feedback and stability of junction transistor circuits
TRANSCRIPT
Retrospective Theses and Dissertations Iowa State University Capstones, Theses andDissertations
1953
Feedback and stability of junction transistor circuitsDonald William GadeIowa State College
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Recommended CitationGade, Donald William, "Feedback and stability of junction transistor circuits " (1953). Retrospective Theses and Dissertations. 12418.https://lib.dr.iastate.edu/rtd/12418
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fMlSISfOI CIHCOTIS
A Bissortfttioa Sttteiitt®d to the
Sradu&t® F&ewlty la Partial FulfiHiB«ttt of
fhe l®ttiir«Beat8 for tfe® of
WfOK OF milDSOPlT
Major Smbjeat* Iltstrleal lagineariag
Boaali William and®
ApproT®^I
H®ad of 'Ifejor iepartm«it
Dean of Wadttate^ Collage
Iowa State Colleg®
19SS
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Signature was redacted for privacy.
Signature was redacted for privacy.
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Pag®
I. IStKiWCfiOS 1
II. rnnm op 4
III. TMISIETOI «lJI?AMt ClKUIfS 7
A. latroductioa to Bquivaltat Clrauits ..... 7
i. Me8h-d«riv«d italvalent Cirouits 11
G. iQdal-d®riT®ji Bq,«lTal«nt Circuits IS
B. iT&luatlott of fh0 EqalTalent Cirsait P«ra««t®rs 20
^ IT. ilMIS Sf4« IMISISIOI GlieUItS 2i
4. BsTslO'Pseat of F9®dbask Oirsuits ....... 2i
B. S©l«®tion of Clreuit farmlMtloas 33
0. ijaalysii of Glrsults eoataiaisag Series or Farall®! p9®dtoa®-lc S§
1. th# gaii«ral transistor ©ircuit .... 36
2. the groaaded baa® transistor oircuit ................. 41
3. Tk0 gro«ad®<i «mitt®r tra.a8i8tor oiroult 48
4. the grouaied ©olleotor transistor oiraait ........... 64
D. jfcaalysia of Giremlts Coataiaisag loth Eari®s Parall®! Feedbaok .......... S6
7"/cf r-2
iii
• trnm OF COlKIfS (ooatlM@d)
F«ig®
V. mokMB fMMBimm eiiGiiis . ........... 6o
A. Iqaiwlsafe Girouits for Caseadad traaaiators ^ . 60
B. Aaalysia of Cstsead®*! Oirotiits Coataiaiag S«rl®8 or Parallel l%®dbaok i i 66
C.. tealyeis of 0asead®fi transistor Sireuits eontainiag Beth Series md F&mllel FmAh&Qk ?1
?!., iWMAlf • 74
¥11. SitmfgD lEfSmCIS 76
VIII. 89
IX. APPlIilOIS 90
APfWilX A. OP tBtfSlSK)! lilWOlI C»iFFICIEifS- . 91
Awmmm b. eittoi DiirsiBiei aid siisiTivni K)S TMlSISfO-M m
I
I. lIf»DWJT10»
Buriag •&« p®riod; from If40 to tha pr«8«at tia«, a 0oasl<i®rabl«
&dTa.mmmnt was mds in the fisM of s»iwnteotors. In partioular,
the ppopartiss of ailieoa aad gemaalm war® studiad. From this,
d«tail«d Infomatlon was obtaiaed about th® «R«rgy and th«
ooBd«©tiag |iroforti9S of sffl®iooa4aot©rs.
As «Tld«ae® of tha ad"wmo«B«ttt, it was anaouaes-d ia 1948 that a
radieally sew typo of amplifying d«Tio® had baoa diseowred^, fhis
amflifyiag dsvi®# was called a poiat-oontaet traasistor. Its ability
to aaplify was based upon th« oondaetiag propartiss of th®
s«®iooad«st®r germaaaduffl.
fraaaadoas progress has beaa made in th® field of transistors
sine® thtir annouaaaasnt. To tha rapidly growing list have been
addsd th® soaxial transistor, th® Janetioa transistor, th® fisld-
0ff«st transistor, the transistor tetrode, aad th« P-H-P-i
lardew' aai W, 1, Brattaia. fransistor, a semieoadwotor triod®. Phys. lev. 74i 2S0-231. lS4a.
W, H. Brattaia and J. Bardeen. Mature of th® forward current in geraanitm point oontaots. Phym, lev. f4i ESWSg. 1948.
W. Shookley aad #. h» Pearson, liodulatioa of oond^otaaoe of thin filas of seaieondactors by surface oharges. Ph;^. lev, 74t gSE-2S3, l®4i.
z
•fcraaaiator. Msaatifaeturiag hav® be®n dsTsloped md improTsd
to the p^int wlisr® polat-eoiifeaot ani JmotAoa traasistors lurs aow
svailabl® in quaatity, frftasiator eirottltry bas bo«tt deTslopad to th«
poiat wbera oaiy the pras®^ oost (aad possibly quality) of traa-
• istors pr®"W:Bts thsm froa rsplaoing mmy -mmmi tubee, lew flslds
baT® b«@a fouai for traaiistors mtoere ttplifyiag deiriees had not
previously baea tissd*
At present, it appears that the Jimotion transistor holds the
great@#t possibilities outsid® the field of arwitohing sirouits. It
has aaay natural adwatages oirer other traasistor types i the theo
retical aspeota of Jmetioa transistor are easily mderstoodj
its eleotrioal eharaoteriatioa saa- be aeemrately predioted; it is
oapable of prodticiag relatiTely large power gainsj as an amplifier,
it is short-eireuit stable j it ia rugged § its powr retair«»8ats are
extrswely aaallj its size aakes it particularly adaptable to
mialattjri««d • eircuits.
la addition to fee above ad-rooatages, the availability of I-F-I
and P-1-.P translators aakes it posaible to talee advantage of ooapl®-
meatary spmaetry prineiples. Using these prinelplea, biasing
problwis are simplified and oiretait-oompoaent retalremeats are
redtieed. la pash-pmll stages, eoapl®m«atary symetry oan be used
to eliminate the need of a phase inverter.
Single umit sy»Hi@try was introdueed by potion transistors,
Using this prineipi©, it is posaible to reverse the dlreotioa of
s
amplification, hj rewrsiag bias -roltagaa.
4» iniisatai fej thas® prosant adwitagas, th® jmaetioa tran-
Bistor is of graat importaaea. Ibis thaaie partaias to junetion
tran8i«t©r8| apeeifioalli', it is oonoarnad with tha applioation of
faedfeaoie to transiator ©ireults'With-tiie rasultittg problaa of
©irauit aaalysis.
