RADIATION LABORATORY SERIES
LouIs N. RIDE NOUR, Editor-in-Chief
GEORGE B, COLLINS, Deputy Ed i tor -in -Ch ief
BRITTON CHANCE , S. A. GOUDSMIT, R. G. HERB, HUBERT M. JAMES, JULIAN K. KNIPP,
JAMES L. LAWSON, LEON B. LINFORD, CAROL G. MONTGOMERY, C. NEWTON, ALBERT
M. STONE, LouIs A. TURNER, GEORGE E. VALLEY, J R. , HERBERTH. WHEATON
1.
2.
3.
‘ “ -4.
4.
--6.
7.
-8.
-“- 9.
10 .
11 .
12 .
13 .
M.
95 .
. .16,
17 .
18 .
19 .
~’ ‘ 20 .
21.
22.
--23.
- 24 .
25 .
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27 .
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RADAR BmcoNs-Roberts
MICROWAVE MAGNETRONS—CO~~in.S
MICROWAVE TRANSMISSION (hRCUITS—Ragan
MICROWAVE ANTENNA THEORY AND DESIGN—&kE~
PROPAGATION OF SHORT RADIO WAvEs—Ker’?
MICROWAVE DuPLExERs—Smullin a nd Montgomery
CRYSTAL RECTIFIERS— TOrWY and Whitmer
MICROWAVE MIxERs—Pound
COMPONENTS HktwmooK—Blackburn
VACUUM TUBE A?dPLIF IERs-Va z/ey a nd wa~~r na n
WAvEFoxkis-Chance, Hu gh es, MaciVich ol, S ayre, an d William s
ELECTRONIC TIME MEASUREMENTS—ChanCe, Huls tz er , MacN i chol ,
ELECTRONIC instrum ents-&eenwood, Holdam, and MacRae
CATHODE RAY TURE D1sPLAYs—&/~er , Sk zTC an d VaUey
MICROWAVE RECENERS— Van Voorhis
THEORY OF SERVOMEkHANIShiS-Ja ?12eS, Nichols, and Phillips
RADAR SCANNERS AND RADoMEs—Cady, Karelitz , and T urner
COMPUTING MECHANISMS AND LINKAGEs—SVobOda
lNDEx—Henney
OFF ICE OF SCIE TIF IC RE EARCH AND DEVELOPMENT
NATION .\ L DF ,F J ?NSE RESl? .UtCH CO\ T ll Wr EE
FIRST EDITION
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EDITORIAL STAFF
S. N. VAN VOORHIS
Foreword
T
HE tremendous research and developmen t effor t tha t went in to the
development of radar and related techniques dur ing World War H
r esu lted not only in hundreds of radar sets for military (and s me for
possible peacet ime) use but also in a grea t body of informat ion and new
techniques in the elect ronics and high-fr equency fields. Because th is
basic mater ia l may be of gr ea t va lu e t o scien ce and en gin eer in g, it seem ed
most impor tan t to publish it as soon as secur ity permit ted.
The Radiat ion Laboratory of MIT, whkh opera ted under the super -
vision of t he Nat ion al Defen se Resea rch Comm it tee, u nder took t he gr ea t
t ask of pr epa rin g t hese volumes.
Th e wor k descr ibed h er ein , h owever , is
the collect ive resu lt of wo k done at many laborator ies, Army, Navy,
univer sity, and industr ia l, both in thk count ry and in England, Canada,
and other Domin ion s.
The Radiat ion Labora tory, once its proposa ls were approved and
fin an ces r ovided by t he Office of Scien tific Resea rch a nd Developmen t,
chose Loui N. Ridenour as Editor -in-Chief to lead and direct the ent ir e
project . An editor ia l staff was then selected of those best qualified for
this type of task. Finally the author s for the var ious volumes or chapter s
or sect ions were chosen from among those exper t s who were in t imately
familiar with the var ious fields, and who were able and willing to writ e
the summar ies of them. This ent ir e staff agreed to remain at work at
MIT for six months or more after the work of the Radiat ion Laboratory
was complete. These volumes stand as a monument to this group.
These volumes serve as a memorial to the unnamed hundreds and
t housan ds of ot her scient ists, en gin eer s, and ot her s wh o actu ally ca rr ied
on th e r esearch , development , and engineer ing wor k the resu lts of which
are herein descr ibed. There wer e so many involved in th is work and they
wor ked so closely t oget her even th ou gh oft en in widely sepa ra ted labor a-
tor ies that it is impossible t o name or even t o know th ose who cont r ibuted
to a pa r ticu la r idea or developmen t .
On ly cer ta in on es who wr ot e r epor ts
or a rt icles h ave even been men tion ed.
But to all th ose who cont r ibuted
in any way to this grea t coopera t ive development enterpr ise, both in th is
cou nt r y and in England, these volumes ar e dedica ted.
L. A. DUBRIDQE.
Preface
T
HE receivers and circuit s t rea ted in this volume have sprung almost
en t ir ely fr om rada r t echn iques.
It is felt , however , that many of the
fea tu res a re a pplica ble in ot h r ser vices wh er e Klgh sen sit ivit y a nd excel-
len t t ra nsien t beh avior a re r equ ir ed.
An at tempt has been made to reach
a sufficien t ly fundamental standpoint in the presen ta t ion t o permit such
u se in a llied fields.
The long and unin ter rupted record of unst int ing cooperat ion on the
pa rt of ot her la bora tor ies an d organizat ion s, bot h industr i l and gover n-
ment , has cont inued throughout the preparat ion of this book. Par t icu-
la r thanks are due to the Raytheo Manufactur ing Company for the use
of illust ra t ive mater ia l for Chap. 13 and to the Hazelt ine Corpora t ion
for the use of repor t s on which some of the disc ssion of Chap. 20 is based.
Ent ire credit for what ever coh erence exist s between this book and the
ot her s of t he ser ies as well as mu ch of t he cr edit for any in tern al coh er en ce
must go t o th e Technical Coordinat ion Group.
S. N. V- VOORHIS.
PREF CE . . . . . . . . . . . . . . . . . . . . . . . . . ix
CKAP.l. INTRODUCTION ..., . . . . . . . . . . . . . . 1
l.l. Noise F are....,.. . . . . . . . . . . . . . 1
1.2. Noise Figure as a Funct ion of Receiver Type and Operat ing
Frequency . . . . . . . . . . . . . . . . . . . . . ...4
CHAP. 2. DUPLEXERS, MICROWAVE MIXERS, AND LOCAL OSCIL-
LATORS . . . . . . . . . . . . . . . . . . . . . . . ...7
Local OsciUators . . . . . . . . . . . . . . . . . . . ...21
Reflex Klystrons . . . . . . . . . . . . . . . . . . . ...21
CHAP. 3. AFC SYSTEMS AND CIRCUITS 27
3.1. In t roduct ion . . . . . . . . . 27
DXFFERENCEFREQUENCY AFC SYSTEMS 28
Systems Opsratc’ng on the Received S ignal 28
32. Cont rol Circu its for Feedback Oscilla tor s 29
3.3. Cont rol Circu its for Reflex Oscilla tors 34
3,4. Discr imina tor Circu it s . . . . . . . . . . . . 35
Systemz Operating on a Local T ransm itter. 39
3.5. General Requirements. . . . . . . 39
3.9. I-f Amplifiers and Discr iminators 48
3.10. General Proper t ies of Control Circu it s for Pul=d Systems . 50
xi
3.12. Gas-tube Cont rol Circuit s. . 56
3.13. Hard-tub Control Circuit s 64
3.14. Cont rol Circuit s for Thermally Tuned Oscilla tors 69
ABSOLUTE FREQUENCY AFC SYSTEMS. . 4
3.15.
3.16.
3.17.
“Video Discr iminator” or “Beacon” AFC ..,....,.,75
The Microwave Discr imina tor . 77
INPUT CIRCUITS ..,,..... ., . . . . . . ...79
Representa t ion of Sources of Signal and Noise. 79
Proper t ies of Amplifier Circuit s 82
Genera l Discuea ion of F eedback Effect s. 88
Miscellaneous Types of Feedback and Their Effect s on Noise 91
Select ion of Tubes . . . . . . . . . . . . . . . . . . ...97
Coupling Circuit s . . . . . . . . . . . . . . . . . . . ..101
Double-tuned Input Circuits 105
Tet rode and Pentode First Stages 114
Tr ode Circuit s ..,...... ,, ...,.,.....116
CHAP. 5. VHF AMPLIFIERS, MIXERS, AND OSCILLATORS 122
COUPLING NETWORKS . . . . . . . . . . . . . . . . . . . . . . .. 122
5.2. Four-t ermina l Coupling Networks . . . 124
AMPLIiwERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3. Stability . . . . . . . . . . .,.....,....,..126
5.7. Gain Attainable at Increasing Frequency 132
5.8. Typical Amplifier .,.... . . . . . . . . . . . . ...133.
MIXERS . . . . . . . . . . . . . . . . . . . . . . . . .138
Nonthermion ic Mixers . . . . . . . , . . . . . . . . ...148
LOCAL OSCKLLA~OES. . . . . . . . . . . . . . . 148
5.19. Colpit ts Circu it . . . . . . . . . . . . . . . . . . ...150
520. Tuned-plate Tuned-gr id Circu it 150
5.21. Actua l Oscilla tor s. .151
CHAP. 6 INTERMEDIATE-FREQUENCY AMPLIFIERS 155
61 .
6.2.
63 .
64 .
65 .
66 .
6.7.
Giin Requirements . . . . . . . . . .,..........155
Synch ronous Single-tuned Amplifier s . la ,
Stagger-Tuned Amplifier s . 162
Double-tuned Circu its . . . . ,169
CHAP.7, SECOND DETECTORS . . . . . . . ,188
Two-elect rode Detectors . . . . 188
Push-pu ll Detectors ...,.., . . . . . . . . . . ...196
Crysta l Detectors, . . . . . . . . . . . . . . . . . ...197
Video Peaking of Detector Circuit s, 201
Mult ielectrode Detector . 204
CHAP. . VIDEO AMPLIFIERS. . .213
H igh -fr equ en cy Respon se.
Bandwidth Requirements Preceding a Limiter .
Pra ct ical Cou p in g Cir cu it s
Vid eo Lim it er s ..,.. ...
Video Outpu t Circu its
D-c Restorer . . . . . . . . .
In tr odu ct ion of pecia l Sign als.
Typica l Video Amplifier s
.,. . . . 213
... 213
,.. . . 215
218
.,. 221
222
225
,.. 229
9.2. Manual Gain Control . . . . . . . . . . . . . . . . . ...238
9.3. AGC Circu it s . . . . . . . . . . . . . . . . . . . . . . . 241
9.4. Instantaneous Automatic Gain Cont rol (IAGC) Circu its . . 248
9.5. Sensit ivity-t ime-control (STC) Circuits. . . . . . . . . . 251
CHAP. 10. MECHANICAL CONSTRUCTION OF RECEIVERS. . . . . . 253
10.1.
10.2.
10.3.
10.4.
10.5.
106.
10.7.
10.8.
10.9.
Holes for Vent ila t ion and Adjustment .
Const ruct ion Mater ia ls. . . .
The I -f Amplifier . .
Typical Construct ion with Large Tubes.
Miniatu re Tubes and Components. . .
. . . . . . . . . . .
11.1. In troduct ion ..,.... . . . . . . . . . . . . . . . .. 277
11.2. R-f omponents ...,. . . . . . . . . . . . . . . . .. 278
115. Accuracy of Signal-generator Test Sets . . . . . . . . . . . . 290
11.6. Noise Genera tor . . . . . . . . . . . . . . . . . . . . ..293
11.7. Miscella eous Equipment . . . . . . . . . . 294
11.8. Coupling R-f Test Equipment to the Receiver . . . . . 296
11.9. Design Considerat ions to Facilitate Test ing and Alignment . . . 300
HAP. 12. I-F TEST EQUIPMENT. . . . . . . . . . . . . . . . .305
12,1. General Considerat ions. . . . . . . . . . . . . . 305
DEVICES FOR PHODUCING SIGNALS . . . . . . . . . . . . . 306
12.2 . Swept-frequency Signal Generators. . . . . . . . . . 306
12.3. Video and I-f P ulse Generators . . . . 311
124. Noise Generators, General Considerat ions. . 31S
12.5. Theory of Noise Genera tors Using Temperature-limited Diodes 318
126. Construct ion of Diode Noise Generators . . 321
12.7. Crysta l Noise Generators. . . . . . . . . . 323
DEVICES FOR COUPLING INTO AND OUT OF RECEIVER . . . . . . . . 324
128. Attenuators . . . . . . . . . . . . . . . . . . . . ...324
12.10 . Traveling Detectors . . . . . . . . . . . . . . . . .328
12.12. Crysta l and Diode Rect ifier s. . . . . . . . . . . 334
12.13 .Bolometers ..,.... . . . . . . . . . . . . . . . .. 334
13.1. In t roduct ion . . . . . . . . . . . . . . . . . . . . . .. 336
13,2. Mechanical Construct ion of Receiver Unit . . . . . . , . . . 336
13.3. Mixer ......,,. . . . . . . . . . . . . . . .. 337
134. I-fAmplifier , . . . . . . . . . . . . . . . . . . . . . . .340
--- --- n... -.
14.1.
142.
143.
144.
145.
14.6.
147.
14.8.
149.
14.10,
14.11,
1412.
14.13.
14.14,
14.15,
Local Oscilla tor ..,...... . . . . . . . . . . ...355
Inpu t Transformer . . . . . . . . . . . . . . . . . . ...357
I-f—AFC Chassis . . . . . . . . . . . . . . . . . . ...358
Video-amplifier Limiter . . . . . . . . . . 366
Signal Discr iminat ion Circu its. . . . . . . . . . . . . 369
The IAGC Circu its . . . . . . . . . . . . . . . . . . ...369
Detector-balance-bias (DBB) Circu it . . . . . . . 371
Fast-t ime-constant (FTC) Circu it . . . . . . 374
Sensit ivity-t ime-con trol (STC) Circuit . . 374
Power Supply . . . . . . . . . . . . . . . . . . . . ...3 8
General Requirements and Descr ipt ion of System
Radio-frequency Input and Local Oscilla tor
Receiver Inpu t Circu it . . . . .
Receiver Inpu t Stages
Second Detector and Video Amplifier in Receiver Chassis
Video Amplifiers for Oscilloscopes an Tracking Circu its
Au tomat ic Gain Con tr ol; Genera l Con sider at ion s
Descr ipt ion of the Demodula tor Circuit of the Receiver .
The Receiver Power Supply
161. General Design Considera t ions
R-F Heads . . . . . . . . . . .
16.8. I-f St r ip . . . . . . . . . . . . . . . . . . . . . . . . . 429
16.9. Video Amplifiers . . . . . . . . . . . . . . . . . . . . . .434
16,10 . Power Supply ...,... . . . . . . . . . . . . . . . . 437
172. GainRequirements . . . . . . . . . . . . . . . . . . ...441
175. The nputC ir cu it . . . . . 446
17.6. The I-f Amplifier . . . . . . . . . . . . . . . . . . . ...447
177, T del imiter . . . . . . . . . . . . . . . . 450
17.8. The Discr imina tor . ,451
179. TheVideoA mplifier . . . . . . . . . . . . . . . . . ...453
1711. Vacuum-tube Voltmeter 454
INTRODUCTION, . . . . . . . . . .455
DESIGN CONSIDERATIONS . . . . . . . . . . . . . . . . . . .461
18.6. Input Cir cu it s . . . . . . .. 468
18.7.
S ingle-S ideband Receiver. .472
18,8. Local Oscilla tor and Mixer 474
189. AFCCircuit .. . . . . . . 475
1812. Genera l Informat ion 482
Switched-LO Receiver . . . . . . ‘,..483
1814. TuningC ircu it s . . . . . . . . . . . . . . . . . 486
1815. Complete Tuning Procedure. 488
1816. I-fAmplifier . . . . . . . . . . . . .. 490
1818. Genera l Informat ion 493
 
