer r ed for these measurements, because it holds its
ca libra t ion well. Resistor -st r ip at t enuator absorb moistu re to some
ext en t a nd, t h er efor e, h an ge ca libr at ion .
The tuner shown in the illust ra t on is used to match the crysta l det ec-
tor . Tuners of severa l var iet ies a r e su itable for this purpose. These ar e
all descr ibed in Yol, 9, Chap. 9, Radia t ion Labora tory Ser ies.
If the r -f
oscilla tor is capa le of deliver in g su fficient power , a m atch ed pad m ay be
38
MEAS UREMENT TECHNIQUES [SEC. 9’2
used in place of the tuner . This pad must have sufficient at tenuat ion to
reduce the voltage standing-wave rat io in t roduced by the crystal to an
acceptable value, abou t 1.05 or less.
When in ser t ion loss is measur ed direct ly, it is necessary t o en su re tha t
both the genera tor and the terminat ion are well matched. A terminat ion
which has a VS WR of 1.2, if used in the measurement of a TR cavity
normally having a loss of 1.5 db, gives values f loss ranging bet ween 1.37
and 1.64 db, depending upon the phase of the impedance: a var iat ion of
approximately t 9 per cent . If, in addit ion , the genera tor were mis-
matched by an equal amount , the range of var ia t ion of loss would be
about twice tha t obta ined with a mismatched terminat ion alone.
The inser t ion loss may be determined also by measur ing the field
st rength and the voltage standing-wave rat io in the line, on each side of
the unit under test , by means of a probe and slot ted sect ion . Let El
be th e inciden t elect r ic field, and ~E, t he r eflect ed elect r ic field, wh er e I’
is the reflect ion coefficient of t e unit being measured, and let Ez be the
t ransmit ted elect r ic field. Since all fields are measured in lines of the
same character ist ic impedance, t he loss is given by th e rela t ion
E,
L = 20 ‘“g’o E,”
The maximum field st rength in the standing-wave pattern in the first
slot ted sect ion is given by
and the minimum by
Hence
of
Th e r ect ified cu rr en t
th e field st rength , or
Em . =
E,(1 + \ r \ ),
Em,. = E,(1 – 1171).
E... + E.,.
E,= ~ .
R from the probe is propor t ional to the square
where kl is the constant char cter ist ic of the probe on the genera tor side
of the tube. A similar rela t ion holds for the second slot ted sect ion , but
with a differen t constant of propor t ionality. If no standing wave is
pr esen t in t he secon d slot ted sect ion ,
R, = k, E :.
The ra t io kl /k, may be determined by compar ing the probe curren ts
when t e unit to be testd is removed from between the slot ted sect ions.
SEC. 9“3]
PAS S BAND OF HIGH-Q TR SWITCHES
385
The inser t ion loss is then
L = 20 log,, ~~= + xl=
J –
—.
~ R,lcl
k,
Th e r eflect ion loss L., in decibels, is given by
L. = 10 10g,o &2~
wh er e r is th e volt age standing-wave ra t io.
Since
(–)_
Ew2_Rmu
‘2 = E& Rmh’
L, = 10 lc)g,, (~RW + V’~a)’.
4 VmIxi
903. Pass Band of High-Q TR Switches.-A character ist ic of grea t
impor tance in the per forman e of a TR tube is the un loaded Q. This is
FJ~. 94.-Methods of coupling to TR cavit ies.
most easily determined by measur ing the Q of a TR tube and its asso-
cia ted cavity, loaded by one window, QL1.
The cavity is moun ted so
that it terminates a t ransmission line and the response cu rve is measured
in terms of standing-wave ra t io and frequency. E ither coaxia l line or
wavegu ide may be used, bu t since the t rend in microwave applica t ions
has been toward the use of wavegu ide, the measurements to be descr ibed
a re for t he wav gu ide a pplica tion .
For a measurement of QLI, a cavity is moun ted on the end of a coaxia l
line or wavegu ide as shown in Fig. 9.4. Th is situa t ion can be represen ted
by the equival n t circu it shown in Fig. 9.5. The coupling of the cavity
to the t ransmission line maybe var ied by varying the size of the open ing
386
MEAS UREMENT TECHNIQUES
[SJ ?C.9“3
in to the cavity. This cor responds to changing the tr ansformer ra t io,
n/nz, and thus changing the termina t ing admit tance of the line.
When
the cavity is tuned to resonance, the imaginary par t of this terminat ing
a dm it a nce is zer o and, lookin g int o t he ca vity fr om t he transmission line,
a pure conductance is seen whose magnitude depends on the coupling—
that is, the size of the opening—and the unloaded Q of the cavity.
If the coupling ir is is very small, a la rge standing-wave ra t io is pro-
duced in the transmission line, since the end of the waveguide transmis-
sion line is essent ia lly termina ted in a very high admit tance wit a la rge
rea l component . Thus, a minimum of the standing-wave pat tern appears
at t he win dow a t r eson an ce, a nd t he ca vit y is said t o be “u nder -cou pled.”
As the opening is increased in size, the rea l par t of the terminat ing
a dm it ta nce a ppr oa ch es t he ch ar act er ist ic a dm it ta nce of t he t ra nsm ission
line, unt il a size of opening is reached for which, a t resonance, Y = YO,
and the cavity is matched to t e line.
The standing-wave ra t io a t
n2
(a)
(b)
FIG. 9. 5.—Equ ivalen t cir cu it for ca vit y wit h in pu t cou plin g.
resonance will be unity. As the size of the opening is increased st ill
fu r ther , the rea l par t of the admit tance decreases below YO and, a t
resonance, a maximum of he standing-wave pat tern appears at the
opening. When this condit ion occurs, the cavity is r efer r ed to as
“ over -c oupled . ”
As a result of this behavior , t wo possibilit ies are to be dist inguished.
The voltage standing-wave ra t io a t resonance is give by
l–g
!
1+ —
l+g
r. =
~_ l–g’
l+g
~
(2)
where g. is the normalized cavity conductance.
If g. s 1, ro = I/g..
This case is of pr incipal in terest in duplexer design. If g. z 1, rO = g,.
In making measurements on a cavity, the informat ion as to whether
g. is grea ter or less than one is obta ined from the phase of the standing
waves. For an ir is-coupled cavity, it is usually easy to determine
whether a maximum or minimum appears at the opening a t r esonance.
SEC. 9“3]
PAS S BAND OF HIGH-Q TR SWITCHES 387
However , a com plica t ed r -f t r ansmission line bet ween t he slot t ed sect ion
and the cavity migh t make this det rmina t ion difficult . Never theless,
the in format ion may be obta ined by a study of the behavior of the phase
of the standing wave. If the posit ion of a minimum in the standing-
wave pat t ern is measured along the slot t ed sect ion from an arbit r ary
or ig n, and if g. < 1, t here will be a quar ter -wavele gth shift from the
posit ion of the minimum at resonance to the posit ion of the minimum at
fr equ en cies fa r off r eson an ce.
If g. > 1, the posit ion of the minimum
will be t he same at r eson ance as for fr equ en cies far fr om r eson ance.
It is
useful t o in ter pr et t he beh avior of t he stan din g-wave pat ter n as a fun ct ion
of frequency by t racing the var ia t ion on an admit t ance char t .
F igu r e 9.6
gc<l
(a )
FIG. 9 .6 ,—Circle-d i:~ gram
9C>1
(b)
explan at ion of sh ift of m in imum,
shows the circle di grams for the t~vo cases. For frecluencies fa r from
r esona nce, t he cavity a ct s as a sh or t circu it , and has, t her efor e, an infin it e
admit t ance. As the frequency ncreases from a value below the resonan t
frequency to a value above it , the susceptance increases from a large
n ega tive va lu e, pa sses t hr ou gh b = O, a nd a ppr oa ch es posit ive in fin it y.
The conductance of the cavity remains co stant . - The cavity admit -
t ance, th r efore, t r aces ou t a circle whose cen t er is on the line b = O, and
at resonance the admit tance is repr esen ted by point A. If g, < 1, t he
cir cle encloses t he poin t b = O, g = 1, an d t he ph ase of t he st an din g-wa ve
pat t ern changes th rough 360° or one-half wavelength , as indica ted in
F ig. 9.6a . If g, > 1, the phase increases t o a maximum value at point
D in F ig. 9.6b, t hen decreases again with the resu lt tha t the value at
resonance is the same as the value far fr om resonance; the phase then
devia t es fr om zer o in t he ot her ch rect ion , and finally becom es zer o again .
The posit ion of the minimum thus var ies with frequency in the manner
388
MEAS UREMEN T TECHN IQUES
[SEC. 9.3
shown in Fig. 97. If t he loaded Q of the cavity is h igh, the circle on the
admit tance diagram is t raversed in a nar row range of frequencies.
The equivalen t circuit given in Fig. 9.5 may be generalized t o include
an output circu it , which can then be in t erpreted in terms of the cavity
cou pled by
Away
from
generator
t
one window by assignment of \ he proper value to t e load.
Away
from
generator
~“’:w~
oward
f,
Toward
f,
generator
Frequency —
generator
Frequency —
FIG. !17.—Variation of minimum position with frequency.
This circuit is shown in Fig. 98. All conductance and susceptances are
r efer red t o t he input line and normalized.
At r eson an ce t h e su scept an ce
terms, lumped together , a re zero and the standing \ vave set up in the
input line resu lt s from the act ion of he cavity and load condu tance,
which are also lumped t oget her .
At fr equ en cies off reson an ce, t he sus-
ceptance terms cont r ibu t e to the reflected power and consequent ly the
I-+ [4
Y. 9,
FIG.9 S.—Equivalentcircuitfor cavity out put loadingwith mat chedgenera tor.
standing-wave rat io at resonance is the lowest value obtainable.
Th e
loaded Q of the cavity is defined in terms of the resonant frequency and
the frequency difference between the ha lf-power poin ts. In order to
reduce the power in the load circu it t o one half its value at resonance, it
is necessary th t a value of tota l load susceptance equal to the total
load conductance be added. The loaded Q can be calcu lated from the
equation
SEC. 9.3] PASS BAND OF HIGH-Q TR SWITCHES
38!?
(3)
where jO and AOare the resonant fr equency and w velength respect ively,
and j~ and jl, X2 a nd x, a re the cor esponding values at the ha lf-power
points. The standing-wave rat io looking into the cavity with an output
c rcuit i given by t he equat ion
v’(1 + q. + g)’ + (b. + b)’ + v’(1 – g, – g)’ + (b. + b)’, (4)
‘=ti(l+ gc+g)’+(bc+b)’-v(l =g. –g)’+(b. +b)’
At the ha lf-power point s, b, + b = 1 + g, + g, so tha t Eq. (4) reduces to
l+(gc+g) +<l+(gc+g)z
r~
l+(gc+g) –~l+(gc+ g)’”
(,5)
It is appa rent tha t Eq. (5) gives the same result if 1/ (g. + g) is subst i-
t u t ed for g. + g. This means tha t the st anding-wave ra t io at resonance
200
100
80
60
40
Y ,h
20
10
8
6
4
/ ‘
/
/
/ ‘
1
2
4
6810 26
40 60801
r .
Fm. 9.9.—P1ot of r j~ as a funct ion of r ,.
10
(TO)can be used in Eq. (5) without regard to the phase of the reflect ion.
A graph of Eq. (5), with g. + g repla ed by ro, is given in F ig. 9.9 . Th e
value of ro determines the va lue of the standing-wave ra t io a t the half-
power point s. The frequency difference between these point s and the
resonant frequency are used to ca lcula te t he loaded Q from Eq. (3).
The det ermina tion of t he unloa ded Q of a ca vit y is pa rt icular ly sim le
if the Q of a cavity loaded by only one window is measured. A sample
curve showing a measurement on a 11127 TR tube in a cavity mounted
on the end of a waveguide is shown in Fig. 9’10. Once Q~l is determined,
t he u nloaded Q, QO,is calcu la ted fr om
()
o=1 + ; QLI = (1 + ~o)QL1.
When an outpu t circu it is added, it becomes necessa ry to separa te the
cavity conductance from the load conduct ance. Another measurement
to det ermine g. or t he inser t ion loss must be made in order to ca lcu la te Q,,
Two cases a re usua lly of in terest : t he cavity and the outpu t load are
25
r
\
20
!/2
A
— —
AX–- .
n
u
.s
‘$ 15
I
>
m
I
%
%
To
“~
–—r ‘—–”
Jg
m
I
5
0
,
I
12
13 ~ 14 15 ~ 16 17
f2 18 19
Frequency inmegacyclesersecond
F IG. 9.10.—Typica l exper im en ta l cu rve for det ermin in g QLJ .
matched at r esonance, or the cavity has equal coupling windows.
Th e
unloaded Q is given by
Qo = ; Q.,
(mat ch ed inpu t)
()
Q,= :+1 QL2
(equal windows).
As an
lterna t ive to the det ermina t ion of gc by measurements at
resonance with no outpu t circuit , the t ransmission T of the two-window-
coupled cavity and the standing-wave ra t io at resonance may be
measured. The unloaded Q may be computed from the expression
4(T, + 1)
— Q.,.
Q“= 4ro – (To+ 1)’T
SEC. 9’3]
PAS S BAND OF HIGH-Q TR SWITCHES
391
If the TR switch is matched at resonance, TO= 1, and
Q. =
&T ‘“”
It is somet imes more conven ien t to measure the standing-wave rat io at
resonance looking in to the TR switch from the two direct ions than to
measure the t ransmission. Let TI and rz be two values of the standing-
wave rat io. Then
Q. = (r l + 1)(T2 + 1)
Q.,.
r lr2 — 1
A check on the accu racy of measurement can often be made using the
relation
4
T = (r , + 1)(T2 + 1)”
In making carefu l measurements of the Q’s of TR tubes in the 3000-
Mc/sec frequency range, it is necessa ry to measure small frequency
differences. For example, with a TR tube hav ng an un loaded Q of
abou t 2500 and a Q loaded y one window of 450, it is necessary to deter -
mine a wavelength difference of abou t 0.020 cm. With most coaxia l
wavemeter , the accuracy of th is measu rement is hardly bet ter than 10
per cen t . A h igh -Q cavity wavemeter , such as descr ibed in Vol. 11,
Ch ap. 5, is n ecessa ry.
Another method by which the er ror can be considerably r educed is by
employing a speci l frequency marker for measur ing small frequency
differ en ce in st ea d of a wavemet er .
The circu it of th is device con ta ins a
microwave oscilla tor in con junct ion with an oscilla tor opera t ing in the
range of 1 to 20 Me/see. The outpu t powers from these two oscilla tors
a re mixed toget her in a crysta l mixer .
This results in a c r r ier with side-
bands cliffer in g fr om t he ca rr ier by mult iples of t he fr equ en cy of the low-
frequency oscilla tor . For example, a car r ier fr equenc of 3000 hIc/sec
and a low frequency of 16 Me/see gi e a car r ier of 3000 Me/see and side-
bands of 3000 + 16 Me/see, 3000 ~ 32 Me/see, and so for th . Thus,
with the car r ier set a t 3000 Me/see, a var ia t ion of the low frequency from
10 to 20 Me/see gives a var ia t ion in the fir st upper sideband over the
range from 3010 to 3020 Me/see.