4
II. llflW OF LIflMfTOl
tittsrally tanireds of artiel@« sonoerning transistors hav®
app©«r®i in tfe« physios Journals aad the sleetrieal engineering
poriodisals sine® 1948. Ihesa arti®l«s pertain to all phases of th«
traasiitor iaolading theory, eirouit properties, and applioatioas.
fwo INioks hair® h««n written dealing exelasiwly with transistors^.
Howeirer, the momt of Information available ©oneerning transistor
feedhaek eirouits and their analysis is rather limited. g
E. L. Wallaee, Jr. a^nd W. S* Pietenpol pablished one of the
first artieles on JnnotioB transistors in ItBl, disomssiag circuit
properties aad applioations of single stage S-P-I transistors.
this diSQUssioa was liiaited to the use of one equivalent oironit
for all eonneetions, aad was primarily ooaeemed with basio oirouit
properties without referenoe to feedback aspeets.
%, ihookley. gleotrons and holes in seaioonduators. let ed. D. Tan lostrand Company, ,Ino. ISK).
I. F. Shea. Friaoipie® of transistor oireuits. Ist ed. John Wiley and Sons, Ins. liSS.
^E. h* Vallaoe, Jr. and W, S, Pieteapol. Some oirouit properties aad applications of I-P-I transistors. Bell Sys. Teoh, Jour, mt S30-M3. 1981.,
§
iiohard F. ©onsidsred feedbaok as a msatts of stabUlziag
Junatloa traasistor oparating points. 1® iaT«stigat®d tho effaot of
addlB^ sariaa rasistora to th® traaaiator teminals la ordar to
radwea tto® mriation la tba aollaetor aaturatloB e«rr»at. This was
a vary Mportant ooatrlbutlsa. Stal>ill»atioa mathods latroduaed lay
hla ar® used la mast prasaat day airauit daaigas.
®. i. fiiowia® atttdlad tlia affeet of faadbaek oa oatoff
3 fraq,«aa©y . He ©onslderad oaly tha faadbaak iaharaatly praaaat in
4 tha traaelstor. Ha ooaeludad that ratura diffaraaea ©oald ¥a «sed
as a maasar® of oiroult aatoff
A atmdy was aada oa traaslator aful'valaat elroaits
E aad assoelatad tarmiaology hy L. J, Siaaalatto . Ia attaaptad to
olasstfy ty^aalstor aquimlaat alrottlt® aad to ataadardlse tha
^liahard F. Shaa. traaslator oparatloai stablliaatloa of operating l^iats. Pro®# of tha^ IIS. 1486-143?, 19S2,
g D. !• fhoiMts. Iranslstor aapllflar-aatoff fraquaaoy. Proo.
of tlja tm, 401 1481-1483. ItSt.
®0utO'ff frataenay is daf laad as. tha fraqaaaoy at whleh the gala is Sdh h9lm tha law fra^uaaoy gala.
%aa Appaadlx B for dafiaitloa of ratara diffaraaae for traz^istors.
s l». J. Siaaolatto, faralaology aad ataatloas for liaaar aativa
faur-tamlaal aatworks laoludli^ traasistors. lOA lavlair, I4i 2S-M. ISfiS.
6
sufesoript aotation for th® ast*ork co®ffiei#»t8 aa4 th« «tuiwl«at
eironit paraa0t®r». It is poisibl® that Ms aotRtloa will b«
fltaadftrdizsd by th® professional groups.
la a r®e®nt artiole by Pstsr 0. Sulzer^, Jattotloa transistor
eirouit applioations ware r«vl«wed, le illastratad several single-
stag® and easeaded trasasistor eireuits *hi®h he termed "building-
blook" eirouits. 411 of tkese ©ireuits were of tli® grownded esiitter
eoimeetion. Pbr d-o stabili8«tioa, h® used a resistor in series
with the Miittsr, a resistor betweem base and oolleetor, and a
resistor between base and ground, this thesis Identifies feedbaek
of this type as series and parallel feedback.
^eter 6. Sulser. JanetIon transistor ©ireuit applioations. Sleetronios. 26t 1?0-1TS. Aug, ItSS.
7
III. iMisiifoi cmmm
4. latrQ^wtion to iqwi-yalent Cirouite
'48 the first step ia naiilyziag the liaear 9p®ra,tio» of traa-
sistor® at 'Im frefasneiea, 0ttitabl® e^tiiTRlent oireuita attst be
seltetea, laay iiffereat traatistor eqaifalent oirenits are
avmilable^. In order to preTeat @®afttSios, it is neoassary to
derive th,® equivalent eirettitt aeeiei.
M. larly, Iffeots of Sfaee-ofaarg® layer widenia^ in ^motion transistors, froo. of the III, 1401-1406. 19§2.
L* J. tiaooletto. Jtmetioa trasasistor efaivalent eirowits and TOOttua tube analogy. Proc. of 14ie ISS. 40» l4iO-l4iS. ltS2.
Ii. J, tiaooletto. Teraiaology wad eiwations fyr linear active foar-teraiaal networks ineluding transistors, MGA leview. 14i 28-46. I»i3.
Seofflrey Knight, ir., Siohard A. Johnson, and loland B. Holt. leasTireiwat of th© small sipial paraaeter® of tranaistors. Proo. of the 111. 4li iSS-SS». 1955.
»• M. lyier ani 1. J. lirohaer. Soae eireuit aapeets erf the transistor. Bell Sys, feeh. Joar. 28i S67-401. 1049.
Wallase and Pietenpol, op. sit,
t. t. Wallaoe scad 6. laisbeok. l^ality as a guide in transistor oiroait design. Bell Sys. feoh. iour. SOi S8l-«417. 1951.
8
Btulwleat ©irouits may b® deriir®<i from, the mesh or aedal
©qaations of a g«a®ral tliree-tarmiaal a«tworfc^. fhis i«®«diat®ly
divides the «tttiml«nt oirouits into turo dlstlaat groapst those
equimleat oirsaits d®rlT«d oa th® bs»is of mesh equations taking
the form of a t aad thos® aquivaleat sirouits darivad on th« basis
of Jiodal aquations takiisg th® form of a «. It will b® ooawniant
to first obtain a general aqmivalaat elreait of aaoh groap, and
from thss® baild lap apteifio oircuits,
fha genaral iolutioa to th« first group ean be found from the
«®8h aqiaatioas of th« active three-teminal nstwork of Figure I.
El
AotiT® Hetwork
h -o
Fifwe I* Aotive thr®9-t«raiaal network
C. PeteraoB* EquiVRlenfc oirouits of lia«ar aotiv® four-temiaal networks, fell Sy», feoh, Joar. ETi §9S-62E. I94i»
^fhe dlr®0tiOB8 ohssan for TOltage# aad eurrent® in this figure are standard bo»«i.olatere and will b® wsed throughout this manasoript.