1820. TuningC ircuit . . . . . . . . . . . . . . . . . . . . . .. 499
1823. General Informat ion 502
CHAP. 19. CRYSTAL-VIDEO RECE VERS . . . . . . 504
INTRODUCTION ...,.... . . . . . . . . . . . . . . . . ...504
CRYSTAL AND CRYSTAL HOLDER. .508
193. VideoCrysta ls . . .. . . . . . . . . . . . . . . . . . . .. 508
VI~EOAMFLIFIER . . . . . . . . . . . . . . . . . . . . . . . ...515
195. Specia l Problems of High-ga in Video Amplifiers 515
196. Circuit s Used in High-ga in Video Amplifiers. . 521
197. S mallAmplifiers . . . . . . . . . . . . . . . . . . . .. 529
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .. 545
Growth and Modes of Oscilla t ion 547
Gainintbe Logar ithmic Mode. 548
Output Character ist ics for the L gar ithmic Mode 550
Determina t ion of Maximum Usable Quench Frequency. 551
Considera t ions for Maximum Gain. 552
Sinusoidal Quench Voltages. 553
Receivers ., . .’.,..... . . . . . . . . . ...558
Output Character ist ics or the Linear Mode. 5 2
Automat ic Gain Stabiliza t ion (AGS) Circuit s 565
Single-cycle Superregenerat ive Receivers 567
Actua l Receivers ..,...... , . . . . . . . . . ...570
21.2. General Requirements and Limita t ions 581
 
214. The Limit ing Receiver 596
21.5. The IAC.CI{cceiver 601
216. (’o]npar ison of Rweivcr Types. 604
217. Best Receiver Type for l’arious .Applicat]o]ls
606
21.8, Coheren t Oscilla tor Circu it s and Considcrat ions 606
INDEX . . . . . . . . . . . . .. 613
BY S. N. VAN VOORHIS
The receivers used with radar systems, par t icu lar ly those opera t ing
in t he micr owa ve r egion , a re usu ally ch ar act er ized by two specia l pr oper -
t ies. In the fir st place it is impor tan t to be able to dea l with the eakest
possible signal, which may be comparable to or even weaker than the
noise in the system. The level of a tmospher ic noise a t these frequencies
is very low, so that it becomes necessary to do everyth ing possible to
reduce the in terna l noise in the receiver and to minimize losses in the
input circu it s. Considerable ga in is then requ ired to br ing th is noise
level and signals tha t a re comparable to it up to a usable level. In the
second place the signals with which the receiver must dea l a r e pulses
cover ing an ext r emely wide dynamic range.
Accord ingly, wide-band
cir cu it s a re r equ ired, an d ext ra or din ar ily sever e r equ ir em en ts a re pla ced
on t he t ransien t beh avior of th e wh ole receiving system.
Almost every common typ of receiver has found applicat ion a t some
poin t . These include
2. The super r egener a t ive.
3. The tuned radio frequency (t r f).
4. Th e crysta l video.
In many cases the choice among types depends on the rela t ive per form-
an ce in picking up a signal tha t is comparable in evel t o noise.
It is well,
t herefore, t o begin with a br ief review of the ult imate limita t ions on
receivers imposed by fluctuat ion noise and of the methods of measur ing
t he per forma nce of a ct ua l r eceiver s in t erms of su ch u lt im at e limit s.
1.1. Noise Figure.—To b usefu l, any receiver must be connect ed to
a source of signals such as an antenna.
If this an tenna could be placed
in side a la rge a bsor pt ive en closu re or bla ck body at a u niform t emper at ur e
2’, it would be in equilibr ium with the thermal or black-body radiat ion at
th is t empera u re. At the terminals of th antenna t here would appear a
voltage equ iva len t t o the J ohnson noise genera t ed in a resist ance equa l
to the radia t ion resistance of the antenna at a t empera tu e T . There-
fore, even if a receiver could be produced that had no in ternal sources of
noise whatever , noise would st ill be in t roduced i to the system from the
1
2
INTRODUCTION
[SEC.1.1
antenna , and weak signal would have to compete with this noise. If
the re eiver does in t roduce addit ional noise, the signal must be cor -
respondingly st ronger . These concepts may be made quant ita t ive by
th e use of noise jigur e or noise factor. 1
This may be defined with the aid
of Fig. la as follo s:
s
~ = lcTB
5’” ‘
(1)
where F = noise figu r e of n etwor k,
S = available signal power from signal source,
S, = available signal power from network,
NO = available noise power from network,
k = Boltzmann’s constan t ,
T = a bsolu te t emper at ur e of sign al sou rce,
B = n oise ba ndwidth of n etwor k.
The available power represent s the maximum po er that may be drawn
from a network with a proper ly chosen load impedance. It is obta ined
when the load impedance is the complex conj ga te o the in ternal imped-
ance of t he n et wor k.
It will r eceive a more deta iled t reatment in C ap.
4. It will a lso be shown there that the quant ity k TB r epr esen ts t he
available noise power from a resistor of arbit ra ry value at a tempera tu re
T and tha t th is is merely a resta temen t of the usual expression for J ohn-
son noise.
The qualita t ive meaning of Eq. (1) is now clear . A signal, no mat t er
how it ar ises, has associated with it a t least a minimum amount of noise,
k TB. If it passes through a network that either amplifies or a t tenuates
both noise and signal witho t adding addit ional noise, the ra t io of signal
power to noise power at the output will be the same as at the input and
t he n oise figu re F will be u nit y.
If, h owever , t he n etwor k a dds a ddit ion al
noise, F will be grea t er than unity.
Equat ion (1) may be rewr it ten as
(2)
where W = available power gain of n etwor k.
A situat ion t at occur s sufficien t ly often to mer it explicit t reatment
is the case of two networks in cascade shown in Fig. 1. lb. The noise
figu r e of t h e combina tion F,z may be shown to be
(3)
1l). O. Nor t h, RCA Rev., 6, 332, January 1942; H. ‘~ . Fr iis ,Proc. IRE, 32, 419,
Ju ly 1944.
where F1 = noise figure of Network 1,
Fz = noise figure of Network 2, under the condit ion that it is fed
from a sour ce whose impedance is equal t o the ou tpu t imped-
ance of Network 1,
w 1 = available power gain of Network 1.
Note the dependence, which is implicit ly admit ted here, of the noise
figure on the internal impedance of the source. It is a lso assumed tha t
,
FIG.1.1.—(a) Setu pfor definitionof noisefigure;(b) noisefigur eof network sn awude.
By defining a new quant ity T , fr om t he r ela tion
No = IcT,B,
(5)
where
t~ = ;.
T , may be called the ‘‘ equ ivalen t noise tempera tu re” of the network in
the sense that the available noise power from the network is equal to
the available noise power from a resistor a t a tempera tu re T1. With
this change Eq. (3) ma be wr it t en as
((3)
where t~now refers to Network 1. This is the form generally used in the
discussion of cr yst al units for m ixer s (see Ch ap. 2).
Another situation of pract ica l in terest may be studied in terms of
Iihg. l.lb as follows. Suppose that Network 1 consists of an amplifier of
an arbit ra ry number of stages and rela t ively good noise figure while
Networ k 2 represen t s some unit of much poor er noise figure. It is desired
 