If t he m icr owa ve oscilla t or is stable,
the frequency difference can be read to the accuracy with which the 1-to
20-Mc/sec oscilla tor is calibra ted. When this a r rangement is used,
power from the marker circuit is supplied to one of the inpu t termina ls
of a spect rum analyzer , and the signal picked up by the probe of the
standing-wave det ector is supplied to the other inpu t termina l of the
spect rum ana lyzer . The signals a re mixed in t he cr ysta l in t he an alyze .
When the two frequencies a re brought in to coi~cidence, the signals cm
392
MEASUREMENT TECHNIQUES
[SEC, 93
t he spect rum-a na lyzer ca th ode-r ay t ube will sh ow in ter fer en ce common ly
pips from any single microwave frequency, because it contains a super -
heterodyne receiver , ca re must be taken to adjust the signals to the same
M
a)
(b)
lr lG. 9,11.—Int er fe rence of s ignak
of two frequencies on spect rum
ana lyzer ; (a ) sh ows sligh tly dif er en t
fr equ ency signals, (b) shows signa fs
of equa f fr equ en cy.
fr equ en cy. Twopips on th e oscilloscope
of apparent ly equal fr equencies might
a ct ually d iffer by twicet hein t ermed ia t e
fr equency of the receiver . The in ter -
fer ence phenomenon will not appear un-
less the two frequencies are the same.
The appara tus is ar ranged as shown in
Fig. 912. Suppose tha t the measure-
ment is to be made of the Q of a TR cavity
loaded by one window, at a fr equency of
3000 h’lc/sec.
Oscilla tor iSo. 1 is set at
3000 Me/see, and the TR cavity is tuned approximately to resonance by
adjustment of the tuning mechanism unt il the standing-wave ra t io look-
ing in to the cavity is a minimum, The tuning may be accomplished very
easily if it is known tha t the cavity is overcoupled. This is done by
.—— —— ———
——— ——— —.
1
Receiver
1-20 Mc
I
Mixer
Oscjl~r
I
I
1
1f
!
Attenuator Attenuator
Mixer
I
l__:
~____
– – – ??”2”9’4
1
FIG. 91 2.—Schemat ic diagram of spect r um ana lyzer , marker cir cu it , and r -f components
a rr an ged for mea sur ement of QL,.
loca t ing the posit ion of two successive minima in the standing-wave
pat t ern with the cavity completely detuned. The probe of the standing-
wave detector is set ha lfway between these two posit ions, and the cavity
is then tuned unt il a minimum in the standing-wave pat tern appears at
this posit ion . Once the cavity is tuned, oscilla tor No. 2 is adjusted so
tha t with the 1- to 20-Mc/sec oscilla tor set at some value, say 14 Me/see,
one of the fir st sidebands has the same frequency as oscilla tor No. 1.
SEC. 9“4]
PASS BAND OF BROADBAND TR TUBES
393
This is indicated by the appearance of rain on the oscilloscope. The
frequency of oscilla tor No. 2 remains fixed for the rest of the measure-
ment.
The marker pip is moved out of coincidence with the main pip
by adjustment of the 1- to 20-Mc/sec oscilla tor , and the standing-wave
rat io looking in to he cavity is measured. Next the 1- t o 20-Mc/sec
oscilla tor is set a t some other frequency, for example, 15 Me/see. Oscil-
la tor No. 1 is tuned unt il t he pips a e coinci en t ; the marker pip is moved
aside, and the standin wave ra t io at this frequency is measured. This
pr ocess is con tin ued at t he desired frequ en cy in terva ls over a su fficien tly
wide band to include the values of r}j necessary according to the value
of ‘i-O.
Some TR tubes, such as the 1B24 and 1B26, a re const ruct ed with glass
windows and there is o way of actually plugg ng these windows for QL1
measurements. The cavit ies can, however , be t ermina ted by means of a
shor t -circu ited line. If the shor t -circu it ed line is one-quar t er gu ide
wavelength long, the gl ss window will be at a point of maximum field
and the loss component of the dielect r ic constan t of the glass adds to the
cavity loss. A shor t -circu ited line one-half gu ide wavelength long does
not place a high field a t the glass window, but it does cause high cur ren t s
to flow out of the cavity in to the ha lf-wavelength sect ion of line. Unless
the coupling between the cavity and the half-wavelength line sect ion is
ext re ely good, t her e will be 10SSca used by high cu rren ts flowin g acr oss
poor contact s. Severa Q measurements on the same TR tube have
shown tha t th e resu lt s were mor e consisten t when a quar ter -wavelength
sh or t-cir cu it ed lin e wa s u sed.
The values of Qo average 2 per cen t o; 3
per cen t h igher with the quar ter-wavelength line than with the half-
wavelengt h lin e.
9.4. Pass Band of Broadband TR Tubes.—The principal measure-
ments of in t erest for bandpass tubes are the measurements of Q and of
resonant frequency, for the windows and for the in ternal elements, as
well as for t e complet e tube. Since th values of Q~z r ange from 1 to
10, a modu la ted oscilla tor an d amplifier pr ovide t he most a ccu ra te mean s
of measuring the standing-wave rat ios in the range from one to two in
voltage.
To determine the Q of one of these elements, the element is inser ted
in a sect ion of waveguide between two slot t ed sect ions, an the line is
terminated in a matched load. The standing-wave ra t io as a funct ion of
wavelength is then measured for several point s and a cu rve plot t ed from
the data . The resonant wavelength is the wavelength for which the
standing-wave ra t io is a minimum, and the Q is calcu la ted from the
formula
(6)
394
MEASUREMENT TECHN IQUES
[SEC. 94
where b is the susceptance a t the wavelength Ah away from resonance,
~Ois the resonant wavelength , gis the tota l loading (equal to g. + g,),
g. is the termina t ing conductance (usually unity), and gc is the shunt
conductance of the resonant element . The susceptance b may be ca lcu-
la ted for any value of r , the voltage tanding-wave ra t io, by the formula
J
b = (r – 9)(9T – 1).
r
Th e con du ct an ce g is det ermin ed by t he st an din g-wa ve r at io a t r eson an ce,
as in the case of a cavity. If g. can be neglected, and g. s unity, then
QL1can be writ ten in terms of r and k alone,
Q., =
(–)
—-lx”
2+. xi”
(7)
A second metho of eva lua t ing Q~I from measurement employs the
fact tha t the absolute magnitude of the refl ct ion coefficien t is a linear
funct ion of wavelength near resonance for negligible g.. By using Eq.
(2.13), d 11’1/d~is calculated,
21rlA#=
(4 f!j2)2 ~“
(8)
If this is combined with Eq. (6 , and db/dk elimina ted, and the value of
lr l is used, then
Q~l = (4 + bz)%
16
(h) g,
or for small b,
(9)
(lo)
(11)
To obtain
dl r~/dX, the slope of t he cu rve of 11’I plot t ed as a funct ion of x
is taken near resonance. If the measurement is made a t b = ~, Eq. (11)
gives a va lue for Q~l within 10 per cent of the va lue obta ined from the
accura te equat ion. Care should be taken to measure the slope far enough
from xo so tha t the effect of conductance is negligible, and the linear por -
t ion of the resonance curve should be used.
Somet imes , for wavelengths
on on side of resonance, nega t ive values o Ir l a re plot ted so d lr I/ d k can
be obtained from data on both sides of resonance.
F igure 3.5 of Chap. 3
shows some theoret ica l curves of the var ia t ion of Ir I with b, and Fig. 3.6
of Ch p. 3 is an example of an exper imenta l determina t ion of Q~I.
Th e det ermin at ion of t he t ra nsm ission ch ar act er ist ics of t he ba ndpa ss
TR tube involves essent ia lly only two measurements: (1) the reflect ion
SIX:. 9.4]
PASS 13AN1J 011’ l~ROAIJ IIAN l) TE TUBES 39
loss over the band and (2) the dissipation loss. The useful frequency
ra nge is det ermin ed mainly by t he r eflect ion loss, sin ce t he in ser t ion less
is small. A measurement of the standing-wave rat io looking toward
a TR cavity terminated in a matched line at var ious poin ts in the fre-
quen cy band enables th e r eflect ion loss t o be calcula ted easily.
Another method of measurement of the bandpass character ist ic of
Iow-Q TR tubes ut ilizes a magic-T impedance br idge. If th magic T is
ar ranged as shown in Fig. 9.13, the power in the ou tpu t arm (4) is a
measure of the magnitude of the voltage reflect ion coefficien t of the
unknown impedance, Z=. The er ror encountered depends on the match
of the det ector and genera tor and the mechanical asymmetry in the
I
4
Det.
I
Zz
Magic T Z. 2
I
Gen.
3
F I_G.9,1 .—Ar r angemen t for magic T or impeda llce-br idge cir cu it .
magic T. If th is magic T is used with a modulated signal source and a
crysta l detector , the tuning of a device which must be matched at one
fr equ ency, or which must h ave a r eflect ion coefficien t less than a cer ta in
value at the one frequency, is s mple. The tuning of the device is
adjusted for minimum power in the ou tpu t arm. With a per fect magic
T, this will be zero for match; otherwise it will depend on the desired
reflection coefficient.
With appropr ia te precaut ions, it is possible to use a single magic T
wit h sever al in pu t fr equ en cies.
By he use of a cor responding number
of local oscilla tors in a circuit similar to a spect rum analyzer , the power
from the output arm may be displayed on an oscilloscope in the form of
pips, one pip for each frequency.
If th ree frequencies a re used, the
behavior of the reflect ing element at the midband and band-edge fre-
quencies is easily determined, and may be observed at a glance. If the
device is calibr ated with a r eflect ion of kn own magn itu de, uant itat ive
data may be obta ined. For example, if it is desired to check a resonant
396
MEAS (J REMI?KT T ECIfA’IQllE ,S [SEC. 9.4
tube, t he t hree frequencies correspondin g t o midband and t he t wo band-
edge fr equ en cies a re set on t h e r idge.
Th e elemen t u nder t est , backed by
a matched load, is pu t on one arm of the magic T. The heights of the
pips then give the desired informat ion. The tun ing of an element can
be accomplished by adjust ing for a symmetr ical pat tern . In addit ion
t o a quick examinat ion of t he character ist ics of single elements, it is also
possible t o t un e two-elemen t bandpass TR tu bes and t o ch eck t he over-all
response curve, that is, t he standing-wave rat io looking through the tube
in to a matched load, a t th ree differen t poin t s in the pass band.
Th is br idge is excellen t for pr odu ct ion ch eck in g of compon en ts, su ch a s
the windows of the bandpass TR tube, especia lly for tun ing, since the
necessary symmetry of the Q-cu rve for the proper frequencies can be
noted at a glance. Any nec ssary changes on t ransmission-resonant ele-
ments, such as gr inding the glass in the windows or filing metal in other
types of elements, may be quickly checked between steps by not ing the
changes in t he pips.
In the preceding discussion it was shown how the bandpass charac-
ter ist ics of TR tubes and filt ers might be checked, and a method was sug-
gest ed for tuning the individual elements of one of these devices. The
elements of a bandpass TR tube are usually spaced by a quar ter wave-
length in the guide and they are all tuned to the same frequency. It is
not pract ica l, however , t o tune the elements of on of these tubes before
the tube is assembled, because st rains set up in the process of assembly
and solder ing may ser iously detun e the resonant elements.
Th e det un -
ing is unpredictable in na ture, so it cannot be compensated for by any
init ial detuning. For this reason the resonant elements of a broadband
TR tube, with the except ion of the input and output windows which have
a very low Q, are made tunable and the tuning is done aft er assembly.
No single tuning procedu re can be out lined which applies t o all band-
pass TR tubes, but the following procedure applies for most tubes.
1. Mount the tube between a slot ted sect ion and a well-matched
terminat ion, and use adapt er flanges wh en n ecessa ry.
2. Shor t -circu it all of the elements by turn ing in the tuning screws
unt il they make contact across the element .
3. Set the oscilla tor at t he proper frequency (usually the cen ter of the
desir ed pa ss band).
4. Set the probe at a minimum in the standing-wave pat t ern .
5. Tune the first element unt il t he posit ion of the minimum moves
toward the tube a distance equal to the spacing between the ele-
ments. If this spacing is one-quar ter gu ide wavelength, as it
usually is, the probe may be set halfway between two minima and
SEC. 95]
IMPEDANCE MEASUREMENT OF A TR TUBES
397
6.
7.
If
the firs element tuned unt il tha t point becomes a m nimum in the
st a nding-wave pa t ter n.
Turn the tube end for end and repea t steps (4) and (5), the third
elem en t is now nea rest t he gener at or .
Tune the middle or second element t o give minimum reflect ion.
This may be done by first tuning the element for maximum power
t ransmission and then t r imming to give the best match. When
this is don e, h owever , t he gen er at or should be fa ir ly well m at ched;
ot herwise t her e may be consider able differ ence bet ween t he point s
of maximum power t ransmission and minimum voltage standi g-
wave r at io.
the higher -mode at t enua t ion in the waveguide is not sufficient t o
elimina te the eff6ct s of higher modes, it is necessa ry t o make t he element
spacing differen t from a quar ter wavelength and to modify the tune-up
procedure. It is usually desirable to tune at the midband frequency, in
or der t o assure t he best symmet ry of t he ba ndpass cha ra ct er ist ic.
When
thk is done the posit ion of the minimum is moved a distance different
from t he element spacing (step 5 of the tuning procedure). This distance
is dete rmined exper imenta lly.
lt is a lso possible t o evolve a tuning pro-
cedure which allows tuning at a point which is not the cent er of the pass
band, this point is usually one of the point s where a minimum standing-
wave a t io is obta ined. This method may give sa t isfactory result s, but
tuning at the cen ter of the pass band usua lly gives a more symmet r ica l
characteristic.
9.5. Impedance Measurements of ATR Tubes.—ATR tubes of two
differ en t t ypes a re of in ter est .
One tube is the high-Q tube and the other
Spectrum
analyzer
Low-Q ATR tube
Oscil.
Iator
Matched
Wave meter
FIG. 9. 14.—Measur ement of standing wa ves on low-Q ATR tubes.
is the low-Q tube. The measurem nts on the high-Q tubes a re the same
as those discussed in Sec. 9.3 for the TR tube loaded by one window.
The measurement of a low-Q ATR tube is xnade in a differen t mannek
from that of a high-Q tube, but again it s low-power behavior is deter -
mined by making standing-wave measurements.
A typica l setup is
shown in Fig. 9.14.
398
MEASUREMENT TECHN IQUES [SEC.9:5
The ATR tube is mounted in the broad side of the waveguide and,
t o a fir st approximat ion, may be represented by a shun~resonant circu it
in ser ies with the line (Fig. 9.15a).
‘?? m
LG
c
%
SWR
&
1.0
Jo
f
(a)
(b)
F IG, 9. 15.—Equ iva len t cir cu it s a nd response
curve for low Q ATR t ubes,
obtained.