9
At low traqnemim., where th® network eoefficienta are real,
% " Tiila. + riglg , (1)
«a«l
B« • • (2)
these etuatloas may be writtea ia the for®
% " rj,xli • » (S)
mad
Bt • * raala • • (4)
l^ttatioas (S) a»d (4) auggeat the eqaimlent ©irouit of Figure 2.
Ia this figHre, the aetwork ooeffioient® mre relatei to the
etaiwlent oireuit parameters as follows i
rx% " rx * ,
Pis •*',«#
rm "
and
rm • »*• * •
r4li **x **» - •—\ •
o—\A/S/ I \AAr*{
figure 2. @eneral msh-deriTed traxuiister equifale&t oireuit
10
i«eausa eosaactioas for the transistor of Figure 1 are aot
specified, the eqaimlent ©irouit ©f Hgare 2 oaa be used for amy
oonaeotioa. Of the six possible oonaeetioas, oaly three produce
appreoiable power gaiaj grauaded base with emitter input aad eol
leotor output, grounded <teittar with base input aad eolleotor
output, aad grouaded eolleotor with base input aad witter output,
these eoMieotions will be referred to as the grounded base, the
p-ounded eaitter, a»d the growided oolleetor, respeetiTely. lo
other ooaaeotioB will be diseussed.
The same procedure ean be repeated with the nodal eiiuations
for the three-teraiaal aetwork ©f Figure I. Ihe equations are
li " Si A ''' gia*® » (®)
and
la • f)»i% • 8iiis% • (7)
lere g*8 are used to iadieate that the adaittanoes are real^.
Rearraage»<mt of equations (6) aad (7) gives
• ixiSi • 8i8®a » (®)
and
I® " gi8% * SaftSg + • (®)
^he g*a used here are sSjaplifioations of adaittanee and should not be eoafused with the network eoeffieiwat resultiag isttiea Ij. and ig are eonsidered- independent.
Suilleain, Irnst A, CoiKUttleatioii networks. Vol. II. 1st ed. I. t, John Wiley aad Sons, Im» IfSi.
11
Sqwtlsas (8) aa4 (9) suggest th« ©tttlvalaat ©ir®uit of Wigwrm 8,.
fh« a®%work oo«»l®i«ats and ©twl-mleirts siretiit faraaetera for this
AAAr
Fipira S, 0«a»ral aoial-dsriwi %r«aslstor ©Ireuit
eirottit «r® reXat«d as followsi
fii - gi • S« »
Ub - -Sa »
Sax • S4 - g8 •
aai
Sun • Ss • §0 •
fh« flquimleat oirotjit of Figure S em fee used for aay eoantotion.
1. l^uiTaleat Cirouits
On® of tfe# first ©oaneetlona «a®i with tranaiatera was the
It
groaM«4 ba»« eonjaeetioa^, wi%b th« etwiwleat eirenit of Figur® 4,
fhis la frofcaWy tfes most familiar ©fttitmleat ©ir©uit at fr®8«nt.
fh9 pari««t®r sufcesrifts w«r« choaea to ©orrespoai to th.® aotaal
t®mljial iasigaatioaa aa tth&m* fh« awbaoript m oa r. i» propar
hm&m0 it oottaa froa a nutttal iap«iaa@a tarn slAilar to ps. ia
m&mm. tmlbaa.
rm^x
lector
rbaae
figara 4. Maah-^darifad aqaiwlaat ©iremit fmr prouadad baaa
Siao® tha aquivalaat airsuit ©f Fifwra € way \)9 uaad in aay of
tka three traaaiatop ©oaaaetioaa toy axahaage ©f tamiaala and proper
iiaatifieatioa of the witaga of the e^uimlaat generator, it aay
appear that oaly this partioalar eqaifalaat ®ir«»it is aaeeaaary*
^.iB^ar mi lirohaer, op. ©it.
IS
lowswr* ®ou,T®nl«ae© la ©irouit amlysia auggeets that th© Toltag®
of th® aetiv® ©leaant be always la tema of the inpat otirrent Ii.
SottS®q«@tttly, two aor® nash-deriwd ©qwimlemt eireuiti eaa be
0QHT®ai®atly UBM.
fke equiwl«nt oirouit fittiag th® gsaeral fem of Fig«r« 2,
for tb® grom4«d «»ltter 0oaa®0tioB, oaai bo foaad witfeaat tatroduoiag
nm par«®et®rs. fb« efuatioas for tfe® eirottit «f Figure 4 eooneoted
as grotiad«d emitter ar«
®i • (rb+i-«)li • , (11)
aad
®a • relj, • (ro**'e)Iji "* • (12)
f|toa r^arrangiag th«sa aqaatioas, w® haT«
% • Crb+Jfe)!! • *•«!« » (is)
aad
»« • - %% • (14)
iquatioas (IS) aad (14) atiggest aa ©taifalsat oirouit whieh fits
tli« fsasral torn aad whieh is ab&m ia Figure 8. itaides haviag
tb# aotiw «l«m®at ia terms of tha iafat baas eurraat, tbis
staiTOlaat eireait has tl» fQrth®r adwatag® of aot iatroduoiag
asir parameters.
14
-r^Ii *"b r^Ti.
o—VSA/—
Figta*« S. Me8.h-d»riTa4 ©Ireuit for ©ro'-aiB^ed «ltt«r
th® afuatiotts for the ©tremlt of Pifare 4 eonaeeted as grounfled
ooll«@tQr sr®
% - (r%^ro)Ix • {r©-ra)l« # (16)
aad
Is - TqIx * (ro^re)Ig - r^I® . (W)
Upon remrangiHg etuatioas as
% • (rb*re)lx (ro-ra)!® . (17)
and
% • (ro-ra)li • • ikli » (18)
tlj® ©ireslt of Figur® 6 is saggseted, with the same admatagos as
thos® of Hgtir® S.
16
rail **0 -/""X +
t>-VsA/ t
*'0~''lBl
Figure @. M9tk«^eriT«t etnimieut 0ir@ni% for greflMi## ©ailtetor
C. Sodal-Iteriired itttivftl«Bt eir«mil!8
the «®eoBd grottf af trans is tdr etmiwleat ©ii^aits eonprise
those based mpon the »iiil eii^tiaas. Oirettits ©f this type were
first itttT'Odmoei by L. J* ©iaeolett®^ of th® .MA labo^mtoriee.
fhe siromits proposed by hla iiaTolye e@»plex systen of aotntloa
iMised «p0-tt three sttbseript® for s*®h ooefPleieat. -Although the
e^tm is faalproef, its pr&etiembility is questiosaable.
Oae way t© siaplify the aotation is to write the fwraaeters
^I,» J, SiaoQlette. f«rmi»iofy aai efttatisas for liaear aetive fottr-teraiwftl aetwerfes iiK)laii»f traaiisters* ISA Mmim, 14t 2.f-4®. ItSS.