INTRODUCTION [SEC.12
in order that the ov r-a ll noise figure be within some specified mult iple
of F’l. Since noise figures are power ra t ios, they are often expressed in
decibels by the ordinary ru les.
The preceding requ irement might then
be sta ted that F,, be not more than zdbabove 1. Equat ion (3) may
be solved for the gain under th is condit ion as follows:
Fz–l 1
(7)
To illust rate the use of th is rela t ion , suppose that a superheterodyne
receiver is to be esigned at a frequency such as 200 Me/see where r -f
amplificat ion is feasible. Suppose that the noise figure of a pract ical r -f
amplifier is 7 db and of the mixer is 15 db and that it is desired to have the
over -a ll noise figure not more than + db worse than that of the r-f ampli-
fier . The gain required is
WI>31.6–1 1
5.01 IoJ f” – 1
From this the number of stages requ ired can be immediately determined.
The noise figure of a receiver may be rela ted to other methods of
specifying sensit ivity by not ing that for room temperatu re (1’ = 300”K)
and a bandwidth of 2.5 Me/see, k TB has a value of 10–14wat t . Suppose
that a receiver of th is bandwidth has a noise figure of 10 db and an inpu t
impedance of 50 ohms. Then a signal voltage of 2.23 pv developed across
the inpu t will produce an outpu t power just equal t o the noise power at
t he ou tpu t.
St rict ly speakin g, t his calcu la tion is n ot qu it e cor rect , sin ce it a ssumes
that the receiver is matched to the signal source. It will be shown later
in Chap. 4 that the best noise figure is usually obta ine with some degree
of mismatch between the receiver and antenna.
T e full expression is
where VR = signal volt age developed across input t o pr odu ce power ou t-
put equal to noise power ou tpu t ,
R. = in pu t impeda nce of r eceiver ,
Rs = in ter na l impedance of sou rce,
F, = noise figu re of r eceiver wit h sou rce of in ter na l impedance R,.
1.2. Noise Figure as a Funct ion of Receiver Type and Operat ing
F requ en cy.—A pr ocedu re has been in dicated in t he precedin g sect ion for
making the noise figure of a superh eterodyn e receiver come within some
specified increment of the noise figure of the r-f amplifier a lone.
For
 
BANDWIDTH REQUIREMEN TS 5
second, it is profitable from the point of view of noise figure to use r -f
amplifiers in this way up to about 1000 Me/see. Above this poin t the
noise figure of the amplifier is no longer bet t er than tha t of the mixer .
The range of frequency from about 150 to 1000 Me/see may be taken to
r epr esen t t he r egion in which va cuum-t ube amplifiers, while st ill u seful,
present specia l problems di fer ing from those met a t low frequencies.
It a lso c ver s the t ransit ion from lumped to dist r ibuted circuit param-
eter s, Some of the special problems met in const ruct ing the high-
fr equ en cy por tion s of su ch r eceiver s will be discu ssed in Ch ap. 5.
Instead f the mixer and i-f amplifier of a superheterodyne circuit , a
detector and video ampl fier might follow the r-f amplifier , making a
t r f receiver . Somewhat similar arguments ma-y be used here t o deter -
mine the amount of r -f gain required to make the noise figure approach
that of t he r -f amplifier a lone.
It must be noted, however , tha t a noise
figure cannot be defined as before for a nonlinear device such as the
detector . Instead, a signal level S1 is found such that the output signal
power is just equal to the output noise power . The quant ity S J k TB
may t en be used instead of the noise figure in the calcula t ion of neces-
sary r -f ga in. It is found that SI lies in the neighborhood of 10–8 wat t
or higher for any of the u eful detector , and therefore considerably
more r-f gain is needed in a t r f receiver .
For the range 150 to 1000
Me/see, the same r-f amplifiers discussed in Chap 5 may be used ahead
of a detector . At frequencies higher than this the complexity and
poor per formance of r -f amplifiers make t r f receiver design in genera l
impractical.
There a re cases in which the rela t ively low sensit ivity of t he det ect or -
video-amplifier combinat ion is acceptable. In such cases the detector
used is almost a lways a silicon crysta l.
This has caused this type of
receiver to be named “ crysta l video” which is the term by which it will
be refer red to in this book. These receivers have been used up to fre-
quencies as high as 10,000 LIc/sec and may find some applica t ions a t
st ill higher frequencies. Some of their fea tures a re covered in Chap. 19.
The superrcgener at ive r eceiver occupies a place midway bet ween t he
cr yst al video a nd t he su per het er odyn e as fa r as sen sit ivit yy is con cer ned.
By the use of velocity-modula t ion tubes, superregenera t ive receivers
have been built for frequencies as high as 10,000 Me/see. Such receivers
can be made to be small and to have low power drain, but they are limited
in the fidelity of reproduct ion tha t they can give.
Ch apt er 20 con ta in s
a discu ssion of su per regen er at ive r eceiver s f or t his fr equ en cy r an ge.
1.3. Bandwidt h Requirements.—The fact that t he signals wit h which
radar receiver s must dea l are pulses tha t m st be reproduced reasonably
well set s a 1o~~er lim it t o t he ba ndwidt h of t he cir cu it s—r -f, i-f, a nd video.
 
6
INTRODUCTION
[SEC.1.3
at l a st 1 Me/see. Amplifiers with bandwidths of this magnitude
usually employ high-t ransconductance pentodes such as t e 6AC7.
The coupling-circu it impedance is low compared with th e in terna l impe -
ance of the tube, and the u lt imate limit on the product of ga in and band-
width set by the quot ien t of t ransconductance and shunt capacitance is
a ser iou s rest rict ion requir in g con st an t a tten tion .
The problems in the
design of i-f amplifiers a re discussed more fu lly in Chap. 6, and those
peculia r to rada r video amplifiers a re t rea ted in Chap. S. Chapter 18
conta ins a t rea tmen t of some of the methods for obta in ing unusually wide
 
DUPLEXERS, MICROWAVE MIXERS, AND LOCAL OSCILLATORS
The microwave su perh et erodyne receiver s under considerat ion h er e
differ from those used in lower-frequency applica t ions in two respects:
(1) the mixer is almost invar iably a cryst a l instead of a vacuum tube,
and (2) no r -f amplificat ion is used ahead of t he mixer .
In r ada r r eceiver s
an addit iona l factor en t er s because of the necessit y for prot ect ing the
receiver from the h igh -power t ransmit t er .
The por t ion of the radar
system that connect s t ransmit ter and receiver to a common antenna and
known as the duplexer. In many cases much of the r -f circu it of the
m ixer is in ext rica bly m ingled wit h
the duplexer so tha t some discus-
-+
/
%
The switch ing opera t ion from
Trab
mitter
complet ed in a mat t er of micro-
seconds a t most . This require-
ment suggest s the use of some
form of ga seou s-disch ar ge device.
F igu r e 2.1 illu st ra tes t h e pr in ciple
of oper at ion of most of t he syst ems
FIG. 2.1.—Duplexing system—two-wire
in common use. It uses two spark
transmissionine.
gaps or switches, one known as the transmit-receive (TR) tube or switch
which effect ively discon nects th e r eceiver dur ing t ransmission , and th e
other known as t e antitransmit-receive (ATR) tube or switch which discon-
n ect s t he t ra nsm it ter du rin g r ecept ion .
The high-power puls from he
t ransmit t er breaks down the ATR gap, and the power flows out toward the
antenna.
The TR gap in the receiving branch likewise breaks down and
(if it is designed so tha t negligible power is required to maintain the dis-
ch ar ge) pu ts a sh or t circu it acr oss t he line t o t he r eceiver , t her eby pr ot ect -
ing t he delica te input circu it s of t he receiver .
Since th e sh or t circu it is a
qu ar ter wa velen gt h fr om t he T-ju nct ion , t he im peda nce in pa rallel wit h t he
1An extensive t rea tment of duplexers is given in Vol. 14, Radia t ion Labora tory
Scrie8.
7
8 DUPLEXERS , MICROWAVE MIXERS , LOCAL OS CILLATORS [SEC.21
antenna l ne at the junct ion is very high and does not affect the power
t raveling toward the antenna.
At the end of the transmit ted pulse the
discharge across the gaps goes ou t and the system is ready to receive echo
signals. The impedance at th e T-ju nct ion looking toward th e t ransmit ter
is infin ite because there is an open circuit half a wavelength away. Look-
ing toward the receiver there is a matched line, so all the power goes in to
the receiver .
Th e requ irements for sa t isfactory transmission of th e ou tgoin g pulse
are ra ther easily met , but the requirements for recept ion are much more
stringent.
1. Dur ing the t ransmit ted pulse, the power get t ing past the TR tube
in to the receiver must be less than 0.1 wat t to avoid damage or
bur nout of th e crysta l.
2. The TR tube must fire in less than 0.01 psec, or a preignit ion
“spike” (see S c. 3.7) of t ransmit ter power will be let th rough and
may burn ou t the crystal.
3. The gap must deion ize in a few microseconds after the end of the
transmit ted pulse so that echoes from near-by objects will not be
unduly at tenuated. A typica l specificat ion might call for an
at tenuat ion of less than 3 db by a t ime 6 psec after the end of the
t ra nsm it ted pu lse.
4. The received signal must see a reasonably good match into the
r eceiver , and the losses must be kept t o a minimum.
Some r efinements in th e rudimen tary system of Fig. 2.1 ar e n ece sar y
to meet the above requirements. Since the fir ed TR-tube gap is not a
per fect shor t circu it , there will be some voltage V developed across it .
If Z is the impedance looking toward the receiver measured at the gap
terminals, the leakage power going to the receiver will be V’/Z. The
voltage may be reduced by having the discharge take place in a gas a t a
low pressure (of the order of a few millimeters Hg), but a still grea ter
r edu ct ion of lea ka ge power is n ecessa ry.
This reduct ion may be accom-
plished by a stepup transformer to the gap and an ident ical stepdown
transformer to the receiver line. In the unfired condit ion the standard
line impedance is maintained on either side of the TR tube, but in the
fir ed condit ion the line impedance Z seen at the gap is much higher and
less power goes to the r eceiver .
The pract ica l method of accomplish ing this is by a resonant cavity.
Figure 2.2 shows a sect ion th rough a 1B27 TR tube and associated cavity,
with input and outpu t couplings. This assembly is designed for opera-
t ion near 3000 Me/see. The gap across which the discharge takes place
is formed by two reen t ran t cones on the axis of symmetry of the approxi-
 