The response curve is such ha t a
high standing wave is produced
at r esona nce, while off r esona nce
the impedance of the ATR tube
is low (F ig. 9.15b).
If the Q of the tube is suffici-
en tly low, t he st an din g-wa ve r at io
will be la rge over such a range that
a coaxial wavemeter is accura te
enough to determine the wave-
length readings. A spect rum
ana lyzer is u sed beca use t he st an d-
in g-wave r at ios a r e so la rge,
Fig-
ure 9.16 shows the type of curve
The loaded Q of such an A1’R ube is defined in terms of the ra te of
ch an ge of su scept an ce wit h fr equ en cy.
If a genera tor of zero interna l
impedance a n d a conductance
b ‘ ‘“R’k
loa din g of u nit y a re a ssumed, t hen
‘“ = 2(g + 1) ~
where Q~l indica tes tha t the tube
f, ;.’4
is loaded externa lly by a conduct -
F IG. 9. 16.—St anding-wave r a tio vs . wave-
length for broadband ATR swit ch .
ante of unity. The reflect ion
coefficien t looking past
t he tube at a matched load is
~=z–l
Z+l’
where
z .l +-–
b
g2 + b’
3’-I
This gives for the standing-wave ra t io
1 + ]r l
‘=l–lrl
<(2gz + g + 2b’)’-+ t)’ + v“-
?=
ti(292 + g + 2b )2 + b’ – ~~’
SEC. 95]
IMPEDANCE MEASUREMENTS OF A TR TUBE~
399
At resonance, b is zero and the standing-wave ra t io will be
or
~=_L
7’0-1
(12)
The poin t at which b = 1 is convenient to se for the determinat ion of
Q.,. The standing-wave ra t io r ’ a t the frequency at hich b = 1 then
depends on the value of g,
V(292+9+ 2)2+1 +J92+I.
“=/(2g’+ g+2)’+1-/g’+l
(13)
Fro Eqs. (12) and (13), r ’ can be expressed as a funct ion of r ,, and
F ig. 9.17 sh ows t his rela tion .
A second method fo determining the Q of a low-Q ATR tube, which
is especia lly suitable a t shor t wave-
lengths, makes use of the mea ure-
ment of the phase shift in the *
neighborhood of r es cmance.
This is
part icu lar ly convenient for low-Q ~
devices because the phase var ies ~ 6
r apidly wh ile t h e st anding-wave r at io
var ies by only a very small amount .
m
The two methods have been found 45
10
15
20
t o give resu lt s a gr eein g with in a bout
TOb
5 per cent at severa l wavelengths.
FIG. 9. 17.—Standing-wave ra t io at
The posit ion of the minimum is
point s for which b = 1 as a funct ion of
measured in the convent iona l man-
st an din g-wa ve r at io a t r eson an ce.
ner . A high-Q wavemeter or a marker cir cu it as descr ibed in Sec. 93 is
r equired, since the r ange of measurement extends over on ly a few mega-
cycles. The va lue of Q is given by
()
C I+zg dl
Q“=ix l+g ~’
where c is the velocity of light , AOthe resonant wavelength in free space,
& the guide wavelength , g is the shunt conductance of the tube, and
d l/ d f is the ra te of cha nge of t he posit ion o-f the minimum with frequency.
The minimum for which the value of d l/ d f applies is tha t which occurs
nearest to the plane of symmetry of the tube. Since this is not usually
the poin t a t whic the measurements a re taken, a cor rect ion for the
400
[SEC. 96
length of line must be made. This is
dl
_ dl’ dk,
_—.
~ df n g’
where dl’/ dj is the measured slope of the line obta ined by plot t ing the
observed posit ion of the minimum as a funct ion of frequency and n is the
number of wavelengths measured, a t resonance, from the minimum
nearest the ATR tube to the probe It is possible to use a magic T in
such an ar rangement and the cor rect ion term is not necessa ry (see Sec.
9.6). In pract ice, kg is best determined by actua l measurement between
posit ions of m nima in t he st andin g-wa ve pa tter n, but k, ca n be ca lcula ted
from the known frequency and a careful measurement of the waveguide
dimensions. It may happen tha t the measurements a r e not cen ter ed
about the resonant fr equency but since d l/ d j is s o nea rly in depen dent of
fr equ en cy, n o gr ea t pr eca ut ion s a re n ecessa ry.
Indicator
Rotatable vane
F IG. 9.18.—Ttming ch eck on fixed-t un ed TR t ubes.
9.6. Low-level Pr oduct ion Test ing.-Standing-wave measurements
a re t ime-consuming and therefore impract i a l for product ion test ing if
sever al m ea su rem ent s a re n ecessa ry.
The opera tor should be able to
get the informat ion by a glance a t a pa t tern on an oscilloscope screen or
eter s of TR and ATR tubes in product ion test in is oft en facilit a ted by
the const ruct ion of specia l apparatus. Some of the quant it ies which
must be measured for each tube are tuning, tuning range (or pass band),
u nloa ded Q, lea ka ge power , keep-a live fir in g a nd su st ain in g volt ages, a nd
inser t ion loss.
F ixed-tuned TR tubes of the 721 type a re checked for tuning in a
cavity of a given diameter . Owing to var ia t ion in const ruct ion, the
tuning of tubes will sca t ter about the desired resonant fr equency and it
is necessar y to specify a tolerance.
It is impract ica l t o determine the
SEC. 9“6]
LOW-LEVEL PRODUCTION TESTING
401
actual resonan t frequency for each tube in a fixed test cavity; therefore,
the tuning of the cavity is var ied through a desired range and the tu e
is accepted if resonance occurs in this range. This tuning is accom-
plished by means of a rota table vane in the cavity (se Fig. 9.18). The
r esonan t frequen cy vanes fr om a maximum, when the vane is perpen dicu -
lar to the axis of the cavity, to a minimum when the vane is para llel to
th e axis.
The amount of tuning depends pr incipally on the vane size
and on the clearance in the parallel posit ion .
Coupling to the cavity
may be either by loop or by ir is as conven ien t . Resonance is determined
by noting the occur r ence of a maximum in the rect ified cur ren t of a
crysta l coupled to the cavity as the vane is tu rned.
Tunable-gap tubes, such as the 1B27, are checked for tuning range
in a cavity of specified diameter at two frequencies, and the tubes are
-i’
rystal detector
Tuning screw
,-.
/
‘1- -U--, -dor
lap .7, LC, , U,
Attenuator pad
Coaxial input
ATR cavity
FIG. 919.-Measurement of Q by power drop in load.
required to resonate at these frequencies within a specified number of
tu rns of the tuning screw. This tuning check is usually done in the same
ca vit y u sed for ot her low-level t est s (for example, Qo) by simply plu ggin g
in oscilla t or s set at t he r equ ir ed fr equ en cies.
The me surement of QO is simplified by the use of he power -drop
method. Figure 9.19 shows a sketch of a test bench in which this pr n-
ciple is applied. Since the coupling to the cavity is constant , the loss is
inversely propor t ional to the Qo of the TR tube. The 10SS,or power drop,
can consequent ly be used as a measure of Qo. In pract ice, the flap at tenua-
tor is calibra ted in decibels and is adjusted to keep the detector cur ren t
constant.
The apparatus is ca libra ted by checking a few tubes of
known QO.
The detector is a crystal in a special holder designed to give a reason-
able match in to an average crystal.
I?in al match in g is a ccomplish ed by
402
MEASUREMENT TECHNIQUES
[SEC. 9.6
means of a sliding-screw tuner .
Figur e 9“20 shows a cross sect ion of the
crysta l holder . The d-c meter on which the crysta l cur ren t is read is
DC out
i
I
FIG. 9.20.—Crys ta l holder .
ca libra ted, by means of the flap
a t tenua tor , in terms of decibel
drop in power from full scale. A
tube is inser ted in the cavity,
t ight ly clamped, and tuned far off
r esonance; the meter is set , by
means of the flap a t tenua tor , to
to resonance, and the meter read-
ing noted. Tubes of less than a
cer ta in power drop a re reject ed.
Keep-a live in ter act ion may a lso be
checked on such a test bench, and, if addit iona l oscilla tors a r e pr ovided,
tuning ranges may also be determined.
The appara tus shown in Fig. 9.21 is designed for product ion test ing
of low-Q ATR tubes in the 10-cm region .
The pr incipa l fea tur e is a
rota table mount for the tube. The axis of rota t ion is coincident with the
axis of the tube, and therefore, a second measurement with the tube
r ota ted 180° from its init ia l posit ion affords a cor rect ion for lack of ym-
met ry in the posit ion of the resonant window. The inst rument is fir st
.- .,.- ,.—.... . .
1
1
.
[
I
I
.“. .,....—. ..— -.,. ., . “. . .
.,. - ..—.
FIG.9.21.—Pr oductiont est benchwith r eversiblemoun t for 1ow-QATR tu bes.
ca libra ted with a tube which is tuned to the cor r ect frequency. This
tube may bean actual tube, or if severa l differen t types are to be checked,
a sect ion of waveguide with a window and movable plunger can be used.
For a tube of each type, t he plunger is adjusted for minimum transmis-
sion past t he tube at the proper frequen y, and the average refer ence
point of the standing-wave minimum for the two posit ions of the tu e is
determined. F igure 9.22 gives a schemat ic view of the apparatus. The
point s .4 and .4’ a r e choke join t s a t t he ends of the rota table mount and
P is the posit ion of the min imum in the standing-wave pa tern when a
cor r ect ly tuned tube is in the mount .
If Al’ is the measured va lue of the
SEC. 96] LOW-LEVEL PRODUCTION TES TING
403
phase shift , Ab may be calcula ted from the expression
Ab= (1 +2g)~A1’.
%
(14)
Once the tolerance in the va lue of Ab a t the frequency for which the tube
is su pposedly t un ed, is det ermin ed, t his m ea su rem en t gives a n in dica tion
FIG
‘Werl ! II i
IIA
~o--A
F IG, 9,22.—Sch em at ic dia gr am of 1ow-Q ATR t ubes wit h r ever sible m oun t.
. 9.23.—Magic T and reversible mount combined as impedance br idge for mea8UI
phase shi t of 1ow-Q ATR tubes.
.ing
of sa t isfactory per formance of the tube. o e poin t t o be noted is that
t he r efer en ce poin t P s ould be as close as possible t o the window. In
the 10-cm region it is easy to make thedistance th ree-quar t ersof a guide
wavelength and therefore, the cor rect ion for line sensit ivity is small. lt
can a lwa s be accounted for in these measurements.
At very shor t
404
MEASUREMENT TECHNIQUES [SEC. 9.6
wavelengths, however , the r eference poin t may be sev ral gu ide wave-
lengths from the tube, and consequen t ly, the frequency sensit ivity of the
line may cause ser ious er rors; sligh t changes in the oscilla tor frequency
are especia lly t roublesome at shor t wavelength s.
These t roubles may becor rect ed by the use of a reversible moun t in
conjunct ion with a magic T. Figure 9.23 shows a photograph of such
an ar rangement used for measur ing 3-cm tubes (1B35 and 1B37 tubes).
A schemat ic diagram of this circu it is shown in Fig. 9.24. If an ATR tube
is placed in one arm of the magic T and a shor t -circu it ing plunger in the
opposit e arm, the plunger may be adjusted to a posit ion where the power
in to the det ector in arm (4) is a minimum.
If, a t th is posit ion , t he dis-
tance b’ from the refer ence plane of the magic T to the open circuit pr e-
sen ted by the plunger (a quar ter gu ide wavelength from the fron t face
(4)
of the plunger ) is equal to the
t --b’+ c’--l
dist ance c’, the line sensit ivity will
be a min imum. Any phase sh ift
2~ ,1,,~, ,: ~dueodetun inof hetub
s compensa ted by ~ sh ift of the
~ ‘3) lunger of the same amount Al
and the su scept ance Ab in t r oduced
by a tube tha t is sligh t ly off resou -
ance may be calcu lated from Eq,
Plunger
(14). The determina t ion of Al is
Fm.
9.24.—Schemat ic d ia gr am of imped an ce
facilita ted by using a dial inclica-
bridge.
tor connected to the plunger .
Using a tunable tube, a reference poin t for a cor rect ly tuned tube is
determined by set t ing the indicator to zero for the plunger posit ion for
which the power into arm (4) is a minimum.
Thus, if a tube inser ted
in the mount sh ifts the phase by an amount Al, t he plunger must be moved
by an amount Al and in the same direct ion rela t ive to the T-junct ion in
order t o get minimum power out of arm (4).
The va lue of the shunt conductance g of the ATR tube maybe d ter
mined by a measurement of th e volta ge standing-wave ra t io at resonan ce,
or the magic T may be calibra ted so tha t the ra t io of power out of arm (4)
t o the power in to arm (1) det ermines g, This can be done only f the
magic T is fa ir ly well matched and n ot ser iously asymmetr ical.
To ca li-
bra te the magic T, it is sufficien t to set the power a t an arbit ra ry le el
and measure the rela t ive power ou t of arm (4) for var ious va lues of
voltage st anding-wave ra t io in the arm which normally holds the tube
mount.
Product ion t est ing of bandpass TR tubes a t low power levels is
accomplished with the aid of the t r iple-frequency impedance br idge.
Th e oscilla tors are adjusted t o midband and ban d-edge frequ encies, a fter
SEC. 97]
LEAKAGE POWEE MEAS lJ REMENTS
405
which it is necessary only to place the tube, backed up with a matched
load, on one arm of the magic T and see if t he pips show a standing-wave
rat io less than a specified value a t t he t hree frequencies.
9.7. L akage-power Measurements.—In addit ion to the determina-
t ion of th e low-power charact er ist ics of TR and ATR tubes, it is necessary
to examine their behavior at h igh power levels, that is, a t t ransmit ter -
power levels from a few wat t s up to powers grea t er han a megawat t .
The pr incipal quant it es of in terest , in connect ion with h igh-power
opera t ion , a re the leakage power through the TR switch wh n it has fired,
power loss in the tube it self, and recovery t ime. The complete informa-
t ion about the h igh-level per formance of TR and ATR tubes involves a
fur ther subdivision of these quant it ies and a wide var iety of carefu l
measurements of each on e,
The leakage power which get s through a TR tube dur ing the t rans-
mit ter pu lse amounts to only a few microwat t average power , for most
tubes, and is most convenien t ly measured by means of a thermistor and
t hermist or br idge, Wolla st on -wir e bolomet er s, t hermocou ples, a nd cr ys-
ta ls a re less r ugged than thermist ors used at microwave frequencies. The
thermistor element mounted in a broadband mount and used with a type
TBN-3EV bridge affords a means of measur ing the low power which gets
th rough the TR switch . The type of mount depends on the output
coupling of the cavity employed
for the leakage-power measu re-
m nt . The cavity may be either
ir is- or loop-coupled to a coaxia l
line whic is t erminated in a
c o a x i a 1-1i n e thermistor mount .