16
of th« iK>«ial-d®riv®d equi-saleat oirouit la tearwi of th© parameters
used for th® aesh-derivod otuimleat olrouits* fhis mathod will ba
usad throughout this fflaauBsript,
Tha laodal-derifad afuimlent oirouit for tha grouadad base
oonaaotioa «ay be easily obtaimed from the oirouit equations of
Figure 4, fhes® aquations are
% " <r8+ri|)lx rijla # (19)
aad
% " (i*b**'%)li * • (20)
Solvlag these Iwo equations for «ad Ig in terms of % Sg
and rearraagin^ th® results. gives
ge*Pb ^ r-b Ii • |p| Ix - |j,j 1# , (21)
aad
lAere
|rl " (r0+r{,)(roi'rb) - ria(r^*rBi) >0 . (23)
Iquatioas (21) aad (28) suggest the equl'ra.leBt oirouit showa in
Fipire ?. fhis eirsuit fits l^a general nodal-derived equivalent
eirauit of Flgare 5. It has the advantage of having the eurreat of
the astiire elfinaeat in terns of the input wltage %.
Ihe grounded ealtter aquival^it oireult ©aa be obtained in a
similar mnaer. Solving for Ix and I# from Iquatioas (11) and (IE)
IT
Figure 7. ioi«l-d®rlir#4 eqaimlert ©irottit far tke gro«ad«i 'base
results in
kl
and
la - - li re
|r| % • |r| li •
Iqiuattoas (24) and (2S) suggest the oirauit of Figure 8.
ro-ra
Figure S. Kodal-derived enii"raleat oirawit for the grounded emitter
18
Solution for 1% and Ig ftrom Iquatloas (15) a,nd (li) produees
th« eq»&tio5a«
|;.| % - -yi Sji , (26)
and
(-)
I<juation« (26) and (2T) a^iggeat thw atttiirsi,l®nt oiromit of Figure 9»
AAA/
Pifar® S. lodal-d«rlT«d equiml^t oireuit for the p-otmded 6«ll«0tor stag®
It should b® aotsd that as etmivalsnt olrouit is not limited
to the pirtieular kind of transistor oomi®®tlon for whioh it was
dtriirad. la®h equi-valeat ©iroait eould b® usad ia any of tJw oon-
neetions. this la tru« &r bo#i muh and aodal-derlTsd eircults.
Flgw# 10 8ti®Hiari»«8 th« work of this aaetloa aM is Inolttdad
m®roly ibr osnfealaa©®.
19
o-AAA/—pAAAr-( V-®
•«o
ar)o«nad«d 1M»«
'b o—v\/v
-r^jlx 15T
VW
I)s , l r
Chroundttd .«ad.tt«r
-e + ju|.
rjgli
Groundwd <»olX»«itor
M«*b-d«ri-r«d lod«l*<l«riv«d
Figttra 10. Transistor aqvii^lftnt alrouite
20
P. 1-wilaAtioa of th® Ifiil'mleBt 6ir®«it Fe^rtm^tets
IftTing »«l0otei tit® traniistor eqmi-fmlsat ©iremits, tt mw
bs0oia®s mtsmaary to th« etulvaltnt eirealt para»«tsrs.
this Is easily 4©n« th® a®tw®rfc ®©«fftei«Bt8 pertainlag to
tb@ nmh or aodal etuatiom.
In geaeral, teoowia^ tii« »twork eooff'ieiaats f©r oa« type of
ooimeotioo of the traasiitor, it la poselhl# to oaleulate the aetwork
eoefflcieats fsr aay other osmsstioa^. fhis Is partleialarly
a<Jaftable to the eitti-ralsat etreuit® ©f Figwe 10. la these
oiroults, all network ooej^ieieats are writtea ia tems ©f the
eqaiiraleat ©Ireait paraaeters of the *ash-4erlTe4 grotmiei hase
stag®, fhis ia stneoaarised ia fable IS> It the aetwork eoeffioieats
for aay oae ©©aaeetioa are kmm., the efttimleat oiroait fArimetera
r@t Pb» eiml«atei." laowiag these -parameters, aay
e%uiml«nt elreait eaa he easily ohtaiaed.
fo evalaate the traaslater fareaaetera, eight aeleeted P-I«»P
junetioa traasistors wei^. ©eaaeetei as grotiadiad emitter m& the
network eoeffleieats fertaiaiag to the aodtel efmtio'as were
I measured « All aeasurwteats were made && the Seaeral Sadio fype
1l. 0iaoolBtt©. lermlBology aad eq^atioas for linear aetive fottr^termiaal aetwerks iaeludiog traneistors. WM, levtew, 14i 28-46. ItSS,
Smilleaia, @p. olt.
%ee Appeadix A.
n
I s I M 'U 0
1 !» u
•H s I I I u
I
J u
if
I
1
5
O <j.
I . r
©
I a
33
Hf
Ts ^ 'H
si f a.
I
«" f
M S.
^ I
. «4 1^ • g
|s!l i-« «9
8 3 S S «
0 i-l -#
1 ^ ?
1 1 0^ 1 § i 1 1 s t
i i
* xp a 1 HI 1
09 § 1 t
M 8 s 0 to 0
i « e m <0 ig If s
S 3 i I i I i $a «
M r4 g »-0 1 •1 $ fr- i|
CM 0 0 rt 0 te r4
r4
s s ©a 1 1
«« 1100
1
0 « 0 • 0 • © •« 0 • ©
* o-« 0 .«
f 1 f4 1
1*4 1 1-4 1
rH 1 iHI 1
g n § 0 i 0 © 0 a 0 lt 0 0
t H? t t U3 1 t f i t
S to «o e ••-» S rt ;5 » iH
0 0 0 0 0 0 • 0 0
g K g 8 0 IS
3 » g g
cm w » iO
o
£6
r »
f §•
I
»< *« n i p s isk<
h»
I
o o (b
3
3 5 f -1^ 1 ^ t? $ i s f o
So m
is
1 m « m «4
8 1 1 m « m «4
i S
i
s,
r §
I
£»
s
a.|» 3 °4
5
i i.
I %
i
,? 4 4 4 » i « n »
•p
i-o 1^ w
Q r
!?
f I I
j* 4' .'• i n ^ - I »
^ ^
4
i i i«i m 03 es) 0 m '3 1§ §
i - f s i s i f
i § i § 1 1 1 ^
s*
i
f I t
f 1^ 1.4 « s
22
23
o-A/W
18,700 H afaoa.