9
in and out on a flexible diaphragm.
The unloaded Q of the cavityl is
about 2000, and with normal input and output loading the loaded Q is
about 350. The ra t io of power lost in the cavity to input power is near ly
equal to the ra t io of loaded Q to unloaded Q. Thus in the present case
17.5 per cent of the input power is lost ; the TR tube may be said to have
a gain of –0.85 db.
Both input and output coaxia l lines end in coupling loops, which play
the role of the stepup and stepdown transformers. They may be thought
FromT.junctmn
Flexible
\n
d!aphragm
~ \ RetainingingI
FIG.2.2.—1B27TR tube an d cavity assembly,loop coupling.
of as single-turn windings which , in propor tion t o t heir area , loop more or
less of t he magnet ic field in t he cavity.
The smaller the loop the higher
the stepup ra t io and the higher the loaded Q. In a grea t many cases
the output loop is a par t of the mixer assembly. Figure 25Z) shows such
an a ssembly complet e wit h cou plin loop.
It will be noted tha t the leakage power through the TR tube is more or
less inversely propor t ional to the square of the loaded Q and the loss dur-
ing recept ion is direct ly propor t ional to the loaded Q. Therefore a com-
promise value must be reached, such as the value 350 ment ioned above.
This va lue corresponds to a bandwidth between 3-db points of about
10 Me/see. Accordingly, it will be necessary t o provide a tuning adjust -
ment for the cavity. By proper design , this same tuning adjustment
1See Vol, 11, Chap. 5, Radia t ion Labora tory Ssr ies , for a discussionof the (J of
cavity resona tors.
10 DUPLEXERS , MICROWAVE MIXERS , LOCAL OS CILLATORS [SEC.2.1
may be made to take care of var ia t ion in mixer impedance resu lt ing from
change of crysta ls. If the r -f impedance of the mixer is measured at the
,
u
FIG.2.3.—Cutawayview of 1B24TR tube.
If u ncor rec~ed, th is would r esu lt
in a change in the impedance pre-
sen ted at the TR cavity that would
change the loaded Q as well as
in t roduce undes ir ed reflect ions and
power loss. By placing the crysta l
an odd number of eighth wave-
lengths from the cavity, these
r esist an ce va ria tion s ma y be made
t o appear as reactance var ia t ions
at the cavity and may be tuned
ou t in t he a dju stmen t of t he ca vit y.
To ensure rapid breakdown of
the TR tube at the beginning of
each transmit ted pu lse, a supply
of ions is mainta ined in the gap by
a cont inuous auxiliary discharge
inside one of the cones. This dis-
ch ar ge r equ ir es a n ext ra elect rode,
k nown a s t he k eep-a live elect rode,
which draws about 150 pa from an
800-volt supply. A ballast resis-
tor drops the voltage to about 400
volts a t the tube itself. Even with
thk+ ar rangement there is a con-
sider able spike on t he sign al t r an s-
mit ted by the TR tube, and this
spike plays an impor tan t role in
the act ion of AFC systems (see
Sec. 37.) The keep-alive cur ren t
must be maintained within the
range of about 100 to 200ga. Too
high a cur ren t will in t roduce ex-
cessive loss dur ing r ecept ion and will cause cleanup of the gas in the tube
as well. Too low a valu e of cu rr en t will cau se fa ilure t o pr ot ect t he crysta l.
F igure 2.3 shows a cu taway view of another type of TR tube, the
IB24, which is designed for frequencies in the region of 10,000 Me/see.
In it the whole cavity is a region of reduced pressure, with a gas reservoir
on one side to increase the tota l volume of gas and so preven t too rapid
 
The loaded and unloaded Q and the t rans-
mission loss are much the same for the 1B24 as for the 1B27. The band-
width is somewhat grea ter , since the opera t ing frequent y is h igher , but
a tuning adjustment for the cavity on the 1B24 must st ill be rega rded as
an opera t ing cont rol. As before, the TR tuning may be used to com-
pen sa te for va riat ion in m ixer impedan ce.
2,2. Noise Considera t ions. —For considerat ion of the influence of
mixer and duplexer per formance on the over -all noise figure of the
r eceiver F , the most s itable expression is t he following: 1
~=(L+&O+F’2–1)
W.wd ‘
(1)
where t.= ra t io of effect ive poise temper atur e of crysta l, when supplied
with noiseless LO power , t o r oom temper atur e,
tLO= ra t io of increase of eff ct ive tempera ture of crystal, when
supplied with actual LO power , to room tempera tu re,
F t = noise figure of i-f amplifier ,
W. = conver sion gain of mixer (usually less than unity),
W ~ = gain of duplexer assembly (also less than unity).
Both F’s and W‘s are expressed as numbers, not in decibels.
expression as umes that the bandwidth of the i-f amplifier is less
This
than
that of the r -f circu it s and of the cir cu it coupling the mixer to the i-f
amplifier . Of these quant it ies, t , and W, are determ ned largely by the
crysta l. Ordinar ily, each type of crystal has minimum values specified
for t h ese pa ramet er s.
2.3. Crystals.-The most sensit ive mixer for microwaves is th e crysta l
type in which a con tact on a semiconductor resu lts in rect ifica t ion of
radio frequency. T e semiconductor may be one of many differen t
ma er ials s ch as silicon or germanium, with very small quant it ies of
added impur it ies. The most common mater ia l is silicon. For mechani-
cal pr ot ect ion t he sem icon du ct or an d met allic ‘‘ catwh isker ” a re mou nt ed
in a car tr idge un it , wh ich is a lmost a lw:ays m ade n on adju stable.
A cross sect ion of a car t r idge is shown in Fig. 2.4a. The silicon A
is soldered to the screw D. A tungsten whisker shown at B is poin t ed
and embedded in the meta l a t C. The whole assembly is held together
by the brass endpieces E and F and the ceramic shell G. The pressure on
the contact is main tained by the spr inglike bend in the h isker and is
adjusted in manufacture by the adjust ing screw D.
The space H is
filled with a powder or wax to hold the pieces in place.
Another type of car t r idge developed more recent ly is shown in Fig.
2.4b. In th is car t r idge the silicon C is soldered to the pla te A, which is a
1Th is will be r ecogn ized a s a r est at emen t of Eq. (1.3) wit h m inor ch anges in
notation.
12 D UPLEXERS , MICRO WAVE MIXERS , LOCAL OS CILLATORS [SEC.24
for ce fit in the tube B. Th e wh isker D is welded to the conductor E,
which in tu rn is held in place by the ceramic washer F. The en la rged
sect ion G on the conductor is an r -f t r ansformer for match ing purposes.
This unit is adjusted dur ing manufactu e by carefu lly forcing in pla te A
u ntil t he ca rt ridge h as t he cor rect ch ar act er ist ics.
(a)
(b)
FIG.24.-Crosssection of (a) crystalcar tr idgeand (b) coaxialcrystalcar tr idge.
2.4. Microwave Crystal Mixers.—To make up a complete mixer , a
mechanica l ar rangement is requ ired tha t will provide r -f circu its, i-f
termina s, andsuitable means forplugging in the crysta l car t r idge. Two
such mixers for use at 2500 to 3500 Me/ see are shown in Fig. 25a and
b. The one shown in Fig. 2.5a is a broad-band mixer with no tuning
and is mean t to be used without a duplexer .
The mixer crysta l is shown
at B. It is inser ted by breaking the t ransmission line at F. Th e sign al
inpu t is at A, thence th rough the broad-band stub suppor t l C to the
crysta l. The LO power is in t roduced at H wit h a t ermin at ion con sist in g
of a resistor disk indica ted at J to the probe L. Th e couplin g of th e local
oscilla tor may be ar ied by the knob K, which var ies the depth of pene-
t ra t ion of the probe in to the main coaxia l line. The distance from the
sleeve M to the knob K shou ld be about one quar ter wavelength . The
i-f signal appears at the fit t ing G. The quar ter -wave cup or choke D
1See Vol. 9, Chap. 4, Radia t ion Labora tory Ser ies for add it iona l mater ia l on
broad-band stubs.
13
effect ively preven ts the signal and LO power from get t ing in to the i-f
amplifier.
The stub C is needed in the mixer to furnish a retu rn to ground for the
@
(
)
VWza
(b)
(a)
(c)
RG. 2.5.—(Q)Cross sect ion of broad-band3000-Mc/sec mixer; (b) cross sect ion of
3000-Mc/sec cryst almixer;(c) photographof 3000-Mc/see crysta lmixer .
the terminat ion in the LO line e fect ive, the ele t r ica l distance from the
end of the probe to the terminat ing resistor should be some mult iple of a
half wavelength.
In Fig. 2.5b and c is another form of mixer for the same frequency
as F ig. 2.5a bu t designed to work ou t of a tuned cavity.
In th is case the
 