For bandpass TR tubes or for
other tubes employed with wave-
gu ide, a t ransit ion to coaxia l line
may be used, or the thermistor
may be moun ted in the wavegu ide.
The outpu t coupling of the TR
cavity is adjusted on low-level
r -f power , and therefore, a match
is seen at the inpu t terminals (see
Sec. 9.3). The reflect io will vary
somewhat among tubes of the .
Matched
load
r
FIQ. 9.25.—Leakage-power equipment for
med ium-power level.
same type, because the unloaded Q’s are difieren t , b t th is var ia ion is
usually not ser ious. A drawing of a typica l r -f circu it in gin. coaxial
line, for use a t a peak-pow r level up to 100 kw, is shown in Fig. 9.25.
At h igh er power levels a wa vegu ide inst alla t ion is u sed (see Fig. 9.26).
The cavity is usually shunt -coupled to the waveguide and pr vided with
406
MEASUREMENT TECHNIQUES
[SEC. 97
a coax al ou tpu t line, termina t ed with the matched thermistor .
The
cavity ou tpu t coupling is adjusted for matched input to the cavity.
This is accomplished in the following way: a plunger is subst it u ted i’or
the t ransmission line. A posit ion
of the plunger is found for which
tuning the TR cavity with no OUG
put coupling resu lt s in no change
in the st anding-wave pa t t ern as
the cavity is tuned th rough eso-
nance. This means tha t the plung-
er is in the r igh t posit ion to
shor t -circu it t he cavity. Next the
plunger is moved by a distance
of a quar t er gu ide wavelength ,
t he t ransmit t er and a low-level signal is in t roduced from the load end of
Matchad load ,
FIQ. 9 .2 6 .—Wavegu ide h igh -p owe r leak age
power m easu rem en t .
and t her efor e, t he low-level signal is effect ively in troduced direct ly in to
the cavity. The output line is added to the cavity, and the coupling is
adjust ed unt il t he standing waves disappear on the input side of the
cavity. The plunger is replaced by the t ra smit t er , a d the appara tus
is ready t o measure leakage power .
A direct iona l coupler to monitor
the line power facilit a tes studies
of leakage power as a funct ion of
line power . For checking the zero
set t ing of the thermistor br idge,
a ga t e, either a t t he input or out -
pu t side of the cavity, which will
cu t the r -f power o f en t irely from
the thermistor , may be used. F ig-
u re 9.27 shows the const ruct ion of
a ga te suitable for 34n. by I+-in .
waveguide.
The t ransit ion from wavegu ide to coaxial line may be made by means
of a probe coupling, or a doorknob or a crossbar t ransit ion may be used.
For wavelengths in the 10-cm region , one of he most sa t isfactory com-
bin at ion s isja t hermist or mou nt ed in &in . coa xia l lin e a nd a cr ossba r t ra nsi-
t ion from 3- by I&i. gu ide to &ii. line. It is necessary t o check the
match in the waveguide por t ion at the wavelength used. In genera l, t be
probe and crossbar t ransit ions a re not matc ed over as broad a band as is
the doorknob t ransit ion. F igure 9.44 is a sket ch of a cryst a l holder using
the crossbar t rans t ion . In the 10,000-Mc/sec region the thermistor
mount is en t irely in waveguide. Built in to the unit is a ga te which con-
sist s of a vane pivoted t o swing between a choke-and-flange join t in a
FIG. 9 .2 7 .—Gat e for la rge wavegu ide .
I
SEC, 9.7]
LEAKAGE POWER MEAS UREMEN TS
4(-)7
wa vegu ide sect ion (see Fig. 9“28).
The temperatu re sensit ivity of the
thermistor can be reduced by enclosing the unit in a box filled with rock
w~ol or ot her in su l t in g mat er ia l.
FIG, 928.-Thermistor mount and gate for 3-cm measurements.
F or measurement of the leakage power of pre-TR tubes, provision for
known at tenua t ion between the tube and thermistor must be made, since
the leakage power is about 1000 t imes that of a TR tube. A direct ional
Fm. 9.29.—Termination for use in measur ing leakage Power of pre-TR t~~.
coupler and matched load a complish this very well. In addit ion, a
plu nger (~ in .-diamet er r od) pla ced a t t he pr oper dist an ce fr om t he pr e-TR
tube acts as a ga te to shut off the power from the thermistor . F igure
408
MEASUR MENT TECH N IQUE,!I
[S EC.–9.7
929 shows this sect ion of wa veguide including t he t ermina tion , plu nger ,
dir ect iona l coupler , andtr ansit ion t o t hermist or mount .
The measurement of the leakage power as descr ibed gives the tota l
average leakage power , that is, both fla t and spike, and both direct and
a rc coupling. The thermistor br idge indica tes the average power inci-
den t on the thermistor , and this va lue is usually in the range of 10 to
150 WVfor line power s up to 100 kw peak power . If P,,. is t he average
power , 7 is the pulse length, and v is the pulse repet it ion frequency, t he
a vera ge power dur ing the pulse, Pi, is
(15)
This is, of course, not the peak r -f power in the pulse. Crysta l-burnout
studies indicate tha t t he quant ity of interest is the tota l energy in the
spike. Thus, some separa t ion of energies of spike and fla t must be made.
The tota l energy per pulse, W., is given by
w= = p+.
(16)
The determina t ion of the spike energy is descr ibed in the next sect ion.
I ’ r
-v-
a)
(c)
F1~. 9.30.—Ch ar act er ist ics of r ec-
t angular pulse: (a ) single pulse; @)
amplitude spect rum; (c) appearance
of spectrum analyzer scope.
The fla t energy per pulse and, hence,
the fla t power , is then found by sub-
t ract ing the spike energy from the
For all these measurements, it is
necessa ry to know both v and r
accura tely. The pulse r ecur rence fre-
quency v is easily measured with a
ca libr a ted audio oscilla t or and oscill~
scope.
Severa l methods may be used
to measure the pulse length. A com-
mon method is to use a sin e wa ve,
wh ose fr equ en cy is a ccu ra tely kn own ,
to calibra te the sweep speed of a
syn ch roscope or r -f en velope viewer .
On ce t he sweep is ca libr at ed, t he pu lse
length is determined by viewing it on
the oscilloscope.
Another method of measur ing the pulse length consists of applying a
small amount of r -f power to a spect rum analyzer and making use of the
ch ar act er ist ic spect rum of t he r ect an gu la r pu lse form.
Th e pu lse len gt h
can be calcula ted by measur ing the wavelength differ ence between a
known number of zeros of the spect r . F@re 9“30 shows the spect rum
SEC. 9.8] MEASUREMENTS OF SPIKE ENERGY
409
of a rectangula r pulse. If j~ is the frequency corr espon~lng t o the mth zer o
on the r ight , and fm is the frequency corresponding to the n’h zero on the
left , t hen
m+n
‘= fro-j.”
9.8. Measurements of Spike Energy. -Once the tota l average leakage
power has been d term ined, some schem e for measur ing the spike en er gy
Line stretcher
R.f &wer
FIQ. 9.31.—Cancella t ion
Probe coupling
/
Leakage power
circuit for measurement of spike energy.
FXCI..32.—Adju st able pr obe cou plin g t o coa xia l lin e.
separa tely from the fla t energy is necessa ry. One method of measuring
the energy in the spike ut ilizes the cancell t ion pr inciple. A por t ion
of the r -f energy is coupled out of t e main line and into the output line
from the TR c vity in the proper phase to cancel out the fla t energy and
leave only the spike energy. The spike energy can then be measured.
410 MEASUREMENT TECHNIQUES
[SEX. 9.8
The arrangement for doing this is shown in Fig. 9.31. The magnitude
of the bypassed power is var ied by means of the adjustable probe at the
main line or at the cavity output
terminal . A cross sect ion of this
coupling is s own in Fig. 9.32.
The proper adjustment of the can-
,,,il,,lll,l!,l,lllll,(llll(a
~ 111,,,1111,,,,,,,,,,,,,,,,,
cella t ion circ it for the eliminat ion
J-L-J-
1111111111111111111lll!!llll 1111111llllllllllllllll
(a)
(b)
(b)
FIG. 9. 33.—Pulse before and
FIG. 934.-Spectr m of pulse befor e
after cancella t ion of fla t . and afte cancella t ion of f a t .
of the flat energy requires some means of detect ion by which the adjust -
ment may be checked. Severa l schemes maybe used. one is to replace
t he t hermist or by a reasonably well-matched crysta l and
140~
to view the out -
J J _ L L —I
0
0.5 1.0 1.5 2.0
7 p sec
Fm. 9.35.—Tot al lea ka ge power vs. pu lse length.
Level at T = O gives spike energy.
pu t voltage on an r-f envelope indicator . On a fast sweep, the spike
energy and the fla t energy are easily visible and the circuit is djust ed
unt il the flat energy is canceled (see ig. 933). When the crysta l has
been replaced by the thermistor , the power in the spike a lone is measured.
Subt ract ion of spike power from the tota l power then gives the flat power .
Conversion to spike energy is made M just descr ibed [Eq. (16)]. Another
SEC. 98]
MEASUREMENTS OF SPIKE ENERGY
411
method is to use a rapidly act ing thermistor br i ge and to adjust t he
circuit for minimum power into the thermistor . This assumes that
the fla t is rea lly fla t and that no harmonic frequencies a re present . The
adjustment may also be made by picking off a por t ion of the energy
from the slot ted sect ion and viewing it on a spect rum ana lyzer as the
coupling is var ied. The spect rum of a rectangula r pu lse is shown in Fig.
9.34. As the fla t is canceled out , the spect rum changes to a er ies of pips
of ver y nea r ly equa l heigh t .
A method that requires less equipment but is capable of giving good
result s is that of using differen t pulse lengths at one peak po~ver .
If the
spike is assumed to be the same for all pulse lengths, a plot f the energy in
Variable attenuators
Rejection
cavity
~
Thermistor brdge
for spike
Transmission
u
cavity
l-@
Therrn:t[a~idge
/
1111
/
\
[
/
Load
Magnetron
Attenuation
FIG. 9.36.—Separa t ion of spike and fla t power by pass and reject ion cavit ies.
the pulse as a funct ion of pu lse length , ext rapola ted to zero pulse length ,
gives a va lue for the spike energy. F@e 9.35 shows some data l t aken in
this manner with a 724B tube.
Another method for the separa t ion of the spike and the fla t energy
has been used by Fis e. 2 Advantage may be taken of the cliffer ence in
the fr equency spect ra of the spike and the fla t by the use of filt ers.
t ransmission cavity plac d a t the side of the waveguide which leads from
the TR tube, see Fig. 9.36, a llows the fla t power to fall on a thermistor and
this power can be measured. Since the spike has such a wide dist r ibu-
t ion of energy in frequency, on ly a small fract ion of it passes th rough the
t ransmission cavity if t he Q is near 1000. The fla t power is forced t o
en t er the t ransmission cavity by means of a reject ion cavity on the side
of the waveguide a quar ter of a wavelength from the t ransmission cavity.
1 J . W. Cla rke, “A Met hod of An alyzin g Leakag P ower Da ta ,” BTL MM-43-
140-54),Oct . 11, 1943.
‘M. D. Fiske, H. N. Walface, and A. D. Wa rner , “Final Technim l I@or t on
Cont ra ot 0E~l$16,” GE , Seh en@ady, Nav. 7, 1946.
412
MEASUREMENT TECHNIQUES
[SEC, 9“10
Thereject ion cavity acts asahigh-QATR tube. The fla t energy passes
both the t ransmission and r eject ion cavit ies and en ter s a second thermis-
tor and th power can be measured.
The method may be difficult to use
in pract ice since the cavit ies must be precisely tuned. W th proper ca re
th e losses in the cavit ies n eed n ot be cxcessivc.
9.9. Direct -coupling Measurements.—T e direct -coupling power is
the power which is coupled th rough a TR cavity by fields other than those
of the normal mode. It is the power which is coupled th rough when the
arc is replaced by a per fect shor t circu it .
Th e equipment and tech niqu e
for measur ing th is power a re the same as those used for measur ing tota l
leakage power , except tha t the TR tube is replaced by a dummy tube, in
which a meta llic shor t circu it is subst itu ted for the discharge gap. }Vith
high-Q tubes such as the lB2’i, 11324, 721, or 724, an old tube with the
cones soldered together is qu ite sa t isfactory as a ummy tube. The
power then measured by the thermistor is the direct -coupling power .
The direct -coupling at tenuat ion for a given tube may also be meas-
u red at low power levels by using a spect rum analyzer .
The TR switch
is adjusted in the same way as
150
E
‘k
for the measurement f Q,,j (see
g 100
Sec. 9.3) with a matched ou tpu t
z
line and with coupling adjusted
% 50
,n~&~&p$~ ~~ for matched input to the cavity.
m
%
~ Arccoupling
The ou tpu t line is connected to a
o
0
100 200 300 400 500
spect r um an alyzer an d th e at ten u-
Linepower.kw
ator is adiusted to a conven ien t
FIG. 9.37.—Variation of dir ect -cou plin g a nd
height of ~ignal on the ca thode-
a rc-cou plin g power wit h lin e power .
r a y-t ube scr een .
The TR tube is
replaced in the cavity by a tube with a shor t -circu ited gap and the
at tenua tor is readjusted to br ing the signal back to the sa e heigh t .
The difference in at tenuator readings then gives the direct -coupling
a tt en ua tion in decibels.
Another , although n ot so accura te, method of procedu re is to measure
the leakage power from the TR switch as a funct ion of the line power
inciden t upon the tube. It has been demonst ra ted (Chap. 5) tha t the
a rc leakage power is ndependen t of the inciden t power over a la rge range
of values, provided that the inciden t power is su fficient ly high. Thus,
by ext rapola t ing t e leakage-power var ia t ion to zer o incident power , the
arc leakage power is obta ined.
The slope of the line is the direct -cou-
pling at tenuat ion . F igure 9.37 shows the resu lt s of a ser ies of measure-
ments on a 721A tube in a cavity.
The arc leakage is 30 mw and the
direc~cou plin g at tenu at ion is 68.8 db.
9.10. At ten uat ion at Harmonic F requ en cies.—An impor tant problem
is tha t of t he t ran smission of h armonic fr equ en cies th rou gh th e TR switch .
SEC. 911]
MEASUREMENT OF ARC LOSSES 413
In high-Q TR tubes this t ransmission may be ext r emely ser ious if the
power in the harmonics is appreciable, since coupling is possible which
t ransmits the harmonics th rough the cavity wit pract ica ly no at t enua-
crysta l may be burned out . The harmonics may be loca ted by means of
a spect rum analyzer . This involves sea rching over a wide r ange of fr e-
quencies and so requ ir es a very-wide-range analyzer or a ser ies of ana-
lyzers. It is more convenient to use some other means of locat ing the
harmonics. One way to loca te the harmonic is t o use a coaxia l wave-
meter as a transm ssion cavity between the TR outpu t terminals and a
crysta l detector . The measurement of the actua l power conta ined in
these harmonics, once the frequency has been determined, requ res a
thermistor matched at the harmonic fr equency and a select ive filt er
device such as a high-Q cavity, r esonant a t the harmonic frequency, t o
r emove the componen ts of other freq encies. The fundamenta l fr e-
quency and frequencies near it can be a t t enua ted effect ively by 60 db or
more by using a shor t -cir cuit ed-gap tube as in the measurement of di ect -
coup ling a t t enua t ion .