8.27 \x nhoa
AA/v-
O.S82, (i i8ho«< 1 10 ''e
eroundvd baa*
34T otau
24.S ofama'
-7.19 X 10®ix
ohms 1570 mhos
0.582 |i a^a aa^t
8.26 mfaoi
ll.71 X 1 lo'^e
QrowsdQd «Bdtter
7181 ohnia
<^aaa^
7.19 X
10®ii
aaar4''"Y-> 24.5
0.582 (1 nhm
1570 u a^a WV
17,100^ fl bhio«< O
-1.71 10'^
Orounded oollttotor
meah-daritqd Kodal-dariTed
Fl£ur« 11. BquiTalent oirouita for a typical junotion tranaiator
24
S®l-S, fae«»» fttTs® lri<ig®» In «a©Ji '©ase.th® oolleotor' to fitter
TOltag® was set at fi-r® "folts d-o ant tfe® d-o bass to emitter
voltage wa« -wiried to give a oollaetor oiirreat of one milliampere.
fMa was ooasidered to be a typical bia« point.
fable I sttwaariaes the results obtained ia measuring the network
eoeffioieats. It will be noted that eoaaiderabl® variation exists in
the mine of eorresponding eoeffioieats. type QtTEl transistors give
slightly higher power gaiaa thaa do type S[722 transistors, however,
the dividing liae is somewhat obseara.
With the help of published imterial aad amnttfaeturer^s iafor-
fflatloa, it was decided that the type ®7EI transistor of line 5,
table I would be ooasidered as the typioal transistor^, therefore,
all ealeulatioas reqairlag valaes are aade aaiag the aeasured values
of this transistor.
fsiag the aeasured aotworic eoeffieieats of the typioal tran
sistor of fable I, the equivalent oirouit parameters r^, r^,, r® and
riR were oalealated. IVoa these oaloulated values, the network eoef
fioieats oorrespoadiB^ to other equivalent oirouits were evalmted,
fable H:,-sww»riies these.
IVoa the evaluated network soeffieieats of Table II, the
Qorrespoadiag equivalent airouits for the typioal.transistor were
drawn and summarised ia Figure 11.
Ifeiytheoa lanuftioturiag, 'eoa^-ny. terasaRalusa transistor data sheets lo, -tS8l aad io. -1884, §8 Chapel Street, »ewton S8, Massaohusetts* lov. l3Sg,
2S
If. SI10» StASB flAHSISfOI illSfltS
A» ®«T«l0pR«it of F««dl»&ek Oiroults
fhs trftusistor is iahereatly t feodbftek devioe. this ausiy be
seezi by tjoasideriag ttoe general »«sli-d«ri*ed e^ui-rsleBt ©ireuit of
Figure 12« lere it is sssaaed tiiat ths transistor is supplied by e
r^lx
Figure It. ©eaeral mesh-dtriTed equimleat eireuit with teimimtloiw
generator Ig ©f iateraal resistanee 1^ and temineted ia the
resistaaee I|,» fhe esqpressiosi for retura dlfferenoe^ for is
^See Appendix 1.
B. W. Me» Xetwork aanlysis sjid feedbaek emplifier desiga. 1st ed. S. %A VostraM lae. 1S4S.
flionas, &p* eit.
Z9
r . i - ; j . (28)
la terms of %h» H«twork ofoemeleats, aftiatloB <Bi) aay fee wrltt^
as
¥ m I , (29)
It is «Ti4«Bt froa afuation (IS) Ifaat f««dba«k «ay b« asgativa or
positive 4«p«»diag ttp©a th® siga of f^thermora, faadliaolE eouM
l>« aliaiaatai if n® ®ottW ®llaiaat«a.. ifcaBfaatttring taoteaigaaa
ean be wsed to eontrol to eliaiaate it^.
Similar reasoaing eaa h@ apfliei to the geaeml aoial-doriTod
etwivalmt eirauit. to thia oase, it oaa 1>e atowa that feedliaek is
dtt© to the p'esenee of the gin^ e09.ffi®ieat,
Feethaek la a traasistor ©irewit aay %e oontrollod through the
r^B or gxm ©oeffieimt, toy oirewit additioma ioh oha'sge theae
0o»ffi®ieats alto change the feedhaek# Additioae dt ^is kiad will
he referred to as added feedhaok, to diatiagttiah hetveea that
feedback whioh i« iahereatly preaeat «ad that whi«A Is added.
1 Ahraham gohleai aad larry Oweas. Tariatioa of traneiator
paraastors with t<»peratiir®» ^ftro®. of the HI, 40i I4f2-1476. l@S2.
. iarly, Of» eit,
jr. A. M0rtoa» 'Prmmnii stataa ©f transistor develofttmt. Free, of the 111. mt It52.
n
fh@ ©irottit of 'figvete lS(a,) r®fr®s«ttts a straightforward asthod
of iMtreasing f«®dbaelt, ii aesh-derlvsd ®g«iital®Bt olrouit Is shown,
hmmsB th® typs of f®#dhftolE usai ii most easily haadlsd hy aesh
©qwatlQW. Irltiag th® ©quatloas for this airoult without
t®raiimtio» glT«s
% - (ri»r,tH,)Ii • (r,«S,)I, , (SQ)
ai3^
»ii • . (si)
ler®, staadard fi3«r-t«r»taal astworl: aotatioa is usad as showa in
Figure I, Coasideriiig th® mm eirowit 9l«K®Kb. to b« a part of
th® «q«iTal#nt eir««lt, w® ®aa d«fia« th® a«w network oofffioiwats
to he
"• *•! + >*8 • % *
sin • 8 •*• % » m
sai - r4 • r# • ig ,
aad
tea * *•» * r» + % . '
l^om the relationships of l^mtioa (32) we see that is added to
eseh of the network eeeffleieats aad that Rj.jg (now replaelag r^a)
eaeaaot he. ooatrelled ladspeadmtly*
Feedback ©an also be ooatrolXed by the ^se of traasforawr
©owpling betweett loops as «hmn by Figures 15(b) and lS(0), la
this «ase the traasformer saa be eoaaeeted either for positive-added
26
r^ii
Rl
Id«al 5 Trana-
fomer
(b)
Ideal jig Trana- ^ fk>ra«r
(e)
Pigxwa 15. Series transistor feedbaok cireuits
2i
or for a®gatiV0-aM«i feedbask. B0oau8« isli® traaalstar aires it
oontaitts ftedbaok' arlgiaally, traasforaer eoupliag oaa b® used to
enh&me, or elsaag® this fssdbaak .fro® positiw to aegati'^a
or nagative to foaitiv® as th@ oaaa aay b®. lafarring to th® natwork
ooeffioiaats far figuras 15(b) aad lS(e) listad to labia III,
iasraaiad, daoraasad, or ohangad in siga, dapandiag upoa th® siz® of
tiia faadbaek resistor (% or %) iatroduoad aad lAia toras ratio of
the trwasforaar. It should be aot ad that %a, or doaa aot ohtt^a
whaa the trans foraiar ooaaaotioaa ara revarsad.
fha faadbaok oiroaita of Figure 15 raqiiira a rasistaaoa to be
placed i» aeries with r^, rg, or r^» therefore, we shall ©all these
oiroiiitB "sarles feadbaek eirouits"* fhia shoaM aot be ooafused
with serias faadbaok oirouits as dafiaed by Itede^.