14 D UPLEXERS , MICRO WAVE MIXERS , LOCAL OS C’ILLA TO.tS ’ [SEC.2.4
E, and t hen ce is applied t o th e crysta l.
The loop also furn ishes t he r et urn
path for in t ermedia te frequency and direct cur ren t . The LO inject ion is
the same as above.
The r-f impedance of a 1N21 crysta l is such tha t it is a match for the
signa l if the input line has an impedance of about 50 ohms and if the
d-c crysta l cu r ren t due to loca l oscilla tor is about 0.5 ma. The i-f imped-
ance seen on looking in a t G will be about 300 ohms but will va ry with the
(b)
10,000Me/see mixer.
photogra phof typical
impedance tha t the crysta l sees on looking ou t in to the r -f line. This
resu lt is to be expect ed if the mixer is though t of as a lossy t ransformer ,
At h igher fr equencies it becomes more conven ien t t o use waveguide
instead of coaxia l t ransmission lines, and as a consequen e the mixer
ch an ges it s form.
A cross-sect iona l view of a ty ica l mixer for use in the icin ity of
10,000 Me/see is shown in Fig. 2.6a. A photograph of a similar mixer is
 
15
field. The signa l comes in through the waveguide, and the LO power is
in jected in the side of the guide with a probe A, the probe in this case being
the outpu t probe of the LO tube.
The amount of LO power in jected is
va r ied by changing the depth of penet ra t ion of the probe. The signa l is
preven ted, by th e chokes B and E, from going ou t the LO line and the
i-f line respect ively. The i-f signal appears a t G. The posit ion of the end
plunger H is chosen to make the crysta l look like a match for the signa l. 1
Another type of mixer using the coaxia l crysta l ca r t r idge is shown in
Fig. 2.7. The direct ion of t ravel of the signa l in he waveguide D is
perpendicu la r to the page. The signa l is picke up on the crossba r C
and fed to th crysta l shown at .4.
No r-f signal appears a t the ends of
the crossba r so tha t no chokes a re necessary in the i-f line B. A mixer
FIG.2.7.—Crosssectionof mixeru singcoaxialcrysta lca r t r idge.
of this type can be designed to opera te at a ll frequencies a t which wave-
guides a re used. As in the mixer shown in Fig. 2.6, he loca l oscilla tor is
in jected in to the wave guide a long with the signal by either a probe or
window coupling.
In all the above mixers any modu at ion sidebands of the loca l oscil-
la tor tha t a re spaced away from the LO frequency by an amount equa l to
the in termedia te frequency will be detected by the mixer as signals and
will com e t hr ou gh t he r eceiver as su ch .
On e of t hese t ypes of modu la tion
of the loca l oscilla tor is noise coming from shot effect and simila r phe-
nomena in the oscilla tor tube. This modula t ion is equiva len t to ampli-
tude modula t ion of the loca l oscilla tor . The noise sidebands so produced
fa ll off in in tensity as the frequency depar ts from the proper LO outpu t
frequency, a t a ra te tha t is determined by the Q of the oscilla tor circu it s.
Therefore, con tr ibu t ions from th is sou rce of noise will be less for a rela .
t ively h igh -Q oscilla tor , such as the type 417, and will a lso be less for a
h igher in t ermedia t e fr equency.
This is the or igin of the term ~LOn Eq.
1Thereis an extensivediscussionof the design of such mixersin Vol. 16, Radiat ion
Laborat orySeries. Somewhat’morecomplicated designs are shown there which give
more un iform and reliableperforman ce.
 
16 DUPL-EXERS , MICROWAVE MIXERS , LOCAL OS CILLATORS [SEC.24
(1). Also if the loca l oscilla tor is not well enough shielded, it is possible
tha t it may be modula ted by i-f signals leakin out of the i-f amplifier
and may thus ca use instability in t he r eceiver or even over-a ll oscilla t ion
One method of preve t ing modula t ion of the loca l oscilla tor from
disturbing the receiver is t o use a balanced mixer . A form of balanced
mixer using a magic T is shown schemat ica lly in Fig. 2.8. The magic T
is descr ibed els ewher e, I a nd it s oper a tion expla in ed.
It will suffice t o say
tha t r -f power fed in Branch 1 (Fig. 2.8a) will go in to Branches 3 and 4,
Signal m
balan cedmixerusinga ma gicT.
and will a r r ive a t the mixer crysta ls A.4, which a re spac d equidistan t
from the junct ion , with 180° phase difference. Also, r -f power fed in
Branch 2 will go in to Branches 3 and 4 and will a r r ive a t the crysta ls with
no phase difference. Thus in the two crysta ls the LO power with it s
sidebands is applied with the same phase, and the signal is applied
out of phase. The i-f signals will thus appear out of phase in the two
crysta ls. If the two i-f output terminals of the mixer go to a push-pull
input circu it in t he i-f amplifier , t he modula t ion of t he loca l oscilla t r will
be canceled and the t rue signals will be reta ined. The use of a ba lanced
mixer , by largely eliminat ing the LO noise, will improve the over-a ll
sensit ivity of a typica l r eceiverz by about 2 db a t 10,000 Me/see or about
5 db at 25,000 Me/see.
1See Vol. 9, Radiat ion LaboratorySeries,
2The receiver is as sumedto have an in termed ia tefrequency of 30 or 60 Me/see,
a nd a bandwidt h of 2 t a 8 Me/s ee and t o u se a loca l oscilla t or su ch w th e 723A/B Or
 
MICROWAVE CRYSTAL MIXERS 17
In the receiver that employs double-mixer AFC (see Sec. 3.8) the
mixer takes st ill another form. Inthis case it isnecessary to have two
mixer s, on e for t he r egu la r ch an nel wit h sign al in pu t t hr ou gh t he du plexer
and anoth er wit h signal input th rou gh an at ten uator for t he AFC channel.
Both of these mixers must get their LO power from the same source.
The top schemat ic view of such a double mixer is shown in Fig. 2.9. It
is composed of t hr ee sect ion s of waveguide fasten ed t oget her a long t heir
nar row sides. The LO probe project s in to the waveguide at E. This
sect ion of guide is terminated in one direct ion by the resist ive mater ia l
F placed a quar ter wavelength from the end of the gu ide. In the other
direct ion this sect ion of guide feeds two
Signal in
- H“
mixer shown at A is the same as that of
G
by having a cu toff waveguide at tenuator
G connect ing it t o it s source of signals.
‘@Q
_@
@
In use, the two resonan t windows are
8H -o
..——
-—- --
--- --
qu en cy t o in cr ea se t he cr oss-a tt en ua tion
FIG. 29.-Schemat ic diagram
a nd t her efor e t he isolat ion between t he OrtOPt d d ou blem ixerfor r eceiver s
two mixers .
havingAFC.
Another way of applying LO power to the two mixers and st ill get t ing
isolat ion between the two mixers is to use a magic T. This method is
used when both the regu lar and AFC mixers are of the balanced type,
as is the case in Fig. 2.8b.
The sensit ivity of a crystal mixer is dependen t upon severa l factors.
(1) It shou ld absorb all the signal power inciden t upon it , because any
power reflected is lost . (2) The impedance for the image frequency is
“influent ial in affect ing the gain of the crysta l for the following reason.
When the signal and LO frequencies are applied to the crysta l, the sum
a d difference frequencies ppear in t e mixing. Fur ther mixing of he
i-f and LO signals will give r ise to a voltage at the image frequency.
If th is image freq ency is retu rned to the mixer in the cor r ect phase, it
will, upon conversion , add to the i-f output . The phase at which it
returns depends on the distance between crysta l and TR tube and on the
impedance of th TR tube at image frequency. If the hase is incorrect
when it is reflected to the crysta l, it will subtract from the i-f output .
The i- impedance of the crysta l is also dependen t upon the impedance
seen by t he image fr equ en cy.
 
18 DUPLEXERS , MICROWAVE MIXERS , LOCAL OS C’ZLLA T ORS [SEC.24
In order that t he mixer may work proper ly, it is necessary tha t it have
ample a va ila ble LO power .
This does not mean, however , that t he more
2L’’--”
tempera tu rerat io, conversionloss, and
over -allnoisefigureof r eceiveras function
of crystalcur rent .
LO power applied t o the cryst a l t he
bet t er . Figure 2.10 shows the var ia -
t ion of crysta l t empera ture ra t io t ,
and crysta l conver sion loss s (the
reciproca l of WC) as a funct ion of
the crysta l cur r en t . Also shown is
t he over -a ll n oise figu re F calculated
on the assumption that t he i-f ampli-
fier has a noise figure of 3.0 db. As
can be seen , t he best noise figure is
obta ined with this par t icular crysta l
a t a cr yst al cu rr en t of a ppr oximat ely
0,4 ma. This is a r epresen ta t ive
case. If t he crysta l cur r en t is a lit t le
h igher than this value, not much
sensit ivityy is lost ; bu t if t he crysta l
cur r en t is lower , t here is a loss in
sensit ivity. It is standard pract ice
to run the cryst l cur ren t a t about
0.5 ma. About 0.5 mw of LO power
is requ ired to give a crysta l cur r en t of 0,5 ma.
The ava ilable power from the l cal oscilla tor sho ld be much la rger
than the above amount . The
more power the local oscilla tor is
capable of giving t he m ore decou-
plin g can be u sed between t h e m ixer
and the local oscilla tor .
This
load seen by the loca l oscilla tor so
tha t t he local os illa tor is stable.
It a lso preven t s loss of signals
down the LO line.
Th e power r equ ir ed in a t ypical
case is shown in Fig. 2“11. To
obtain this cu rve, the power from
t he local oscilla tor was r edu ced by
the use of 10SSYine. The availa-
ble power plot ted on the abscissa
is t he power t hat cou ld be obt ained
~1~
o
20
FIG.2.11.—Curveshowingover-allnoise
LO power.
a t t he end of the lossy line into a at ched lo d. As would be expect ed,
 