When a discharge occur s across a resonan t window as in bandpass
TR tubes and pre-TR tubes, a measurement f the a t tenuat ion of the
fundamenta l fr equency probably gives the a t t enuat ion factor for the
harmonics a lso, since the disch rge cover s the en t ire window with a
conduct ing screen of ionized gas. This haracter ist ic a t tenua t ion of
harmonic fr equencies has been emphasized as an addit ional advantage
of bandpass TR tubes over h igh-Q tubes.
9.11. Measurement of Arc Losses. —When a TR tube fires, some
power is dissipated in the gaseous discharge of the a rc. Since this dis-
sipa t ion may be a funct ion of the shape of the elect rodes and especia lly
of the gas filling, complete informat ion about a TR tube requ ires a
measurement of the pow r lost in the a rc. Because th is loss is small, it
is r ather difficult to measure accura tely. A simple method for measur ing
this quant ity consists of set t ing up a TR cavity, with or withou t an
outpu t circu it , with a power measurer in the load end of the t ransmission
line, and then compar ing the powe reading P,, with a shor t -circu ited
tube i place, with the power reading PI, when a good TR tube is inser ted.
Th e r at io R = P,/ P” gives the fract ion of power t r ansmit ted, and 1 – R
gives the fract ion of power lost in the arc. This measu remen t may be
made either in coaxia l line or in wavegu ide, with eith er h igh - or low-Q
tubes. Accura t ely ca libra ted direct iona l couple s with thermistor s
provide an easy way of measu r ing power ,
Since the loss in one tube usually amoun ts to on ly a few per cen t of
t he in ciden t power , with a possible er r or comparable in magnitu e with
the measllr ement , it is somewh t more sa t isfactory to use severa l tubes
414
MEASUREMENT TECHNIQUES
[SEC. 9-12
of one. The grea ter loss with severa l tubes can be mea su red
to
within t he same limits of er ror as for on e tube, and if it is assumed tha t
t he tubes a re reas nably a like, the average loss may be measured with
more accuracy than or a single tube. Figure 9.38 shows a waveWide
lin e wit h
two
direct ional couplers ,
set
up for mea su rin g arc loss of severa l
tubes. With this ar rangement “dummy” tubes are used to secu re t he
zero readings P 1 and PZ at the two couplers.
The tubes to be meas-
ured a re inser t ed in place of the dummy tubes, and the power readings
P; and P; a re t aken. The fract ional loss of power is 1 – P~l/P~Pt.
If the a t tenuat ion of either direct ional coupler is known, the absolu te
power los s can be ca lcula ted .
Directional coupler
Directional coupler
R.f Power
/
Matched load
FIG, 9.38.—Equipment for measur ement of a r c loss on severa l bandpaas tubes.
9s12. Minimum Fir ing Power .—This quant ity is of lit t le interest for
most pract ica l applica t ions, since the power level of the t ransmit ter is
usua lly very much in excess of that r equir ed to inaugura te the discharge.
The min imum fir ing power is used as a test to determine the quality of
some tubes. The measu rement is ext remely simple, the necessary
equipment consists of an r -f oscilla tor wh ich has a con t inuously var iable
outpu t power , a t ransmission line with mount ing for the tube under test ,
and a power-measur ing device which indica tes the power level in the
line. The a r rangemen t is very compact if wavegu ide is used. The
fir ing poin t is determined by increasing the power level un t il the discha rge
can be seen (or otherwise indica ted) th rough a small hole in the TR
cavity or in the waveguide opposite the tube, and by not ing the rea ing
on the power monitor . The power may then be decrea sed unt il the arc
goes out , thus giving the ext inguish ing power for the tube.
If a pulsed magne ron is used as a power sou rce, some means of
a t tenua t ing the inciden t power must be provided. The most conven ien t
form of a t tenua tor for h igh power levels is known as a power divider .
F igure 9.39 shows a schema tic diagram of th is device in a coaxia l t rans-
mission line. Two stubs, each a quar ter wavelength from the inpu t
termina ls, a re provided with plungers. The motions of these pl~gers
SEC. 913]
AN RF PRESSURE GAUGE
415
a re ganged together so tha t the stub lengths always dhler by a quar ter
of a wavelength . As t e plungers are moved in and out , the ra t io of the
powers delivered to loads (1) and (2) changes over all va lues from zero
to infin ity. This can easily be seen from a simple ca lcu la t ion . The
susceptance of the stub, with the
-1.. -.-.” “ A:. +.... a
. $.,. - +1...
pluugcl a uln lJzk l lGc .L 11Uul t)llc
line, is
jb, = –j cot k z ,
!El
— ——— -—— ——
where
~=~r
h“
r
The admit tance of load (1) plus
the stub admit tance U1 as seen
I
--
/4
-i-
x
from the input T-in junct ion is,
& &
k
therefore,
(:
I
1
)
Load 2 1
I Load 1
Y,=l
- j cot kz”
+ ~/4 – + - — v4 -d
Similar ly, the admit tance of the
second br an ch is
lnDut
1
termmals
‘Z=l+jtankz”
FIG. 9.39.—Diagram of a power divider .
The cur ren ts divide in the rat io of these admit tances, and the ra t io of
t he powers, R, equ als t he rat io of the squares of the absolu te magnitudes
of the curren ts. Thus
~= l–jcotkxz=cotzkx
l+jtankx
1
wh ich t akes all values from O to cc as kz var ies from T/2 to O. The input
admit tance is equa l to unity for a ll plunger posit ions, since
1
1
‘“=l–jcotkx
+
I+jtankx
= 1.
Th e admit tance lookin g back fr om eith er of th e loads, h owever , var ies as
the posit ions of the plungers vary. If load (2) is a matched dummY
load, the power from the other termina ls can be va ried and used for the test
bench . It should be remembered tha t the genera tor is not ma tched,
and it delivers maximum power when t e load is rea t ive.
9.13. An R-f Pressure Gauge.—The character ist ics of any TR, ATR,
or pre-TR tube depend on the pressure of the gas with wh ich the tube is
filled as well as on its composit ion , With in cer t in limits, it is possible
to judge the qua lity of a TR, ATR, or pre-TR tube by measur ing the
416 MEASUREMENT TECHNIQUES
[SEC. 9.13
pressu re of the gas inside it . One method of doing this ut ilizes the elec-
t rodeless discha rge of a gas at radio requencies. The gas is excited by
the applica t ion of a radio-fr equency pote t ia l. The voltage at which
the glow is fir st excited is a funct ion of pressu re, and can serve as a
measure of pressure.
Astudyof the breakdown voltage foranelect rodeless discharge, for
var ious gas pr essur es, yields th e typica l Paschen curve, very similar to
the d-c voltage-breakdow character ist ic, or to the var ia t ion of leakage
power with pressure (F ig. 5.28). The quest ion of in terest for pressure
measurements is whether reproducible cu rves can be obta ined with
slopes of such values that they are usefu l for pressure measurements.
The change of slope of th e cu rve with th e fr equency of th e applied voltage,
and t he effect of elect rode sh ape, a re m at ter s for exper im en ta l det ermin a-
t ion . The st ructure of the elect rodes should be such that pressu re
determinat ions are independen t of slight var iat ions in posit ion and
ir r egular it ies in t he tubes un der t est .
An oscilla tor of convent iona l design with a built -in , sh ielded, vacu-
um-tube voltmeter is used. The oscilla tor opera tes at a fr equency of
6 Me/see and produces a voltage
across the elect rodes which is var i-
able up to more than 3000 volt s.
For pre-TR tubes (1 B38, 1B54) and
low-Q ATR tubes (the 11M4 and
To oscillator
ot her s) t he elect rode st ru ct ur e sh own
in Fig. 9.40, which rest s on the glass
window of the tube, is sa t isfactory.
I’1o. !140.—E lect r od e s tr u ct u re for t est in g
With the elect rode and tube in plac~,
re-TR and 1ow-Q AT tubes.
the applied r -f voltage is slowly
increased until the glow discharge in th tube appear s.
The voltage”a t
thk poin t is compared with the calibrat ion curve and thus indicates
the pressu re in the tube
The ca librat ion curve depends on the gas mixtu re and the type of
tube. A differen t mixture or a tube of a different type requires a new
calibrat ion. A 11338 tube with the elect rode st ructu re illust rated in
Fig, 9.40 has a var iat ion f st r iking-voltage with pr essur e which is essen -
t ia lly a st ra ight line ~vith a slope of 30 volt s/mm of Hg, for argon pres-
sures UP to 30 mm of Hg, For air , the slope is 100 volts/mm, up to
pressu res of 18 mm of Hg.
These values are sufficien t ly accura te for
checking 1ow-Q ATR tubes and pre-TR tubes whose gas fillings can vary
in pr essu re by sever al m illim et er s ~~it hou t impa ir in g per formance.
This
pr essur e gau ge has been successfu lly used t o h eck h ydr ogen thyr at ron s, 1
(3C45, 4C35). The range of pressures in this case ;s much lower , and
ISee Vol. 5.
SEC. 9“14]
MEANIREMENTs ON RECOVERY TIME
417
th e pressure r egion of t he Paschen cu rve below the minimum is employed.
The voltag~pressure character ist ic has t her efor e a la rge nega tive slope.
Severa l factor s influence the per formance of thk ressure gauge. The
composit ion of the gas should be the same in all tubes for which the same
ca librat ion curve is used. The effect of very small amounts of impur it ies
is ser ious and usually unpredictable. Each type of tube equires a
sepa ra te ca libr at ion if t he st ru ct ur e is a ppr ecia bly differ en t.
If the tube
has been in opera t ion , it is possible tha t a sput ter ing process has resu lted
in the deposit ion of mater ia l on the glass.
This deposit does not ordi-
nar ily affect the ca libra t ion unless the deposit is an opaque metallic
coa t ing wh ich r esu lt s in appr eciable elect r os ta t ic sh ielding.
Temperature
effect s a re qu it e negligible.
coupler
Load
FIG. 9.41.—Arrangement for measur ing r ecovery time of a TR tube.
9.14. Measurements on Recovery Time of TR Tubes.—The deter -
minat ion of the recovery t ime of a TR tube requires more equipment
than any other single measurement .
Th e essen tia l equipmen t inclu des
a modula tor (preferably of the synchronous type), an r -f system, with
dir ect ion al cou pler s for mon it or in g t he po er a nd in tr odu cin g a low-level
signal, a matched high -power load, a TR cavity, a mixer , a local oscil-
la tor , a preamplifier , a receiver , an A-scope, a pulsed signal genera tor ,
and a synchronizer or t iming unit .
Th e schematic ar rangement of th ese
componen ts is shown in Fig. 9.41. This is one of severa l schemes which
have been used for this purpose.
The problem is t o measure t he a t tenua-
t ion of a low-power signal (the “echo” signa l) as a funct ion of t ime after
the occu r rence of the hig -power t ransmit ter pulse. This low-level
signa l is a t tenua ted because of the presence of elect rons around the gap;
the a t tenua t ion decreases as the number of elect rons decreases. Thus, a
low-level signal of constan t power t races an envelope curve, such as b
418
MEASUREMENT TECHNIQUES
[SEC. 9“14
in Fig. 9“42; as the t ime of occu r rence after the t ransmit ter pulse, a, is
varied.
Be inning with the -f t ransmission line, the necessary adjustments
are st ra ight forward. Fhstof all, inorder that therecovery t ime of the
TR tube alone will be measured, no ATR tube is used and the distance
from the magnet ron to the TR branch is so chosen that the largest
possible fract ion of a low-level
signal coming from the antenna
tiafreuencyapPoximtey30
___ line will be t ransfer red th rough
the TR cavity to the crysta l detec-
tor . The local oscdla tor M set a t
FIG, 9.42.—Recovery-t ime curve for low-
Mc/sec (that is, t he in termedia te
leve l s ignal.
frequency) from the frequency of
the signal genera tor , which is usually, but not necessar ily, close to the
magn et ron frequency, and t he crysta l cu rren t is adju st ed t o t he opera t in g
level of 0.5 ma. When the local oscilla tor and signal genera tor are prop-
er ly tuned, the pulse should appear on the A-scope when the receiver
sen sit ivity is high en ou gh t o make t he n oise visible.
L
c
F 1o. 9,43.—Pha se-con tr ol cir cu it for sin e wa ve.
An essent ia l par t of the measurement is the adjustment of the t ime
of occur rence of the low-level pu lsed signal with respect to the main
t ransmit t er pu lse. It is impor tant to be able to adjust the low-level
pulse so t hat it occu rs just befor e t he t ransmit ter pulse, in or der t o pr ovide
a reference level at a t ime when the tube has made as complete a r ecovery
as possible. For one method of t iming control, the sine-wave voltage of a
master oscilla tor is used. This voltage is split , by means of a phase-
on t rol circuit , F ig, 9.43, in to two sine waves having phases that are
SEC. 9.14]
MEASUREMENTS ON RECOVERY T IME
419
var iable with respect t o each other . Two t r iggers may be genera ted
from these two sine waves, and their rela t ive t imes of occur rence will
depend on the rela t ive phases of the sine waves. One t r igger may
be used for the t ransmit ter tube, and the other for the signal genera tor .
A synchroscope’ is a convenien t device to use as an A-scope; it provides
the sine wave whose phase may be var ied, a fast sweep for viewing
the pulses, and one t r igger .
.4 t r igger genera tor can form a t r igger
from the phasable sine wave.
An alternat ive, and somewhat bet ter ,
method is t o use a Model G synchronizer .
This device provides two
t r iggers, one with a fixed delay for opera t ing the modula tor , and on e with
a var iable delay for opera t ing the pulse signal genera tor . This gives
mu ch mor e posit ive oper at ion t han t he sin e-wa ve ph ase-c on tr ol cir cu it .
The signal genera tor is an important item of equipment . It must
provide a reasonably good rectangular pulse, of approximately 1-~sec
durat ion , in the desired frequency range. If a calibrated at t enuator is
not built in to the r -f outpu t line of the signal genera tor , sllch an at tenu-
at or must be pr ovided ext ern ally.
The syst m may also be designed so
that the at t enuat ion may be provided in either the i-f or the video-fre-
quency line. A signal genera tor such as the type TGS-5RL facilita tes
a wide var iety of measurements (see I-ol. 11, Chap. 4). This signal
genera tor uses a wide-range 707B or 2K28 tube and has a variable pulse
length , a built -in variable delay for t iming cont rol, and an r -f a t tenuator
in the ou tpu t line. These featu res make it a very useful inst rument in
the 10-cm region . Other signal genera tors are available for the other
wavelength regions .
.4 method for measur ing the t ime scale of the sweep is necessary.