Feedbaak oiroaita whieh are most easily haadled by use of the
nodal-dariTsd ©taimleat eirauits are showa ia Figure 14. fhese
oiroaits will be oallad "pkrallel feedbaok oiroaita" beaaaae added
faadbaek requires a ooaduotaaee to be plaoed ia parallel with g^,
g®,. or Sa-
table 1? swBMi&rijEes the network eoaffioiwits for the parallel
feedbaok oiroaits. It idll be aoted that these aatwork ooeJ^ieiaata
^Bode, Of. oit
J
m
«?l^ m
m + • * *
« u S # h
* 4 * * 4 m
tn «
1 1 m < | m 0?f M M + * f + 1
.f w k
m u « t* .?
* * * • +
^1 H ijS'I m f^l m Ssffj* • • 1 • •
m « U
« i« « u
«§• * + + * •
to »? !» »<
jBt t<.
« tk
* • + * + . t4 $4 »<
rt »<
f4 t«
•4
Jf <3?
s 1 1 -s
! M m 1 M m
n
s .s
a -sw w thl »-(
o
f*
s 1 s i f
31
i
(a)
O Id«al O Traits• O fomsr
o
o
itl (b)
Waal 0( Q Traa«-0 Olg
O
Htl
Figura 14. Parallal translator faedbaek olrouita
table IV
ietwork Ooefficiaats for Par«ll®l F««4b*sk 0irealts
Gireait fr&mtormsr Oonasetioa
fsadbaek £lm»afe
le^work Coeffioleata
%*
figare 14C*) —
Flg«r» 14(b) As almim
M@r@rs0
Flguro 14(e) Ae sh&m
tevarsed
%.
%
%
%
%
cfl+gg'nig)
csi*«s*%) '(Sm-m)
•c-s4*s«^»%)
<g8+is*%)
cgg*ia*s^9i)
(g8*sa+®8)
33
ar« vary stoilar ia foi* to th« aetwork ®o«ffiolsnts of th« aerlm
feeilbftok ©iromits. this is «xpl«ia®d Ijy the ds«lity rselatioashlp
wMeh exists b«twe®H th® a»8h- wsd aodal-derifod oqwivalsat oiro«it*
th® most iaportast f®«dbask ©irewits of Pigur«8 IS aad 14 ara
th0 oirssttits not raqairiag traasformer#. Wiar® traaaformsrs aro
wsed, th® aatoral advaatagas whish th® traasistor has ia sis®, ireight
aad 0981 ar® 8a®rifl®«d* Hswe-rar, wher® thts® adtuatagos ar® act
iap>rtaat, traasformars oaa h« used fyr more T®rsatil® eirouit
dasiga. Se-rsral types of traasformars d9sl®s®d partisularly fbr
traasistors haT® h®ea wid® amilahle^,
1. S®laoti0a of Sirsttit fsrainatioas
:jBp®danee witohii^ is oa® of th® friaolpal difficulties ia
desigaiag transistor eireaits. Ws.@n dealing with vao«um tahes at
low frequsaei®#, the iafwt imfedan®® is usaally ©onsidsred infiait®
ia grouaded eathod® or groandod flat® ©paratioa. Toltag® gaia is
0oa8id®r@d th® ali-iaportaat factor bseaas® pow«r gaia is Meaaiaglsss,
la traasistsr ©ireaits, th® iapiit iapadaae® is net aagligihl® aad
mst h® ®oasid«r®d as a load for the preeediag sts^.®. fhia is
Staadard frsasformer Corpswtioa. Staaeor trwisistor trans-fdrmer data sheets. . Ibrm 4@2, t-S3 aad Italletla So. MS, l-fH. SSSO llstoa Avoatt®, Ohieago, Illtaois. Ifi®.
M
similar to fromaded grid ©paration in vaoutm tabes. Power gain
reappears in these eases as tise mast fwndiitental ©oasideratioa of
gain,
in designing traaaistor olrealt8,-e^ry effort should be wide
to witeh ttoe traJMflstor in its iaiage ispedaaoea. this permits the
BaxSaaia allowable pow®r gala, fkilure to reeogalKe this may require
additional etages in the over-all mplifiar#
The use of transformers greatly atmpliftes the problm of
•aatehing. lowever, the additioMil weight, apaee, and ooat Is
undesirable.. Shis is eapeoially true la aiaiaturiised ©ireuits for
whieh the transistor is ideally suited. Stability may also be a
problem when traasfomers are used.
In eases where transformers eaanot b« used, aatohed eonditioae
are seldom obtained* Ihere only one stage is needed, it is
sometises possible to dasign the drivlag eouree and load to aatoh
the transistor. In eases where transistors are easeaded, the
aiatohlng of souree and load does not solve the problem, A ais-
aatsh still exists between stages. A better »eteh eaa be obtained
ia easeaded eireults by alternating stages trom one type eonaeotioa
to another, fhis will be disoussed in Seotion ?-B.
In th® diseussion whieh follows, we will be priaarily eonoerned
with Biatohed oonditlons at th® iajwit and output of aingls-Btage or
©asoaded transistor sireuits.
Sft
e. Amlysii of eiwttti-fcs Coatalaiag Series or fturallsl F««dMalc
1. the general traaaistor ©Irgatt
4 syatswitis apfroRoli to tk® mnalirsls of f«®dbaelc and stability
oan b®st b® mad® by first ooasldsriag ths g©tt®r®l traasistor oireaits,
&®a®ral etuatloas psrtaiaing to th.®8® oireuits eaa b® derived aad
sasily applied to spteifi© ©asas,
Figur® 12 shows th® gsaeral ffie«h«deriir®d tqaivaleat eirouit with
temiaatioas. Ig is th® iatsraal impedam® of th® drlviag souro® or
th® outpat iapsdaao® of the pr®0«diag stag®. Il is th® load im-
p®daao® or th® iapat isifadan©® of th® auoeeediag stage, fh® a«sh
9%«atioa® for th® oireait ar®
Mere rij., r^a, rgi, refresent the astwork 0o9ffi©i«ats of th®
transistor whea iapmt and output teraiaals ar® shorted* fhia
ao-bfttioa will b® adhered to throughout.
fh® iaput aad output impedaaoes* m^easured at th® traasistor
terminals, oaa be writtea as
(ss)
aad
q • r»xlx • (rt«+%)ig . (S4)
®i» • A« (ss)
ig • 0
m
am
% • o
(36)
ler® th« fiubseript 1 or o ieaignatss input or output resiataaoo and
th® subsoript a daBigaatea tfe® mosh-dsrivad aqui-mlsat olrouit. The
s^bol A® raprasants tha oirauit datamiaaat obtainad trom
aqaatioaa (5S) moA (34).
the wltaga, eurrant, aad powar gain of tha translator from
input tarmimls to output taraiMils raprasantad by Ag, Aj, and Ap
raspastlTely, ara
fhaia gain axpraaaions must be properly iatarpratad. Bquation (37)
raprssants the mtio of output wltag® to input toltaga. Both
TOltagai are measured at the termiaals of the tranaistor. Iquatioa
(SS) rapraaaata the ratio ©f output aurraat flowing in the load to
input aurrant supplied by the sourea. Ifuation (59) is the product
of these two aad repraBaabs the rati© of powar out of the traaaiator
to the power supplied to the input t8»4nal8 of th® transistor.