19
is mor e than about ten t imes that required by th e mixer .
As the ava ilable
power approach es that required for th e mixer , h owever , t he loss of signal
down th e LO lin e becomes appr ecia ble.
In this case the loss is about 3 db
wh en t he ava ilable power get s t o 1 mw.
Another in terest ing crystal mixer is one in which a harmonic of the
local oscilla tor is gen er ated in th e cr ysta l and then mixed with th e signal
to give the in termedia te frequency. To preven t the receiver from
respon ding t o th e fundamenta l, some select ivity, usually in t he form of a
sect ion of wa vegu ide t hat will pass t he h armon ic an d n ot t he fu ndamen tal
fr equency, is requ ired. A cho e system is also necessary in the LO line
to pr even t loss of signal.
A cross sect ion of such a device is shown in
Fig. 2.12. The LO power is fed by the crossbar B through the coaxia l
FIG.2.12.—Cr0sssectionof harmoniccrystaImixer.
chokes C to the crystal A. Here the harmonic is genera ted and mixed
with the signal to give the in termedia te frequency which is taken off
the crossbar . The chokes a re tuned to the signal frequency and have
ver y lit tle effect a t t he loca l oscilla tor a nd in termedia te fr equ en cies.
Not many measurements of noise figure have been made on this
h armon ic mixin g. A ser ies of m ea su remen ts wh er eby t he local oscilla tor
at 5000 Me/see was used for signals in the vicin ity of 10,000 Me/see
gave a conversion loss of abou t 12 db and noise tempera tu re ra t io of
about 2. Thus over-all noise figures of around 17 db cou ld be expected.
2.5. Thermionic Mixers for Microwaves.—Although crystal mixer s
have been fou nd t o give t he best per forman ce in th e frequ en cy ran ge fr om
about 2500 Me/see u p, par t icular ly for cases wh er e good n oise figu re is of
pr im ar y in ter est , t hermion ic mixer s a re n ot complet ely r uled ou t. Veloc-
ity-maculat ion tubes may be used as mixers at almost any frequency at
wh ich a na logou s t ubes may be ma de t o oscilla t e, 1a lth ou gh t hey a re some-
what noisy. They will not be t rea ted here. More conven tional tubes
‘W. C. Hahn and G. F . Metca lf, “Velocit y Modula t ed Tubes,” P roc. IRE, 27,
106, February1939.
 
20 DUPLEXERS , MICRO WA V-E MIXERS , LOCAL OS CILLA TORS [SEC.2.5
such as diodes and negat ive-gr id t r iodes do find some use up to about
4000 Me/see. The operat ion of such tubes at somewhat lower fre-
quencies is covered in Chap. 5. For the frequency range 2500 to 4000
Me/see, t ransit -t ime effect s becomes so importan t as t o preclude almost
any t reatment other than a purely empir ical one.
In the design of tubes suitable for use in this frequency range two
r equiremen ts must be sat isfied.
(1) Transit t imes must be kept small
and un iform.
This requ irement demands close spacing of elements and a
fine mesh for the gr id, if one is use . (2) The connect ion from the actual
tube elements to the external circuit s must be shor t and have low imped-
ance. The planar-disk-seal const ruct ion used in the so-called “ligh t -
house” tubes is one approach to these requ irements. Both diodes and
tr iodes, such as the types 559 and 2C40, have been made with this
construction.
Another method of assembly is used in the CV58, a Brit ish diode,
which has found some use at 3000 Me/see. In it both anode and cathode
L.-
FIG.2 13.—Crosssection of CV58mixer.
ar e cylindr ica l, wit h fla t ends th at
are the act ive reas. The anode
is a solid tungsten rod sealed
through the glass bulb, and the
cathode is a thin n ickel cylinder
with one end closed by a flat dkk.
Th e oxide coat in g is applied t o this
end. A he ical heater is placed
inside the cathode cylinder . The
spacing between cathode an anode at opera t ing temperatu re is about
0.001 in . Different ia l expansion of the var ious components of the tube
makes the achievement of such a spacing both complica ted and difficu lt .
A cross sect ion of a mixer using this tube is shown in Fig. 2.13. There
are var ious methods of tuning the device and inject ing LO power . At
3000 Me/see, the noise temperatu re ra t io is about 3 and the conversion
loss is approximately 13 db, giving an over-a ll noise figure of about 20
db. Because the diode does not burn ou t as a crysta l does, the duplexer
can be much si pler and h ave a somewh at lower in ser t ion loss.
The LO power requ ired is about 3 mw, which gives a rect ified curren t
of about 1 ma.
For some purposes where on ly medium sensit ivity is required, t r iode
mix rs have been used. One tube, the 2C40, has already been ment ioned.
Another tube used as a t r i de mixer is the WE708A, a grounded-gr id tube
with cylindr ica l elect rodes. The filament leads a re brought ou t through
coaxia l leads, and two connect ions to the pla te a re also brought ou t
th rough coaxia l leads. The gr id is connected to the main metallic base
 
21
ment leads, and LO and signal power fed in to these lines.
Some gain is
rea lized in the p ate circu it of th is mixer , bu t the noise ou tpu t power is
grea ter than tha t given by crys a ls or &lodes. Over-a ll noise figures of
abou t 24 to 25 db were measured on receiver s using these mixers.
2.6. Local Oscil a tor s. -To be suitable for use in a superhete odyne
receiver , an oscilla tor must possess the five following qualit ies. (1)
It must have adequate power ou tpu t . As has been seen , the po er OUG
put must be at least about ten t imes tha t actua lly requ ired by the mixer
in order to preven t excessive loss of signal in to the local oscilla tor . For
any of the mixers tha t are likely to be used in the microwave region ,
25 mw of LO power is adequate. (2) It must possess adequate frequency
stability. If au tomatic frequency con t rol i to be used with the receiver ,
th is requ irement can be relaxed considerably. (3) It must possess suf-
ficien t tun ing range.
Most of the radar receiver s descr ibed in th is book
h ave been design ed t o cover a rela tively n ar row fr equ en cy r an ge, usually
cover ing not more than 5 per cen t of the opera t ing frequency. Accord-
ingly, the oscilla tor tubes have been built to serve such a purpose. (4)
Th e oscilla tor must h ave reason able power-su pply requ ir em en ts; tha t is,
it should not t ake an unreasonably h igh voltage or requ ire an unreason-
ably h igh power input . (5) If the receiver is to have automat ic frequency
con t rol, a fifth requ irement may be imposed, namely, adaptability to
mech an ica l con tr ol t o th e tu nin g of a local oscilla tor , but such systems ar e
lik ely t o become t oo complica ted t o be of good ser viceabilit y.
Tu bes for LO s r vice may be of eit her th e con ven tion al n egat ive-gr id
type o the velocity-modula t ion t pe. At frequencies up to abou t 1000
Me/see the nega t ive-gr id type is a lmost un iversa lly used. Such tubes
a re descr ibed in Sec. 5.21. From abou t 1000 Me/see up to perhaps 4000,
the ligh thouse tube 2C40 or similar tubes can be used. Above about
4000 Me/see, th e velocity-m odu la t ion tubes offer a lmost t he on ly pr act i-
ca l tube for r eceiver use. They are suitable for use over the en t ir e range
fr om 1000 t o 25,000 Me/see.’
2.7. Reflex Klyst rons.-Veloci y-modula t ion tubes may be divided
in to two pr incipa l classes: (1) those in which an elect ron beam goes
th rough two resona tor s in succession and (2) those in which ther e is
on ly one resona tor , the elect ron beam being reflected back th rough this
a second t ime. Tubes of the fir st class are ra ther more dificu lt to tune,
since two resona tor s must be ganged ogeth er or otherwise set to the same
frequency. Accordingly they have been used ra ther lit t le in most
1An extensivediscussionof oscilla tor tubes suitable for use in receiversof both
velocity-modulationand negative-gridtypes will be found in Vol. 7 of th e Radiation
Labora torySer ies . SeealsoVol. 17, Chap. 16, for a lis t ingof many of the typea with
the frequencyrangethat they cover .
(a)
KIG.2.14.—(a) Photogra phof type 417 Mystr on;
Me/see. As examples of the second class, the 707A or 707B or the 2K28
may be ment ioned. Many of the fea tures of opera t ion of such reflex
tubes are descr ibed by E. L. Ginzton and A. E. Harr ison .1
Figure 2.14a and b shows a photograph and cross sect ion of a type 417
klyst ron . In th is tube tuning is accomplished by mechanical dis or t ion
of he cavity. This distor t ion changes the spacing between the r ids of
the cavity, which is roughly equivalen t to changing the capacity of the
equiva len t lumped circuit . Major changes in spacing are made by
1E. L. Ginzton and A. E, Harr ison ,
“ Reflex-Klyst ron Oscillators,” Proc. IRE,
94, 97, March 1946.
23
adjust ing the th ree suppor t ing screws, and fine changes may be made
with the tuning knob provided. Typica l power-supply circuit s for use
with this tube a re shown in Fig. 2.15. The resona tor volt age may be
about +300 vol s, and the reflector volt age var iable between —50 and
-2OO volts. Both of these volt ages a re measured with respect to the
m
b’
I
(b)
FIG.2.14.—(b)cross section of type 417 klystr on
ca thode. The resona tor cur rent is usu lly about 25 ma. The reflector
or din ar ily dr aw a negligible amount of cu r ren t .
In ma ny of t he velocit y-
modula t ion tubes the resona tor const itu t es a large par t of the out side of
the vacuum envelope. It is accordingly inconvenien t to opera te it a t a
pot en tia l 300 volt s a bove gr ou nd.
F or this r eason, if possible, a sepa ra te
power supply is used in which the posit ive en is grounded. If it is
necessa ry t o use a power supply in which th is cannot be done, some means
for insula t ing t he cavity, tuning con tr ols, and ou tput leads must be t aken.
See t h e r eceiver descr ibed in Chap. 14 f or an example of th is sor t .
 