This is often accomplished by means of a l-IUc/sec oscilla tor which
provides a sine wave of accur tely known frequency. This sine wave,
applied to the signal pla tes of the .4-scope, affords a calibrat i n of the
sweep since a complete cycle cor responds to 1 psec for a l-Me/see wave.
When a gr id is placed over the face of the cathode-ray tube, t ime intervals
can be est imated t o ten ths of microseconds.
.L st ill bet t er scheme is to
use a sweep cal bra tor which provides a ser ies of equally spaced, very
narrow pulses, and to ar range a switch so that these pulses are displayed
on the tube. Sweep calibra tors are descr ibed in Vol. 22 of th is ser ies; a
suitable one is type B81 27.
Once the system is tuned, the measurement is easy. The choice of
the or igin of the t ime axis is arbit rary.
It is possible either to measure
the t ime in terval from the leading edge of the t ransmit t er pulse, since
in a great many instances the leading edge of the pulse is sh rper and
bet ter defined than the t raili g edge, or to measure thr in terval from the
1For descriptions of this :lnd other dcvimw nlcntionmi Iler{,, the retzder is referred
to Vol. 22 of this series,
420
MEASUREMENT TECHNIQUES
[SEC. 9“14
t ra iling edge, since the recovery of the tube cannot begin unt il thet rans-
mit ter has ceased to oscilla t e.
E ither of two reference levels for the
a t t enua tor set t ing may be used: the a t t enua tor reading for which the
signal level is r educed t o noise level, or the reading for a given amplitude
of signal immedia tely pr eceding t he t ra nsmit ter pulse.
The det erm in a-
t ion of the fir st r eference level is dependen t upon the exper ience of the
observer , but with pract ice a given observer can repea t readings to
0.5 db consistent ly. In addit ion , t he possibility of sa tura t ing t he r eceiver
is clea r ly avoided and ir regula r it ies in the sweep base line do not affect
the result s. The second eference l vel is easier t o set , but ca re must be
taken to avoid the sa tura t ion level.
To determine the recovery t ime of a TR tube, the following procedure
is u sed.
1. The TR cavity is placed at the opt imum distance from the t rans-
mit t er for the opera t ing frequency of the signal genera t or , which
is app oximately the same as for the t r ansmit ter frequency.
2. The TR cavity is tuned for resonance at the fre uency of the
s igna l genera tor .
3. The loca l oscill tor is tuned unt il a pip appea rs on the A scope.
The loca l oscilla tor should provide a crysta l cur ren t of approxi-
ma tely 0.5 ma.
-L. The r-f h igh power is turned on and the signal genera t or is adjusted
unt il the pip appea rs immedia t ly ahead of the t ransmit t er pulse.
5. The at t enua tor reading for a given height of low-level signal (or
the reading or which signal disappears in o noise) is determined.
6. The signal genera tor is adjusted unt il the pip appea rs a t the desired
t ime in terva l as measured from the leading edge of the t ransmit t er
pulse (or from the t ra iling edge if desired).
7. The a t t enua tor reading for which the signal is the same height as
in (5) is det ermin ed.
8. F rom readings (5) and (7), the los in signal a t the pa rt icula r t ime
in t erva l is ca lcu la t ed.
Essent ia lly this same ar rangement is used to measure the r ecovery
t ime of pre-TR tubes, with a standard TR switch and mixer following
the pre-TR tube. The usual a r rangement of pre-TR tube and TR tube
is employed, with the dist ance to the magnet ron adjusted so tha t the
mixer r eceives t he maximum amou t of low-level power from t he antenna
line.
It might be though t tha t the presence of the TR tube would com-
plica te the determinat ion of the r ecovery t ime of the pre-TR tube, but a t
t he power levels a t ~vhich systems using pre-TR tubes opera te, the recov-
ery t ime of a new TR tube is very shor t , about 3 db down at 1 psec, since
the leakage power of the prc-’fll tube produces a very weak discharge in
SEC. 9,14]
.IIEASURE.WE.%’TS ON RECOVERY T IiIfE 421
the ‘l’R tube. An a t tenua tor behind the pre-TR tube, to cut down the
power t o a level which will n ot damage crysta ls, requires a cor responding
increase in outpu t power of the pulse signal genera tor .
Consequently,
the a t tenua tor method has not been applied for measurement of the
recovery t ime of pre-TR tubes.
13andpass TR tubes are mounted in much the same way as pre-TR
tubes. .4 wavegu ide mixer , such as tha t shown in Fig. 9.44, is used with
tubes of this type. The steps just ou t lined a re followed except for
tuning f the TR tub which is, of course, unnecessary.
In another method for measur ing the recovery t ime of a TR tube,
differen t frequencies are used for signal genera tor and t ransmit ter , and
Local
oscillator
Crystal
l-f
output
/
/
FIG. 9.44. —~aveguide mixer used with bandpass TR t ubes.
an addit iona l h igh-Q TR tube is used as a filt er . This ar rangement is
somewhat simpler since it elimina tes th e loca l oscilla tor and h eter odyn e
receiver , and requir es only a video amplifier . F igure 9.45 shows the
ar r angement of the component s. The frequency of the signal genera tor
is differen t from t he t ransmit ter frequen cy.
Both TR tubes are tuned
to the signa l-genera tor frequency. The second TR tube reduces the
t ransmit ter signal to a va lue which will not cause undesirable t ransien t
effect s in the receiver . Enough of the t r nsmit ter power get s through ,
however , to furnish a reference t r ace n the oscilloscope. A modifica-
t ion of the modula tor , t o make it pu lse the t ransmit ter tube only four
t imes, for example, for every five signa l-genera to pulses, a llows every
fifth low level pulse to come through unat tenua ted. The t race on the
A-scope shows two super imposed pulses, t he unat t enua ted pulse and the
pulse affected by the r ecovery t ime of the tube. The difference in height
of the pulses is a measure of the at tenua t ion due to the recovery t ime of
422
MEASUREMENT TECH.Y IQUES [SEC. 9.14
A- scope
V!deo receiver
w
Directional coupler
Matched load
FIG. 945.-Two-fr equ ency method for measu ring r ecover y t ime.
I
Fm.
SEC. 916]
LIFE TES TS
423
t he tube. This a t tenuat ion is measured by inser t ing an a t t enuator in
the video circuit . F igure 9.46 shows a photograph of an A-scope t race
obta ined with this a r rangement .
A point of in terest is the apparent
displacement in the maximum of the low-level pulse which is a result of
the var ia t ion of the r ecovery t ime over the length of the pulse.
9.15. Measurement s of the Recovery Time of ATR Tubes.—For
pra ct ica l purposes, t he r ecover y t ime of cell-t ype tubes, such as t he 1B27,
the 721, and the 724, is measured by using the tube as a TR tube. The
effect ive recovery t ime when the tube is used as an ATR tube can then
be calcula t ed. The low-Q ATR tubes should behave in very near ly the
same manner as pre-TR tubes with the same gas filling. A check of th is
is somet imes desirable and the following method has been used. For
th is det erm inat i n , t he ar ran gem ent illust ra ted in F ig. 9.47 is em ployed.
The distance from the TR junct ion to the t ransmit ter is adjusted to
~w,,fdspyJ
~r~. 9.47.—Relat ion of components for determina t ion of t he effect of ATR tube recovery
time.
exact ly the wrong length ; tha t is, to such a length tha t the smallest
possible fract ion of low-level signal power goes in to the TR branch.
This adjustment is m de with a shor t -circuit ing blank in place of the
ATR tube, and it s purpose is t o place the ATR tube in the posit ion where
it s r ecovery t ime is most effect ive. The blank is then removed and t e
ATR tube to be test ed is inser t ed in the mount . With the except ion of
st ep (1), the procedure for measur ing the recover y t ime as out lined in
Sec. 9.14 is applied. After this measurement is completed, the ATR tube
is replaced by the blank, and the dist ance from the magnet ron to the TR
branch is adjusted for maximum signal in to the TR branch. The recovery
t i e is then measured as before. A compar ison of these two measure-
ment s then indica tes the effect of the r ecovery t ime of the ATR tube.
9.16. Life Tests.—A gr ea t many fa ct ors, which include bot h mechani-
ca l and elect r ica l effect s, determine the useful life of TR and ATR tubes.
Since a large number of thes gas switching tubes conta in wa t er vapor in
a ddit ion t o ot her ga ses, t he life ch ar act er ist ics r equ ir e ca refu l con sider a-
t ion . In developmenta l work, the only sa t isfactory way to determine
424
MEASUREMENT TECHNIQUES
[SEC. 9.16
t he life of these tubes is to set up a sufficient number of tubes to ensure
reliable stat ist ical data under condit ions approaching actual use.
This
is easily accomplished with a waveguide line having many TR cavit ies
mounted on the nar row side of the guide. Broadband TR and low-Q
ATR tubes maybe provided with special mounts on the broad side of
the waveguide. A “doorknob” t ransit ion, or other suitable device,
connects the magnet ron to the waveguide sect ion , and a high-power dis-
sipa tive loa d t ermin ates t he lin .
A similar bench can be built in coaxial lines by using T-sect ions with
coupling loops for th e individual cavit ies; t he coupling loops ar e placed
F IC. 948.-Illust r at ion of ca vit y equipped with out put gat e for cr ysta l pr ot ect ion,
a t such a point on the branch line that when the tube fires, the cavity
bra nch , wh ich is a shu nt br anch , pr esen ts an open cir cuit a t t he T-sect ion .
Th e wa vegu ide line is pr efer red beca use of it s simplicit y.
This bench provides a good oppor tunity to study cryst l prot ect ion
as a funct ion of life. The TR cavit ies or bandpass tubes are provided
with mixers of the convent iona l type whi h have shor t -circu ited i-f out -
put lines and no local-oscilla tor connect ions. To avoid possible damage
to the crystal when the r -f power is turned on, output gates (see Fig. 9.48)
in front of the mixer coupling ir is protect the crystals unt il it is cer ta in
that stable opera t ion has sta r ted. For opera t ion it is also necessary to
pr ovide a keep-a live power su ppl .
The gate is r emoved after the r -f power has been turned on and the
character of the discharge between the cones examined through a small
hole in the cavity in or der to check the opera t ion . The gate is const ructed
from thin sheets of phosphor bronze, spot -welded together at several
poin ts along the cen ter and curved outward in opposite direct ions. This
SEC. 916]
LIFE TESTS
provides good con tact when th ega te slidesin
of the cavity. The crysta ls a re checked by
425
the groove cut in the sides
measurement of the back
cur ren t at one volt and the fron t -to-back resist ance ra t o, by means of a
standard crysta l-rect ifier test set , t ype TS-268 B/U. Measurements of
such quant it ies s lea ka ge power , r ecover y t ime, Q, an d keep-a live in ter -
act ion are best obtained on the special equipment in tended for each
ind ividual character is t ic.
F igure 9.49 shows the var ia t ion, with t ime,
of r ecovery t ime and other parameters of a TR tube.
Cer ta in mechanical t est s a re closely connected w th the useful life
of TR tubes. One of the most impor tan t of these test s is that of tem-
600
0
500
n
-0
~ep -ahve vokege
al B
g:34 r
!400 ~ ;30 —
~
—
4
— — — — —
~
-0
~~
g
,~ $26 -
.@
:300 :;22 -
II
#
S ’
lax
q
=
QO
- 2500
~~18
z 200 ~ ,5
Q.
%
MC14 -
x
> ,-
%
- 1500
100
~ 10 –
6 -
Signal loss at 6 z sec
- 50
0
: -
20
40 60 ~ 100 200
400 600 1000
Time in hours
FIG. 9.49.— ypic8l va r ia t ion of tube arameters with t ime.
pera t ure changes because of the mult iplicity of meta l-to-glass sea ls
involved in the const ruct ion of the tubes and of joint s betvieen metals
with different expansion coefficient s. Individual tubes and, when
appropr ia te, tubes such as the 1B27, 721, 724 clamped in the type of
cavit ies in which they will be used, undergo a t empe ature cycle from
room temperature to 100”C, to room tempera tu re, t o - 40°C, and back
to room tempera ture. Aft er each cycle, or small number of cycles,
th e tubes are ch ecked t o determine wheth er th e ext remes of t empera ture
have caused cracks to occu r in the seals of the tubes. Measurement of
the fir ing volt age is sufficien t to indicate an increase in pressure in the
tube. Other mechanical test s, such as vibra t ion and shock test s, a re
t rea t ed in t he same manner , and increased fir ing volt age again indicates
t ube fa ilu r e.
426 MEASUREMENT T.ECHNIQUES
[SEC. 9.17
9.17. Proper t ies of the Keep-a live.-The funct ion of the keep-a live
elect rode in a TR tube is to provide a supply of ions near the discharge
gap so tha t the r -f discharge will occu r a t as low a volt age as possible.
This elect r ode is loca ted near the gap, and a d-c p ten t ia l is applied
between the elect r ode and the adjacen t par t of the tube. This potent ia l
i h igh enough to cause a d-c discharge to occur , the in it ia l break-
~-ammeter
down poten t ia l being a funct ion
of the gas filli g and the shape
of the tube. The volt age charac-
t er ist ic is specified for a given
value of cu r ren t flowing through
TR~Ube the keep-a live cir cu it in terms
+
of the volt age drop between the
a
keep-a live elect rode and the ad-
F IG. 9.50.—Cir cu it for mea su rin g k eep-a live
jacen t par t of the tube. In addi-
voltage cha racteristics.
t ion , the init ia l breakdown voltage
should have a reasonable va lue. A circu it for test ing the keep-a live volt -
age character ist ic is shown in Fig. 9.50.
When the switch is th rown , the
voltage applied to the keep-a live is a llowed to build up slowly, by mean
of a circu it wh ich h s a long t ime constant , so that the str iking
voltage and then the susta in ing voltage at a specified cu rren t may be
determined.
Since the d-c keep-a live discharge cont inues for a t ime long com-
pa red with the du ra t ion of the r -f pulse, the life of TR tubes conta in ing
H,O and H, depends on the num er of hours of opera t ion of the d-c
keep-a live This has been ver ified and, in some cases, tubes may be
li e-t est ed by oper at in g t hem wit h
a d-c keep-a live and then measur-
ing the susta ining voltage at de-
sired in terva ls. It is, of cour se,
necessary to cor rela t e th is infor - m
mat ion with the result s of actual z
opera t ion by measurements of
r ecover y t im e, lea ka ge power , a nd
inser t io loss. This d-c-keep-
/-
~za. 9.51.—Cir cu it for k eep-a live elect rode.
alive life test will not revea l such
effect s as the sput ter ing of copper from the cones on to the glass by the r -f
I
discharge, a phenomenon which may occu r at sufficien t ly high r -f power
levels. The presence f th is metallic film may increase the inser t ion loss
I
of t he t ube an d gr ea tly im pair low-level oper at in g ch ar act er ist ics.
As can be seen from a considera t ion of the keep-a live st ructure and
power -su pply cir cu it , t he essen tia ls of a r ela xat ion oscilla tor a re pr esen t,
(F ig. 9.51). These oscilla t ions may be viewed on an oscilloscope if the
SEC. $18]
DUPLEXER I,V,YERTIO ,V 1>0SS
427
keep-a live elect rode is coupled through a very small condenser direct ly
to one of the pla tes on the ca thode-ray tube.