4;^ • is " ^a.a-% % pia. ('•«#'*'%,) *
(37)
(S8)
and
(39)
3T
In ttost oasssf th,® retmra differenfie ©an be us«d as a meaaur®
ot saaaitiTlty. If gala is dafiaed as ia equatioaa (S7) or (38)»
thaa th« sanaitivity would be ealoulatad on the basis that ooaetant
•sraltag® or ourrant was suppliad at tha iaput terainals of tha
transistor, this is th® sam® as sayiag that tha input iapadaaoe of
tha transistor doas not ehanga with ohaagas in r^, fhis is not true.
Iharafora, as a mora uaaful aaasur® of sensitivity, the Toltaga or
oarrant gain will b® defined as
aad
ala = - . W
where Ig is the generator voltage of tha sourae as shown ia Figure
IE and Ig is -ttie ourrant of the ©urrant-souroe aqwiTalent. Ia
ail^er ease* Kg must be iaoluded in the ©ireuit. This appliea to
tha aaloulatioa of return differanee aad sensitivity only.
If the return differenee for r4 were used for eaoh of the three
ooaaaotioas of the transistor, the return differanoe would have a
different meaning in eaeh ease, this is explained by the faat that
is not found ia r4 alone (see fable II). On the other hand, if
return differeaoe for r® were used, thea there would be only one
meaning. As a meaaure of feedbaek, the return differenee for r^
would indieate the amount feedbaok has reduoed tha gain in teras of
the grounded base parameters. As a measure of sensitivity, the
m
retwra diff®r®B©« for would inilcat® the sffeet that ohanges in
Tm. hfiive te ©haagiag gala. fh« r»tum ilfferaaoe for r^ will ba used
for all aash-derived eqwiTalsnt elrstilts. Both retura differsase and
seasitiflti' will h® derived 8#,pirat®ly for ®aoh ooaaaetioa.
fh© stability liiait for th« traaaistor is datsraiaed by the poiat
at Tifcioh th® dataraiaant gom to zaro. for the general mash-darivad
oirouit this oaa be writtaa as
A» • <%*rii)(r«a«»>%) - riaraa. • 0. (42)
All of the above expressioas ©aa also be used with added
fsedbaek. thia is handled by wsiag %a., S^a, Mgx, and f*'®®
fable III to replaea rxt$ r%,s* **»« respeetively.
•for aatahad ©oaditioaa, where l|a • % • Ij,, equatioaa
(36) thrott# (8t) are greatly aiaplified a« follows i
»i» - . («)
»om - . «*)
as. , («)
ai,.—Caavb* , (46) i • (l-ft)
aad
•'^•aaala •
In these expressions, a is defiaed by
a = £i£2l, (48) rxxTMM
For the eireuit to be stable, a must be less thaa aaity. fhe poiat
S9
of iastafeility for aatoh«d osnditioas oooars at
i. (49)
Wiea addad f®edbaok is usad, th,® aIjovs exprasaions for ®atohad
ooaditioas ar® Talid proiridlag tha aatworlc eoaffisiaats of labia III
ara wsad#
Figtir® IS shows tiia gaaaral aodal-dariwd aqulvalaBt oiremit
•with termlaationa. fbr aaa© ©f haniliiag, th.a driving so«r©® ia
aasmad to ba a mrrmis sotwoa Ig ahaatad ty tha eonduotaaea ®g.
Tha tranaiator load ia rapras anted by ©!,•
For aatehad ooaditions, tka aquatioaa for tlia nodal-darivad
atittimleat airouit, aaalogoua to aqaationa (4S) aad (44) oan ba
writtaa^ aa
L
Figura !©• ®aneral nodal-derivad aquifalaat eirauit witJi tamiimtioaa
®ia * (SO)
and
son - » (81)
40
whera th® 4 or o subsortpt iasignatsa i»put or output ooadaetanee
aM th® a 8igaifi®8 th® aodal-ieriTsd ©quivalsnt oircuit.
fhe tquations aaalogous to equation# (46) through (47) are
In thsaa axpretsiong, b If iaflnsd as
b = |4S5Si. (66) sa.a.g#8
For aatehai ooaditioaa, the eirouit is stabla whan b is leas
than unity, fha point of instability is than datermiaad by the
condition
b » 1. (66)
If addad faadbaek is to be uaad, the network ooeffiolants
%8J ®ai ani^ ®s® table 1? must b® substituted by $xm>
fei and gjgg respeetiTely for these relationahips to r^awiia "mild.
It would again be desirable to us® the return differenee for
ra when aaloulating return differenee for the nodal-derived equiva-
laat elreuit. lowerer, due to tte extreme oomplexities in oomputation,
it is neeesaary to introduce a nw paraaeter. Ih® parwaeter chosen
is whioh is the aegati-re of §4 tor the grounded base eonneotion.
% -i "SMx/sm
•gfi/w
(62)
(ss)
and
apn " %ialn • (84)
41
Ih® retttra dlffereae® for will ba tt8®a for all of the nodal-
d«riT®4 ttairaltat eiretilts. Both retwra diffsrene® mud ianaltitlty
will b® d®ri-w<i sepirately for «aoh ©ai® that follows.
2. fh® groTOigd. bag® trantistor elreait
Without added f®«dba®k, ths laatohsd irapedane®® for a typieal
jttootioa transistor ®oatt®at«d as groaaded ba®« ®an b® calculated
fro* s^mationa (4S) aad (44) using mla®» from fable II. fhey ar®
8i»b • Sf2(l-0.»S4}^^ - I4g ohaa. (6f)
moA
Roab • fi&*000{l-.0.8S4)^/® - 800,000 ohm®. (S8)
fh,® aubiaript b has b«®a added to i»di©ate ^9 grouaded baa®.