24 DUPLEXERS, MICROWAVE MIXERS , LOCAL OSCILLATORS [SEC.2.7
load, and var iable r eflector volt age, and if measurements a re made of
power output and opera t ing frequencies, a set of curves much like Fig.
2.16 may be drawn. It will be not iced that t here are discret e regions
of r eflector volt age in which the tube does not oscilla te a t a ll. The
regions in which the tube does opera t e a re usually known as modes.
For successive modes the t ransit t ime of the elect rons, as they go from the
resona tor to the point a t which they are reflect ed and back to the r sona-
tor , cliffer s by just one cycle of the radio frequency. Within any one
(a)
Resonator
311
Cathode
T
E-I!
FIG.2.15.—Typicalelectr onically egula tedsuppliesfor r eflexoscillat ors.
mode this t ransit t ime is changing cont inually and is responsible for the
shift in opera t ing fr equency within the mode. The change in t ransit
t ime may also be produced by a change in resona tor volt age, and with it
a cor r espondin g ch ange in fr equ en cy.
Th er efor e, r egu la t ed power supply
is provided for the resona tor . Severa l parameters of impor t ance in
receiver design may be obta ined from the curves.
The fir st of these is
the so-ca lled electron ic tu nin g coe$cien t. This is the slope of the curve
of frequency vs. reflector volt age and is expressed in megacycles per
second per volt . The second parameter is oft en called the widthof the
mode between ha f-power point s. It is t he fr equency spread between
poin t s on a given mode at which the power outpu t has fa llen to half it s
maximum value. It is usually taken as a measure f the fr equency
range over wh:ch the tube will fu rnish useful ou tpu t with elect ron ic
tuning. The third parameter is the width of a mode between zero outpu t
 
T RIODE OS !CILLA TOR 25
it determines whether or not a receiver may be tuned to the wrong side-
band (s ee Sec. 3’10).
Both the half-power width and the zero-power width of a mode depend
on t he r eson at or volt age, bot h in cr ea sin g a s t he volt age is in cr ea sed.
The
zer o-power width also depends on t he loadin g applied t o t he oscilla tor . If
a r ea ct ive loa d is a p lied t o t he oscilla tor , it will a lso ch an ge t he oper at in g
frequency. With the ver y high ope at ing frequencies of some thousands
of megacycles per second, it is easy to have a condit ion where the load is a
number of wavelengths away from the oscilla tor , the in tervening con-
n ect ion being eith er a coaxia l cable or wavegu ide.
This condit ion may
at t imes lead to a peculiar effect kn own as a ‘t1ong-line effect , ” in which
f
FIG.2.16.—Modesof oscilla t ionof reflexklyst ron.
the oscilla tor will r efuse to work over a band of frequencies. If an
at tempt is made t o tu ne it elect r on ica lly t hr ou gh this band, t he fr equ en cy
will jump from one edge to the other .
In ext r eme cases, the opera t ion
may actually be unstable, the oscilla tor jumping back and for th from one
frequency h another in a random manner . 1
Cer ta in of the newer tubes such as the 2K45 and 2K50 utilize a dif-
fer en t mea ns of mech an ica l t un in g.
These tubes a re known as thermally
tuned tubes. In them the resonator is en t ir ely with in the vacuum
envelope. As before it is tuned by mechan ical distor t ion . This distor -
t ion is produced, however , by the expansion or con t ract ion of a str ip of
meta l as it is heated or cooled. This str ip of meta l ordinar ily forms the
anode of a separa te t r iode placed with in the same vacuum envelope.
Accordingly, con t rol of the potent ia l of the gr id of th is auxiliary t r iode
su ffices t o t un e t he main oscilla tor over its en tir e oper at in g r an ge.
Since
the opera t ing frequency of these tubes changes rapid y with changes in
any of the supply voltages, they are ordinar ily useful on ly where some
form of AFC is pr ovided.
2s8. Tr iode Oscilla tor .-A type of t r iode oscilla tor tha t is usefu l at
3000 Me/see used the lighthouse tube in what is ca lled a reentrant-
 
26 DUPLEXERS , MICROWAVE MIXERS , LOCAL OS CILLATORS [SEC.2.8
line is used to connect the pla te to the ca thode. A schematic cross
sect ion of such an oscilla tor is shown in Fig. 217. In the diagram, a
sleeve B is suppor ted by the gr id disk of the lighthouse tube A. A res is tor
G serves to connect the gr id to ground for direct cur rent . A rod E is
connected to the pla te of the lighthouse tube and is slid on and off the
pla te line by th screw S. A movable plunger with a choke join t on the
pla te lin e D is used to close the line.
The feed ack line is from the pla te
through the coaxial line between B and E, then arou d the end and
FIG.2.17.—Cr sssectionof reen t rantoscillator.
toward the ca thode by way of the coaxial line between B and F. Pulling
the pla te lead off the tube changes the oscilla tor frequency over nar row
limits. Large changes in frequency are accomplished by changing the
length of the grid sleeve B. The posit ion of the plunger D determines
the feedback .
b oscilla tor of this type has a good frequency stability as a funct ion
of voltage varia t ions on the heater and pla te. It is easily tuned by a
single knob. The power output with 250 volt s on the plate is about
50 mw, which is ample for all LO uses.
 
BY G. H. NIBBE, F. E. OWSLISY,AND E. DURAND
3,1. In t roduct ion .—The pr imary con sider a tion of aut omat ic fr equency
con tr ols,l AFC, is t he fr equ en cy st abiliza tion of some sou rc of r -f en er gy.
This chapter will d scuss the var ious types of AFC that have been used in
receiver s to maintain the cor r ect tuning rela t ions for opt imum per form-
ance. These may be rough ly divided in to two classificat ions: (1)
difference-jrequency systems and (2) absolute-frequency systems. A differ -
ence-frequency system of AFC is on e in which the difference frequency
obta ined by mixing two signals is maintained at a constan t va lue, ir r e-
spect ive of t he a bsolu te st abilit y of eit her sou rce.
An absolute-frequency
system is one in which the receiver is tuned to a specified frequency and
ma in tain ed t her e wit hou t r ega rd t o t he fr equ en cy of a ny in com in g sign als.
All the FC systems to be descr ibed are used with superheterodyne
receiver s and opera te by on t rol of the frequency of the local oscilla tor
in t he r eceiver , wh ich has a con ven tion al fixed-t un ed i-f amplifier .
The
method used to maintain th is con t rol or to obta in the desired stabiliza-
t ion is to compare two frequencies and obta in an er ror volt a e tha t is
dependen t on the devia t ion from the desired frequen t y. This er ror VOlt -
age is used to cor r ect the LO frequency in a manner similar in pr inciple
to a servomechan ism. As in a servomechanism, there must always be
a small er ror to provide a cor rect ion voltage, bu t the er ror requ ired may
be decr eased by incr easin g t he amplificat ion in th e system.
Systems using the propagat ion of r -f energy for the conveyance or
gather ing of in format ion may be divided for presen t purposes in to th ree
categories:
1. Normal communicat ions systems. The in telligence is impressed
on the r -f power sen t ou t by a t ransmit ter by means of some form
f modu ation and is r ecover ed at a distant receiving poin t by an
app rop ria t e p roces s of demodu la t ion .
2. P ropagat ion study systems. The transmit ter serves as a source
f con stan t power , and var ia t ions in th e signal r eceived at a distant
point a re in terpreted in terms of var ia t ions in the medium through
wh ich t he n er gy h as been t ra nsm it ted.
I The ent ireAFC problemwith pr imaryemphasison the radar aspect is presented
in Vol. 16, Chap.7, Radiat ion Laboratory Series .
27
[SEC.~~
Echo or rada r syst ems. Again the condit ion of the medium of
transmission, in pa r t icu lar the presence of sca t t er ing or reflect ing
objects, is determined by effect s on the received signal, bu t , in
con t rast t o the second ca tegory, the t ransmit t er and receiver a re
loca ted a t the same poin t .
Whether or not the t ransmit t er hose signal to be received is near
the r eceiver in quest ion plays an impor tan t par t in the choice of an AFC
system. As indica ted above, radar systems involve a loca l t ransmit ter .
Since much of the work on which the presen t discussion is based has
been concerned with radar systems, the applicable types of AFC will
r ece ve t he major emph asis.
DIFFERENCE-FREQUENCYAFC SYSTEMS
In on e of t he fir st systems for AFC, t he loca l oscilla tor was main ta ined
a t the cor rect frequency by tuning it elect ronica lly with an er ror voltage
obt ain ed fr om t he i-f amplifier . 1
The method was used with a select ive receiver and ach ieved the dual
resu lt of simplifying the mechanica l tun ing of the receiver and reducing
the stability requirement s t o be met by the loca l oscilla tor . The same
pr inciples were applied in another AFC system used to main ta in the
cen ter frequency of an f-m transmit ter a t an assigned value. 2
The increased use of ver y high frequencies and microwaves has placed
grea t demands upon AFC systems as a means of obta in ing constan t i-f
signals, since bot h th e r eceived signa l and loca l oscilla t or often h ave poor
frequency stability. The use of AFC becomes even more impor tan t in
the case of a radar receiver , where the t ransmit ted signa l fr equency may
shift or be pulled a t a fa ir ly rapid ra te as a resu lt of varying loads due to
the antenna rota t ion react ing upon the unstable t ransmit ters tha t a re
used.
SYSTEMSOPERATINGON THE RECEIVED SIGNAL
AFC systems opera t ing on the r eceived signa l can funct ion on ly
a fter the r eceiver has been tuned to an incoming signa l by other means.
A block diagram of such an AFC system is shown in Fig. 3.1.
The discr imina tor supplies an er ror volt age indica t ing the degree of
mistuning, and th e con tr ol cir cu it ch an ges t he LO fr equen cy in t he cor rect
dir ect ion t o r edu ce th e er ror volta ge n ea rly t o zer o.
Since the mixer and i-f amplifier of the signal channel a re oft en used
for the AFC signa l, a convent iona l a -m receiver may be provided with
AFC by the addit ion of on ly a discr imina tor and a con t rol circu it . How-
‘ C. Travis, “Automatic FrequencyContr ol,” Proc. IRE, 23, N o. 10,October 1935.
2I. R. Weir , “Field Tes ts of Frequency-and Amplitude-modula t ionwith I ’lt ra -
high-frequencyWaves,” GemEke. R ev., May 1939.
 