9.18. Duplexe Insefi”on Loss.—The inser t ion loss of a duplexer is
ma de u p of t he followin g compon en ts,
1. Reflect ion loss tha t results from mismatch , This mismatch will
be formed by the combinat ion uf the TR s~vitrh , ATR switch ,
a nd magnet ron impedances.
2. The TR-switch loss. This is dissipa t ion loss unly.
3. The ATR-switch loss, which may be divided into two parts:
a . Dissipat ion loss with in the ATR cavity it self.
b. Power lost in to the magnet ron becalme the ATR switch act ion
is not complete. The ATR loss is somet imes called branching
10ss.
If duplexers employ waveguide m xers, as, for example, at the 3-cm wave-
length , the direct measurement of inser t ion loss (see Sec. 92) is quite
simple. The mixer may be replaced by a ~vell-matched detector and the
magnet ron may be replaced by a movable plunger \ vhich produces the
proper reflect ion , TMs reflect ion will vary somewhat in magnetrons of
different types, but a typica l va lue is 20 db. The input side of the
duplexer must a lso be well matched. If the TR and ATR tubes a re
tunable, they should be tuned for maximum signal into the mixer . The
shor t-circu it ing plunger is then moved to the posit ion where the TR
signal reaches a minimum value
This is the worst condit ion that will
be encoun tered in service. After reading the dete tor -cur ren t meter ,
the duplexer is removed from the matched r-f genera tor , the detector (or
mixer ) a lone subst ituted in its place, and the detector -cu r rent meter
rea again. On the assumption tha t the crysta l has a square-law
response, the power loss expressed in decibels is ten t imes the logar ithm
of th e ra t io of the crysta l currents.
If a calibr at ed a tten ua tor is in cluded
in the setup, the meter reading is brought back to its former value and
the difference n the a t tenuator readings is the inser t ion loss.
any 10-cm waveguide duplexers have coaxia l mixers which are
soldered in to the TR cavit ies.
Under these condit ions, a standard
tunable mixer is needed to make the measurement of inser t ion loss. The
crystal detector should be selected so that it is near ly matched in the
mixer , since the loss is dependent on the crysta l conductance.
The TR
and ATR tubes are tuned and the plunger adjusted as a lready descr ibed,
except tha t the r -f level should be kept at such a poin t tha t the crysta l
cu r ren t is 0.5 ma. After this has been done, the duplexer is removed
from the matched r-f source and the standard tunable mixer is connected
t the r -f source. The tandard mixer is tuned until the cr sta l is
matched and the rect ified crysta l cur rent , in milliamperes, is read. The
loss will be ~ log& where m is the crysta l law (see Sec. 9 1). The value
of m is usua lly ver y close t o two, as cr yst als a re n ea rly squ are-law devices.
It is somet imes desirable to measure the impedances of the TR tube
and ATR tube separa tely, and from these data ca lculat e the losses.
This
method gives result s which check well with those of the more direct
method, but it is used only when a carefu l analysis of a duplexer is being
made, since th measurement s a re more difficult than those in a simple
loss determinat ion . Equiva lent circuit s of duplexers and methods for
calcula t ing losses ar e discussed in Chap. 7.
9.19. Effect of Transmit ter Impedance.—In some cases t ransmit ter
tubes a re [’consist ent enough in cold impedance to enab e the duplexer
to be preplum ed; tha t is, the distance from the t ransmit ter tube to the
4
n
u
k
.s— —___ _
——
%
‘—Max. loss
=
2
~
0
-
,=
~
<
0
5
6 7
8
Plunger position in cm
FIG. 952, -Waveguide plunger wi h
FIG. 9.53. —Variat i0n in low-level
resistance st r ip to give lower alue of
signal loss through TR cavity with
stan ding-wave rat io t han plu nger alone.
posit ion of p u nger in t ran smit ter line,
TR junct ion may be so chosen tha t the largest fract ion of the received ;
signal is t ransmit ted in to the TR branch.
When TR tubes a re used,
most , but not all, of the dependence on the t ransmit ter impedance is
eliminated. However , var ia t ions in the impedance of t ransmit ter tubes
cause varia t ions in the duplexer loss (see Chap. 7). The effect of t rans-
mit t er impedance is measured by replacing the t ransmit ter tube by a
plunger and observing the change in received signal, as indica ted by the
mixer crysta l cur rent , when t he plunger is moved over a half-wavelength
range.
This provides a knowledge of the loss for all possible phases of
t ansmit t er impedance. The magnitude of this impedance maybe var ied
by means of a piece of resistance st r ip extending beyond the face of the
plunger to reduce the magnitude of the reflect ion to any desired value,
(s ee F ig. 9.52).
The result s of a ser ies of measurements which used two low-Q ATR
tubes resonant a t 9.03 cm and a bandpass TR tube opera t ing at a wave-
length of 9.1 cm are given in Fig. 9.53.
A or respon din g set of mea su re-
SEC. 9.20]
HIGH-PO WER OPERA TZON OF D UPLEXERS
429
ments over a band of wavelengths, if the dissipa t ive loss obta ined by
oth er m eth ods wer e taken into con sidera t ion , would give th e cu rve sh own
n Fig. 9.54. (See also Chap. 7.) The area between the curves represen t s
t he spr ea d of loss for all possible t ra nsm it ter impeda nces.
6 ,—
5
k
+4
.E
d
Max. loss
A in cm
FIU. !]54-Effect of t ra nsm it ter im [)cd:mce 011 Iou -1cvc-1 ~igr ,:d low u ,,cr a bimd of wave-
lengths.
9.20. H igh -power Oper at ion of Du plexer s.—L)u rin g t he h igh -pot ver
pulse of the t ransmit ter , the funct ion of the TR t be is to disconnect
the receiver from the transmission line and to allow most of the power
o reach the antenna, The h igh-power character ist ic of th tube mllst
pu lse, essen t ia lly a cont inuous t ransmission line exists between the
transmit ter and the an tenna. The TR tubes of the cell type depend
for their h igh-level act ion on the proper t ies of the gaseous r -f discharge
between the cones of the tube.
The cloud of ions and elect rons a t the
gap is equivalen t in its act ion to the inser t ion of a shor t circuit , in place
of the gap. In order to measure the standing-wave ra t io in t roduced
dur ing the h igh-po~ver pulse by the TR and ATR tubes, the t~lbes a re
replaced by others which have their cones soldered together ,
The
t ransmission line \ vhic leads to the nnterma is termina ted in a matched
load, and the standing-\ \ avc rat io is then mc[wlrcd n n lo~v-po,ver
bench.
430
MEASUREMENT TECHNIQUES
[SEC. 9.20
The ow-Q ATR, bandpass TR, and pre-TR tubes dur ing high-power
opera t ion also make use of the conduct ing character of the ionized gas
r esu lt in g fr om t he r -f disch ar ge.
This discha rge occurs a cross t he input
window of the tube and, t herefore, the tubes are mounted on the broad
side of th e waveguide; consequent ly, this effect ive conduct ing sheet pr e-
serves the cont inuity of the waveguide line th rough the duplexing sec-
t ion . This condit ion may be simula ted by taking an old tube and cover -
ing the inside surface of the window with a layer of Wood’s meta l. In
th is way the effect s due to the presence of the glass and shape of the input
window are preserved. Again, as with the cell-type tubes, all tubes in
the duplexer a re replaced by these
“fir ed” t ubes, a nd low-level st an din g-
wave measurement s are made looking through the duplexer a t a matched
load in place of the antenna line.
The use of shor t -circuited tubes does not reproduce the high-po~ver
condit ion exact ly, since the gas discharge does not have zero impedance
and some power is dissipa ted in the arc.
The exact effect of the power
loss is best measured using the individual tubes and not the duplexer
itself.
The r ecovery t ime of a duplexer can be determined by the procedure
descr ibed in Sec. 9.14. If the duplexer conta ins an ATR switch , the
recovery t ime depends upon the recovery of this switch, and also upon
t he t ra nsm it ter impeda nce.
Index
A
A-scope, 41
Admit tance t ransformat ion ra t io, 27
Alper t , D,, 60
Ambipolar diffusion , 184
Antennas, microwave, 3
Arc leakage power, 140, 171
dependence of,
upon t ransmit t ing
power , 175
with gap length , var iat ion of, 174
from lB27TR tube, 180
th rough 3-cm bandpass TR tube, 239
Arc loss, 240, 242
measurement of, 413
in 1 B3 5tube, 240
Arc power , 140
ATRcavity, loaded-Q of, 118
susceptance of, 118
ATR circu it s, fixed-tuned, branch ing
loss for , 292
mult iple, duplexers with , 308
wideband, double tun ing for , 317
ATR s itch , coaxial, 132
duplexing loss with , 279
for equivalen t circu it s, 115
1ow-Q, 127
Q~for , 128
3-cm wide-range, 132
and TR, distance between, 288
tuning of, 284
ATR tubes, available, branching loss
with , 322
fixed-t un ed, 134
irnpedanc emeasurement sof, 397
Iife of, 142
low-Q (see Low-Q ATR t bes)
recovery t ime of, measurements of, 423
(See a lso specific ATR tube)
At tenuat ion , direct -coupling, 13, 24, 55
through 721 AT cavit ies, 57
at harmon ic frequencies, 412
At tenua tor , sliding-vane, 3s3
At tenuator switch , 349
B
Bandpass charact er ist ics, 78
exper iment al, 91
Marcus’ calcu la t ion of, 84
for lB63TR tube, 112
for lo-cm tubes, 109
Bandpass TR tub s, fu tur e sta tus of, 252
h igh -level ch ar act er ist ics of, 250
9.2-cm-band, 107
3-cm, arcleakage power through , 239
leakage power envelope of, 232
tun ing procedu re for , 396
Barnes, J . L., 158
Beam width, 3
Bell Telephone Labora tor iesj 36, 130,
334, 337
Berger , R., 336
Bethe, H , A., 34, 35, 172,231
Bloom)L. R.,253
Bradbu ry, N. E., 188
Branch ing loss, 427
with available ATR tubes, 322
for fixed-tuned ATR circu it s, 292
forgenera l T-junct ion , 323
Branching-loss factor , 277
Br idge, impeda nce (see Im peda nce br idge)
thermist or , 405
Broadband T-stub, 266
Brown, S. C., 179
Burnout test s, simulated spike, 152
c
Cables, lossyj 378
Caldwell, . C., 114, 138,235
Capacit ive tUnirLg s@ 43
Cavity, coaxial, 45
coupling of, to coaxia l line, 50
equivalen t circu it for , 386, 388
ir is-coupled, coaxial du plexer with , 337
431
432
31ICROWAVE DUPLEXERS
Cavity, loade&Q of, 388
for 1B23 tulm, 41
phase of standing wave from, 387
resonant , voltage t r ansformat ion ra t io
of, 21
shunt -mounted, 120
TR (see TR cavity)
Cavity couplings, 49
Cavity losses, 16
Gavity Q, 30
~hemical reservoirs , 219
Choke coupling, flush, 333
Chokes, split , 333, 334
Cir cu it , cancella t ion, for measu ement of
spike energy, 409
equiva lent , for TR switch , 115
for cavity, 386, 388
for 1ow-Q ATR tubes, 398
jun ct ion , 262
keep-a live, 211
mu lt iple-element , 91
ph ase-con tr ol, 418
Cir cuit ca lcula t ions, equiva lent , 29
Cir cu it elements for waveguide T-junc-
t ions, 122
Clark, J , E ,, 130, 138, 346
Clark, J . W., 228, 411
Clark, M., 339
Clarke, H,, 236
Coat ings, iner t , 221
Coax al cavity, 45
Coax al junct ions, 265
Coax al T-junct ion with broadband t rans-
for mer , 268
Cobine, J . D., 147, 172, 184, 187, 198,
203, 210
Comp on, K. T., 187
Cork, B,, 59, 226
Couplings, cavit , 49
opt imum, 31
to TR cavit ies, 385
through TR cavity, formulas for )
summary of, 33
Crandell, C. F ., 130, 138, 346
Crawford, A. B., 334
Crysta l, ca libra t ion of, 38o
Crysta l burnout , 1,51
Crysta l ga te, 406
Crysta l law, 380
Crysta l per formance figur es, 152
Crysta l protect ion , ga te for , 424
(!ur t im, T. P., 260
CV221 tube, 64
D
Darrow, K. K., 14
Dear rdey, I. H,, 193, 224
Dickey, F. E ., 260
Dielect r ic constant s of glasses, 39
Direct -coupling measurements, 412
Discharge, decay of light intensity from,
196
keep-a live (see Keep-a live disch ar ge)
Dnple ers, ba lanced, 35o
branched, 329
cir cu la r-pola riza tion , 369
coaxia l, with ir is-coupled cavit ies, 337
double-t un ed, 339
for 8.5 cm, 342
elect r ica l design of, 329
high-power opera t ion of, 429
linear ba lanced, 352
loop-cou pled coa xial, 336
mechanica l design of, 333
with mult iple ATR circuit s, 308
nonlinear balanced, 355
1.25-cm , 346
using circu la r pola r iza t ion, 372
1050 Me/see, 339
pr essu rized coa xial, 335
recovery t ime of, 430
r in g-cir cu it , 357
10. 7-cm band, r ecept ion loss for , 343
10.7 cm, 342
3-cm, 343, 344
t ur nst ile, 372
frequency sensit ivity of, 375
t wo-cha nnel, 347
wa vegu idc, 341
wi eba nd, for 3-cm, 345
Duplexer cir cu it s, basic, 279
Duplexer inser t ion loss, 427