29
ever , t he dkcr imina tor for t he AFC channel som t imes follows a separ ate
i-f amplifier stage br idged across the input to the last i-f stage in the
r eceiver . This a rr an gemen t affor ds isola tion between t he discr imina tor
and signal det ect or . Becau se f-m r eceiver s alr eady h ave discr imin at or s,
on ly t he con tr ol cir cu it n eed be a dded.
An ou tpu t volt age vs. fr equ en c~-
character ist ic typica l of the dis r iminators used for AFC is shown in
Local
1- :
Mixer
oscillator
FIG. 3.2.—Discrimina torout pu t
AFC.
as a functionfrequency.
Fig. 3“2, and the cir cu it diagram of a commonly used discr iminator is
shown in Fig. 3.3. The i-f signal input to the discr imina tor can be
main tained at a near ly constan t va lue with automatic gain cont r ol, AGC,
of the i-f amplifier .
The funct ion of the cont rol cir cu it is to conver t the er ror voltage out -
pu t of t he discr im in at or in to a fr equ en cy cor rect ion of t he loca l oscilla tor .
FIG,3.3.—Foater-Seeleyiscriminator.
The type of AFC desired, the discr iminator character ist ics, and the type
of loca l oscilla tor used set the requ ir ements for the design of the cont rol
circuit.
3.2. Con t rol Circu its for Feedback Oscilla tor s.-At h igh and very
h igh fr equ en cies, or din ar y n ega tive-gr id oscilla tor s a re common ly u sed
for the loca l oscilla tor in the receiver .
The frequency of oscilla t ion is
largely determined by the constants of the associa ted tuned circu i s,
 
[SEC.3.2
must be var ied. It is possible, for example, to vary mechanica lly the
capacity, inductance, or resistance of the tuned circuit with a motor tha t
is par t of a servomechanism con trolled by the amplified discr iminator
ou tput vo tage. E lect ron ic va ria t ion of the tuned-circuit pa ramete s
is a more common means of con t rol, however , and numerous amroaches
Hartleyoscilla tor Reactanceube
rea ctan cetu be.
suggested.
A widely used method for ob-
ta in in g a fr equ en cy va ria tion fr om
a volt age va ria tion is t he in ject ion
of a r ea ct ive cu rr en t in to t he tun ed
cir cu it wit h a ‘{r ea ct an ce t ube. ” L
A circuit diagram of a H rt ley
oscilla tor and one t ype of r ea ct a nce
tube is shown in Fig. 3.4. Here C!
and RI act as a voltage divider and
ph ase sh ifter , so t ha t t he,gr id volt -
a ge of Va leads t he pla te volta ge by
almost 90°. The pla te cur ren t of Vz is then almost 90° from the volt age
appear ing across the tank circu it LI, Cl.
The net effect is equiva lent to a
sh un tin g ca pa cit y a cr oss L l, Cl, whose valu e is C’i = gmRIC~.2
A pentode is usually used for V, in order to obta in a high va lue of
g~ and thus a large var ia t ion in in jected capacity. The in jected capacity
can th en be var ied over a con siderable
ran e by changing the bias voltage E,
in Fig. 3.4, thereby changing g~.
Therefore, a frequency var ia t ion is
obta ined tha t corresponds to the bias-
voltage var ia t ion . The per formance
of such a circuit may be shown by a
cu rve of fr equ en cy vs. con tr ol olt age,
such as Fig. 3.5. (Frequency is chosen
as the abscissa to facilita te a subse-
quent use of the curve. ) This curve is
FIG.
vs .
seen to cover a range of frequencies extending fromfl to f2. The end of the
curve at fl cor resp~nds to ~he h ighest usabl~ valu~ of g; and is marked by
the drawing of gr id cur ren t in V .
The lim it ing fr equency fz cor r esponds
to gn equal to zero, with complete cu toff of Vz; therefore the frequency of
the oscilla tor no ~onger depends on the con t rol voltage. Obviously the
ran e (jz — jl) represen ts the grea test possible frequency coverage of the
1D. E. Foster, S. W. Seeley, “Automatic Tuning, SimplifiedCircuits,and Design
Practice,” PmJc.IRE, 25, No. 3, March 1937.
 
31
system. The frequency fO corresponds to the opera t ing frequency with
no applied cont rol volt age. It maybe va ried by changi g t he mechanical
tuning of the oscilla tor . This var ia t ion essent ia lly displaces the whole
curve to the r ight or left . Another pa rameter of impor tance is the tuning
coefficien t in megacycles per second per volt , which is the reciproca l of
the slope of the curve s drawn.
E xa ct ly a na logou s qua nt it ies, t un ing
coefficien t and maximum frequency
range, will be impor tant proper t es of
any of the other oscilla tor systems
considered.
Th e oper at ion of t he complet e AFC
syst em may now be con sider ed gr aph i-
cally by combining t he curves of Figs.
3.2 and 3.5, as shown in Fig. 3.6.
The zeros on the frequency sca le will
differ for the t wo cur ves by an amount
f, , t he fr equ en cy of t he signal, wh ich is
here assumed to be a constant . As
drawn, the curves apply to the case
where the LO frequency is above the
s igna l fr equen t y.
F igur e 3.6a cor respon ds t o t he ca se
where the mechanica l tuning of the
oscilla tor is such as to produce the
desired frequency w thout any help
from the cont rol circuit . The discr i-
minator then provides no output , and
t he ent ire syst m t herefor e remains a t
this poin t . F igure 3.6b cor r esponds to
the case where the mechanical tuning
is off on the high-frequency side. For
any frequency between jo and j’, the
output voltage of the discr iminator is
+
‘?
lat or frequ encycor rectwithoutcont rol;
(b) oscillator fr.quency somewhatt oo
highin absenceof cont rol; (c) oscillator
fr equency st ill h igher in absence of
control.
more than enough to bring the oscilla tor to tha t frequency. Therefore
f’ is the equilibr ium opera t ing point for the system. The op ra t ing er ror
is thenfl — ~“, and the er ror tha t has been cor rected isfO — j“. The ra t io
(f’ – f“)/(.fo – j“) is thus a measure of the efficacy of the system. It may
be expressed in t erms of t he tuning coefficient T, of t he oscilla tor system
expressed in megacycles pe second per volt and the slope D of the dis-
cr iminator output expressed in volt s per megacycle per second
f’ -f”= 1
AFC SYSTEMS AND CIRCUITS [SEC.32
assuming tha t both curves are linear over the range involved. This
equat ion is ana logous to the expression 1/(1 + @) for the reduct ion of
er ror in an in ver se-feedba ck syst em.
Consider now the situa t ion shown in Fig. 3“6c. Here the mechanica l
tun ing is off st ill fa r ther on the high-fr equency side. There are therefore
two new poin ts of in t er sect ion of the two curves labeled f’” and ~.
I
For any frequency between j, and j’” the dis-
cr imina tor output volt age is more than suffi-
cien t to br ing the oscilla tor to tha t frequency,
but for frequencies between~ and j’” the dis-
cr imina tor outpu t is insufficien t to mainta in
the frequency at tha t va lue. Therefore’” will
be a poin t of stable equilibr ium, as will j’.
On the other hand, P will be a posit ion of
the system is pu t in tha t sta te, a sligh t dis-
go to either j’ or j’”. For th is condit ion of
mechanica l tun ing, the opera t ion is sa t isfactory as long as the received
signal is mainta ined provided the system has in it ia lly been put in the
sta te j’ by some means. However , if the signal is in ter rupted, the oscil-
la tor fr equ ncy will shift t o jo; and if the signal is then restored, it will
300v
FIG.3.8.—Direct-coupledamplifier,rea cta ncetu be, and Ha rt leyoscillator. At th e fre-
quencyof operat ionunma rkedcapa citorshavelow reactan ce. X., = IOR6:R5 s 10%.
retu rn only to j’”,
where opera t ion is defin itely unsa t isfactory. Thk
behavior may be descr ibed by saying tha t the system will not pull in
from the condit i n shown in Fig. 3.6c but it will hold in if proper ly set to
begin wit h.
Two sets of limit ing condit ions may now be defined for the opera t io
of the AFC system; these limits may be ca lled the pull-in r ange and th
ho.ki-zn range. To avoid useless complica t ion , the maximum range of
 
33
grea ter than either of these ranges, and the tuning curve over the range
of in terest will be considered to be a st ra ight line. The condit ions a t
the limit ing cases may be represen ted as in Fig. 3.7, where j~, jBj jc, and
f. r epr esen t four differen t mechanical set t ings of the LO frequency.
8ince the system will pull in to the cor r ect opera t ing frequen y under all
condit ions if the mechanical tuning is between fB and fc, th is may be
ca lled the pull-in r ange. On the other hand, it will hold it self a t the
proper poin t , once set there and bar r ing in ter rupt ions of the signal, if
the mechanica l tuning is var ied over the range from j. to jD, so tha t th is
may be called the hold-in range. If it is set ou tside the range from j.
toj., it will n ot lock at t he cor rect poin t u nder a ny con dit ion s.
A direct -coupled amplifier can be added to the system between the
disc iminator and the reactance tube to increase the loop gain . A circu it
diagram of the elements of such an AFC system is shown in Fig. 38.
Th e adva nt ages of in cr ea sed loop gain
a re grea ter range, both pull-in and
6+
h old-in , and mor e accu ra te tuning. In
(
ou tpu t curve without affect ing the To
oscilla tor -tun ing curves .
m
1
- Bias or
d irect -coup led amplifier inver t s the d is -
1
J
+ control
cr imin at or ch ar act er ist ic, it is n eces-
voltage
sary t o r ever se th e act ion ” of on e of t he
!!lt
R-f
elem en ts if t he discr im in at or ch ar ac-
L~ R
ter ist ic is as shown in Fig. 3.2. The
local oscilla tor can be oper ated on th e
FIG.3.9.—Reactance-tubecircuit .
low-frequency side of the signal fre-
quency, for example, or the reactance tube can be connected as shown in
Fig. 3.8 so tha t it will in ject induct ive reactance ra ther than capacit ive
reactance.
L. – C2R6.
9m
The reactance-tube circu it s shown in Figs. 34 and 3.8 de end on a
phase-shift ing network to supply the gr id with a voltage that leads or
lags the pla te voltage. At h igher frequencies the in ter elect rode capaci-
t ies of the tube load the phase-shift ing n etwork, and transikt ime effect s
add an addit ional phase lag between gr id voltage and pla te cur ren t .
These f ctor s tend to make the design of such reactance-tube circuit s
difficu lt . As a result of these effect s, a resist ive componen t of pla te cur-
ren t as well as a react ive componen t is in jected in to the tuned circu it .
~Ibid,
[SEC.33
Th e r esist ive compon en t ma y load t he oscilla tor so hea vily t ha t it becomes
difficu lt t o maint ain oscilla tion , especia lly wh en t he r esist ive compon en t
is var ied by th e controlling voltage.
A reactance-tube circu it ’ that is more suitable for opera t ion in the
vhf region is shown in Fig. 3.9.
If X., = X~, = R, ithas been shown
t ha t a r ea son able va lu e of r esist ive in j ect ion , wh ich r emain s subst ant ia lly
constan t over the useful range of opera t ion , can be obta ined. Other
r ea ct an ce-t ube cir cuit s th at ha ve a dvan ta ges over t he simple forms sh own
in Figs. 3.4 and 3.8 have been descr ibed2 in the lit era ture.
3.3. Con tr ol Cir cu it s for Reflex Oscilla tor s.—Reflex velocit y-modu -
la t ion oscilla tors such as the 707B, 2K28, 723A/B, and 417 are com-
From
discriminator
output
+300
monly used as local oscilla tors in microwave receivers.
Inasmuch as a
var ia t ion in reflector voltage in these tubes pr duces a la rge var ia t ion in
frequency, it becomes easy to provide AFC for receivers using this type
of local oscilla tor . The reflector is usually opera ted a t a poten t ia l from
100 to 00 volt s nega t ive with respect to the ca thode. A direct -
cou pled amplifier is oft en u sed betw en t he discr im in at or a nd LO r eflect or
elect rode to obtain grea t er loop gain. The proper op