Duplexing cir cu it s, br nched, 262
Duplexing loss with ATR switch , 279
without ATR tube, 274
Duplexing switch , requ irements of, 4
E
E-plane junct io , 269
equiva lent cir cu it Of, 121
INDEX 433
I
E -pla ne mount in g, 117
Elect rode, keep-a live (see Keep-a live
electrode)
E lect ron a tt achmen t, 187
E lect ron ca pt ur e, m ech an ism of, 188
F
Fano, R. M,, 114
Farr , H. K., 138, 293
F ir in g power , m in imum , 414
Fiske, M. D., 68, 14, 169, 235, 238, 243,
253, 257, 411
Floyd, G, H,, 260
Frequencies,
harmonic, a t tenua t ion at ,
412
F requ en cy differ en ces, sm all, m ea su re-
ment of, 391
F requ en cy mar ker , 391
F requ en cy sen sit ivit y of modified magic
T, 365
of t ur nst ile duplexer , 375
G
Gap design , 235
Gap length , a rc leakage power with ,
va ria tion of, 174
effect of, on spike lea ka ge en er gy, 170
Gardner , hf. F., 158
Ga roff, K., 227
Ga s clea nup, 217
Ga s-fi lin g, effect of, u pon h igh -po~ver
character is t ics , 239
u pon spike en er gy, 167
Ga te for cr yst al pr ot ect ion , 424
Gen er al E lect ric Compa ny, 68
Gilbarg, H. G., 227
Glass windows, low-Q, leakage ener gy
cha ract er is tics of, 233
r esonant , 102
Gla sses, dielect r ic con st ant of, 39
Gu illemin , E. A., 114
Guldner , W. G., 217, 221
H
H-pla ne ju nct ion , 269
equivalent circuit of, 121
If-plane-mounted cavity, 119
Half-power points, 389
Hall, R. N., 114
Hansen , W. W., 17, 26, 34
Her lin , M. A., 179
High-power character ist ics, effect of gas-
fillin g on , 239
High-power opera t ion of duplexers, 429
High-Q TR switches, pass band of,
measurement of, 385
High-Q TR tubes, h igh-power char -
a ct er ist ics of, 227
volumes of, 218
Holstein, T., 156 162
I
Impedance, cold, of t ransmit ter , 275, 336,
428
Impedance bridge, 395
magic-T, 395
schemat ic diagram of, 404
Impedance measurements of ATR tubes,
397
Impedance t ransforma ion , 14
Induct ive tun ing screws, 43
Inser t ion loss, 29
du plexer , 427
measurement of, 382
J
J epson , R. L., 253
J unct ion circu it , 262
J unct ions, coaxial, 265
wavegu ide, 269
K
Keep-alive cha ract er ist ics, 208
Keep-alive cir cu it s, 211
prepulsed, 212
Keep-alive dischmge, 143
low-le~.cl sign al at tenu at ion ca used by,
209
st ructure of, 206
volt -ampere character ist ics of, 205
Keep-alive elect rodes, 245
coaxial, 200, 245
within cones of 11124 and 1B27 tubes,
posit ion of, 205
434
MICRO WAVE DWPLEXERS
Keep-a live elect rodes, proper t ies of, 426
side-a rm, 206, 245
Keep-a live pressure-volt age character-
ist ic of 1B24 TR tube, 209
Klyst rons, 377
Krasik, S,, 60
L
Langmuir , I., 187
Lawson, A. W., 114, 229
Lawson, J . L., 35, 226
Leakage, r -f, 335
Leakage character ist ics, effect of line
power upon, 243
Leakage energy, spike (see Spike leakage
energy)
Leakage energy character ist ics of low-Q
glass windows, 233
Leakage power , 140
arc (see Arc leakage power)
dir ect -cou pled, 13
harmonic, 59
of pre-TR tubes, 407
I,ea ka ge-power m ea surem ent s, 405
Leakage-power envelope of 3-cm band-
pass TR tube, 232
Lee, Gordon M., 154
Leiter , H, A., 114, 190, 228
LHTR, 339
Life test s, 423
Light intensity, decay of, from discharge,
196
Lighthouse tube, 77
Line power , effect of, upon leakage char -
a ct er ist ics, 243
Imaded-Q of ATR cavity, 118
I,oaded-Q of cavity, 388
Loeb, L. Il., 149, 169, 187, 188, 194
I.ongacre, A., 68
Loss conto r s, 283
Lossy cables, 378
Low-Q ATR switches, 1 7
Q~ for , 128
Low-Q ATR tubes, equiva lent circu it s for ,
398
high-power cha ra ct er ist ics of, 248
product ion test ing of, 402
reversible mount for , 402
Low-Q gla ss win dows, leakage energy
characteristics of, 233
M
McCarthy, H. J., 61, 221
McGrea , J . W., 36, 173, 227
McCreery, R. L., 56
Mch’a lly, R., J r., 148
Magic T, 350
modified, 365
frequency sensit ivity of, 365
r ing-circuit (see Ring-circuit mag c T)
using round waveguide, 369
hfagic-T impedance br idge, 395
Magic T’s, pract ica l, 361
hfagnet ron, 2
Magnet ron buildup, 154
Malter , L., 253
Mansur , I., 236
Marcus, P. M., 114
Marcus calcula t ion of bandpass cha r-
a ct er ist ics, 84
Marcuvit z, N., 34
Margenau, H., 175, 181, 182, 185, 194
Marshak, R, E,, 34, 172, 231
}Iassey, H. S. W., 187
Mat r ix calcula t ion, 85
Measurement techniques, 376
\ fechanica l t est s, 425
Lfeng, C. Y., 114, 238
Met al-t o-gla ss sca le, 255
Microwave antennas, 3
Microwave region, 1
Mount , reversible, for Iow-Q ATR tubes,
402
Mult iple-element cir cuit s, 91
Mumford, W. W., 36, 173, 227
N
Naval Resea rch Labora tory, 339
9.2-cm -ba nd ba ndpa ss TR t ube, 107
Novick, R., 341
0
1B23 tube, 36, 38
cavity for , 41
tuning curve for , 42
1B24 TR tube, 60, 62, 65, 171, 179, 201,
227
INDEX
435
1B24 TR tube, keep-al ivepressure-volt-
age cha ra cteristicof, 209.
life tes t of, 223
temper at ur e-tu ningcl,rve for, 66
tuning cu rve for , 65
1B26 TR tube, 61, 65, 201, 227
life tes t of, 223
spike-pr essu re ha ra cter isticfor , 169
tuning cu rve for , 66
11327 TR cavity, 59
1B27 TR tube, 36, 37, 39, 168, 170, 171,
227, 256
ar c leakage power fr om, 180
cur ren t vs. v lt age in discha rge of,
179
differ en tia l t un in g scr ew for , 44
lif t est of, 222
r ecover y cu rves of, 190, 191
tun ing ran ge of, 44
t un in g-t emper at ur e cu rve of, 49
1B35 ATR tube, 134, 135, 240, 244, 248,
249
ar c loss in , 240
and moun t , 138
1B36 t ube, 134, 135, 248, 249
and moun t , 137
1B37 t ube, 134, 135, 138, 248, 249
1B38 pre-TR tube, 148, 154, 164, 223,
249, 250
oscillogr am of spik e fr om , 164
r ecover y-t im e cu rve of, 224
1B38 tube with pu re a rgon , r ecovery
ch a ra ct er ist ic of, 192
1B40 tube, 36, 38
1B44 t ube, 134, 136, 248
1B50 TR tube, 61, 63, 65, 201, 227
1B52 t ube, 116, 134, 136, 248
1B53 t ube, 134, 248
1B54 pre-TR t ube, 249, 250
1B55 t ube, 108, 239, 250
1B56 t ube, 134, 248
1B57 t ube, 134, 248
1B58 bandpass TR tube, 108, 223, 250
1B63 t ube, 111, 250
bandpa ss ch a ra ct er ist ic for , 112
Opt imum cou plin g, 31
P
Pass band of broadband TR tubes, 393
Pearsa ll, C, H., 19 , 224
Phase-cont rol cir cu it , 418
Phase sh ift , impedance br idge for measur -
ing, 403
nea r r esonance, 399
Pickup probe, 378
Posey, W. T., 260
Posin, D. Q,, 236
Pound, R, V., 266, 336
Power , a r c, 140
dir ect -cou pled, 140
harmonic, 140
Power divider , 414
Pre-TR tubes, leakage power of, 407
(See cdso par t icu la r pre-TR tube)
P ressure gauge, -f, 415
Pressur ized coaxial duplexer , 335
P ressu rizin g, 334
Preston , W., 60
P robe cou plin g,
adjustable, to cozxiol
lin e, 409
P roduct ion test ing, low-level, 400
PS3S tube, 108
P seu do-fla t, 163
Pulse, rectangula r , spect ru of, 408
Pulse length , measurement of, 408
Q
Q, cavity, 30
defin it ion of, 11
input , 12
measurement of, by power drop in
load, 401
output , 12
unloaded, 12
Q~ for 1ov,-Q ATlt switch, 128
QL,, 385
experimental curve for determining
390
Qu :~r tcr -\ vz,\ c-len gt h pla te, 37o
R
Rzdar equat ion , 1
Radioact ive cobalt chlo ide, 216
Radiomt i\ -c pr imin~, 216
Ikx!cp tion los s for 1O,7-CI I1hand dup ]exer ,
343
It ecovcrv char : mtcr ist ic of 11338 tube
with pure argon, 1!)2
of Tl{ t ,,~),;, ]!}()
RecO\ -cry t ime, 141
of .\ TR tulles, measurements of, 423
436 ,IIICROII”AVE D[:PLEXERS
Rcco\ -er ~< t ime, of du plexer , .130
of TR tubes, measurements on , 417
two-frequency method for measur ing,
421-422
Recovery-t ime cu rve of 11338 pre-TR
tube, 224
Relaxat ion oscilla t ions, 201
Reservoirs, chc,r l ic:d ,219
s ilica -gel, 220
Resonance, phase shift nea r , 399
Resonan t elements, 70
equivalent circu it of, 71
with posts, 97
with t runca ted cones, 97
Resommtgap, equivalen t circu it of, 74
Resonan t glass window, 102
Resonan t t ransformers, 9
Itesonan t window, 128
It -f discharges, similar ity pr inciple for ,
181
spect rogr ams of, 148
It -f leakage, 335
It -f pressure gauge, 415
Ring, D, H.,272
Ring circu it at 3.33 cm, dimensions for ,
359
It in g.cir cu it du plexer , 357
Ring-circu it magic T, 357
coa xia l, 368
r igh t-a ngle, 367
standing-wave rat io of, 359
s
Samuel, A.l,.j 36,130, 138,173,227,292,
298, 346
Schafer j J . P., 337
Schelkunoff, S. A., 34
Scbwinger , J ., 34, 172, 231
Series molmt, 117
721 TRcar ity, conductanceof, 54
d~mensionsaf, 54
721 ATR tube, 36, 142, 227
a rgon -filled, 197
dir ect -cou plin g, 57
life test of, 222
recovery of, 1 8
tun ing-tempera tu re character ist ics of,
48
721B TR tube, 37, 39
life test of, 222
721BTR tube, tuning character ist ics of
41, 42
724.! TR tube, 36, 167
7~~~TRtu1,c,37, 39, 227
tun ing character ist ics of, 41
Shunt mount , 119
Shunt-mounted cavity, 120
Shunt resist ance, equ ivalent , 17
Signal a t tenuat ion, low-level, caused by
keep-a live disch ar ge, 209
Signal genera tor , 419
Signal sou rccs, 377
Silica -gel r eser voir s, 220
Sinclair , B. H., 227
Slater , J . C., 114
Sliding-vane at t enuator , 383
Slot ted sect ion, 378
Smullin , L. D., 57, 114, 166, 190, 209, ?28,
229, 238, 251, 347
Smythe, IV, R,, 114
Spcctograms of r -f discharge, 148
Spect rum of rectangu la r pu lse, 408
Spect rum analyzer , 380
Sper ry Gyroscope Company, 108
Spike, 153
and fla t power , separat ion of, 411
linear theory of, 156
nonlinear theory of, 162
oscillogram of, 164
Spike leakage energy, 140, 143, 235
cancella t ion cir cu it for measurement
of, 409
dir ect -cou pled, 237
effect of gap length on , 170
effect of gas-filling on, 167
effect of m on, 166
effect of repet it ion ra te on , 167
measurements of, 409
for var ious gap spacings, 236
for var ious gases, 168
Spike-pressure character ist ic for 1B26
TR tube, 169
Split chokes, 333, 334
Sput ter in g, 210
Standing wave, phase of, from cavity, 387
Standing-wave rat io of r ing-cir cu it agic
T, 359
Standing-wave-ra t io ru rvw for T-junc-
t ions, 272
Standing-wave rat io r -, 30
Stra t ton , J . A., 185
INDEX
437
Sut ton tube, soft , 36, 68
Sweep calibrato s, 419
Switch , ATR (se ATR switch)
a t tenua tor , 349
duplexing, requirmnrut s of, 4
Sylvan ia F3cr t r ic I’rod(icls ( ‘omparry,
36, 60, 65, 136, 256, 25!)
T
T-junct ion , coaxia l, ,r ith hrmdh :~nr l
t ran sformer , 268
general, branching loss for , 323
standing-wave-ra t io cllrvm for , 272
waveguide, circu it elements for , 122
T-stub, broadband, 266
Tatel, 188
Taylor , R, E ,, 339
Telecommunica tion s Reserwch f3st ablish -
ment , 364
Temperature-tuning curve for 11124 TR
tube, 66
IO-cm tubes, bandpass charact er ist ics
for , 109
Test bencb, typical, 381
Test equipment , low-level, basic, 376
Thermistor br idge, 405
Thermistor mount , 407
Ting-Sui 1{6, 166, 209
TR cavit ies, coupling to, 385
TR cavity. 39
coupling through , summary of for -
mulas for , 33
methods of coupling, to rect angular
wave guide, 51
(See also specific TR cavity)
TR switch , and ATR, dist ance between ,
288
TR tubes, bandpass (see Bandpass TR
tubes)
broadband, pass band of, 393
cell-t ype, 35
fixed-tuned, tun ing check on , 400
in tegr al-cavit y, 59
life of, 142
9.2-cm-band bandpass, 107
recovery character ist ic of, 190
recovery t ime of, measurement s on , 417
(See also specific TR tube)
Transformer , broadband, coaxial T-jun c-
t ion with , 268
Transformer , resormnt , 9
Transmission , 29
Transmit ter , cold impeclancr of, 275
Trrmsn lit t cr impcdsncr j 42s
Tuhc life, 21
Tuhcs (.wr sp cr i I ir t Ill)c)
Tlm gst rl,-wm tr r cycle, 211
Tllning, l,,r tho(ls of, 27
Tlln ing cilrvr for 11324 TR t t ll>~, 65
for 11326 TIt tuhc, 66
Tuning range of 11127 TR t llhc, 44
Timing screw, diffcrcn t i: , for 11327 TR
tuhc, 4-I
il]d uct i~,ci 43
T~millg slt lg, c:lpt cit ive, 43
T~ln illg-t rlllpcr :lt clrc ch :~mct er ist ics of
721:\ Tlt t uhr , 48
T(l,lil]g-t c,lllp cr a t(lr (! compm]s~t ioll, M
Tuning.tem era ture curve of 1B27 TR
tube, -!9
Tunnicliffc, P. R., 364
Turnst ile duplcxcr , 372
frequency sensit ivity of, 375
Tyrrell, IV, .\ ., 353
Y
Vcst igizl 120” junct ion , 273, 334
Volt -ampere ch smct er ist ics of keep-alive
disch ar ges, 205
Voltage t ransformat ion ra t io of resonant
czvity, 21
w’
Tyallm-e, H, N., 243, 411
t f-a rner , .\ . D., 114, 243, 411
Wavegu ide duplexers, 341
\ Vaveguide jun ct ions, 269
Wavegu ide T-junct ions, circu it elements
for , 122
Wavemeters, 381
West inghouse E lec ic and Manufactur -
ing Company Corpora t ion , 66, 132
West inghouse Research Laborator ies, 60
W’iesner , J . B., 60, 204
Window, glass, 1ow-Q, leakage energy
character ist ics of, 233
resonant , 128
z
Zabel, C. W., 60, 154, 164, 234