Ih.® translator gains for ajatebed soaditloaa, uslag ©quatioaa
(4®), (46) a»d (47) ar® r««p®otiTr®ly
i • (l^s.sm)^^
_ 7It,O0O/7SS,OC» _ « ^ittb " -—
1 • (l-0.s64)^/^
am
Ai^tj • (1400)(0.662) • 924 . (61)
rfaa retara differeBO® for r® for the |pro«nded ba®® meah-
d«rlT«d 9t»i'ml®Ht eirewit ia
fj^ - , (g2) AS -'1.*
wh®r« is the vala® of tk« oiretjit ieteraiaaat where r^i is 8«t
to zero. With reftrsmse to table II, a good approximatioa caa be
made by negleetiag the ammi. term in the ienomiaator. iKking
this apfroximatios, the return differenoe mader matehed eonditions
beoomes
fab: 1^ (@S)
IwluatiBg the return differeno® with the help of Table II gi-rea
• O.SM . (64) 8(l-0.864)^>^
1 • (1-0.ss4)^/^
fh® seaaitivity f«r in this ease is
1 d^iab . y« *
r»x
Here, a qA appiroxiiaatioa is
(%*rii)(r8#+ti.) (66)
^ 1 .
With this approscisaitioa, the aeaaitivity for mat®he4 oonditioas is
®mb (66) 1 • (l-a^)
whiah is the saM as the express ioa obtaiiwd for retara differeaoe.
For the grouaded base aodal-derived etuivaleat eireuit without
43
•added feedbaefc, the jreturn differenoe for is
(ysxxxwl.) - fa.6.x _
Aab {%*gn)(s»a*®L) " Sa.«
wiiere A&b is the aireuit deteraimat with -^i" set eqttfil to «ero.
48 ia the previoae ease, refsreaee to f«hle II shows tlmt the second
term ia the deaomiaator can he aegleoted. fsiag this approxiaation,
the retm-a differenee for *teh®d eoaditioaa oan he written
1 • (l-hb)
Without added feedbask, this has the same mlue as equation (64).
"»>>= ips- '®"
ThB «enaitiTH;y for Is
%b • ' »
^ inb ,
a(^) • ainb
)(!««•%) -(69)
_Ssi"*Si.a.
OKitting the first faetor, the seaaitirity for saatohed
ooaditions beeomes
(70) i • (l-b^)^/2
whidbt is the saute as et^ation (@@)*
Without added feedback, the eire^it is stable sinee afe or b^ is
44
always 1®8S tliaa uai-fey.
llgare 16 lllustratsB ths ©ffaots of adding series feedback to
the. grouaded bat® traasistor ©ireuit. Siaoe series feedbaofc is most
easily iiaadled by t^ aesb-derived aquimleat oireuit, tb® network
ooeff lei eats B^x* %».» Rai fr« table III were used in place
of yix» attd rjga rsspeeti-rely* Tq simpli.!^ the problm, it
was assttaed that 1 • 1 for those elrouits ooataiaiag traasformers.
Ihat this assimption does oaa b® seaa fro» the aetwork ooeffioieats
of table 111 aad the eireuits of Ilgtire 18. With the traasfor»ers
©oaaeoted as shown, the aetwork ©oeffieieats have the saa® fora ia
all three eases.. This represeats added positiw feedbaok aad its
®;M'eet upon the oiroxiit eharaeteristies is sbowa by the solid curves
of Figure li.
With the transformer reversed, the aetwork ooeffioieats of the
©ireuits of Figures ISCb) aad 1S(@) have the same fora. this repre-
seats added aegative feedbaek aad its effeet upoa the oiroait
eharacteristies are showa by the dashed earves ©f Figure 16,
It will be aoted that both positive aad aegative feedbaek tend
to raise the iaput impedaaoe. fhis is as expected siaoe i®
iacreased sharply whea either positive or aegative feedback is added.
Ijga* ott ^5he other haad, la TOt greatly affeeted by feedbaek, the
output impedaaoe is therefor® controlled prlwarily by the factor
(l-»a^)^'^®. this explaias the decrease ia the output impedaaee whea
positive feedback is added,
Fower gain decreases for aegative feedback as would be eaqpected.
45
lo^pr
10*'zr
1.4
lllLtoh«d Output lBip!8d«noes
Poslti-r* Fvedbtiok Added
Hegative Ftadbaok Added ^ /
: • : J. 10^
/
1.2
1.0
/ Mktehed Input / ' ^pedanoe^
/ / —i
10^
10®
10
Power
Return Dlffereuoe
10 102 105
Feedbaek reBistanee Ej,, fia or (ohaui)
Figure 16. The typloal grounded base Junotion transistor olrouit with series feedback added
m
Ibr positive tfe®, pewar gaia iaor®aB«B oaly slightly at first
and th«a also iaereases, Shis &$m h® attributed to the rapid inoreasa
ia %3. which affaets th« voltag® gaia as shown by aquation (48).
iqmtioB (SS) Twis used ia ©aloalating the ratum diffaraace in
Figur® 16. the aaximim arror introduaed by th® approxiaatioa is less
than one peroant fQv the rang® of feeibaek rasistana® used. Z4Jc0«ri8a
ti» aaxi»w error introdueed by the appro3ci«ation for aensitlTity
(efuation 6i} is lass than an® aad oae»half paraent. • these errors are
subtraetive so 'ttoat the aurva for retwn differaaee represwts
sansltiTity within one per®eat,
^en series feedbask is added, the eirouit will be stable if
%iSa8 - > 0 . (71)
this eaa easily be determined by smbstituting the network ooeffioients
fr©a table III int@ etw&tlon C^l)* It eaa be shown that Itoe oirauit
is stable when I • I.
Parallel feedbaok is most easily handled by the nodal-derived
et'Oivaleat eireuit. figure IT shows the effeat of adding parallel
feedbaek to the gromded base eonneatioa. the ourTes are drawn for
the typieal jtmetion transistor with I • I. the solid euTTes
represent the eharaateristias of all three parallel feedbaek eirouits
of Figure 14 liioa the added feedbaok is positive (transformers eon-
aeeted as shown), Ihe dashed ourves represent the ©haraoteristios
of only those oireuits eontaiaing traasforaers aad with the added
feedbaok negative (traasfomers reversed).
47
1.4
Matched Output Mpedanoe
1.2
Return. Difference
1.0
PoBitiTe Feedback
Negative Feedback
'Power Gain
Ibitohad Input Impedanoe n
0.6
-Return Diffarenee
0.4
Feedback ooaduotanoe Gxt ('s (nioromhos)
Figure 17, The typical grounded baae ;Junotion transistor oirouit with parallel feedbaek added
4S
It will b® noted that the eharaoterlBties of the parallel feedbaefc
eireuits are ©onaiderably different from those of "^e series feedbaek
olrouits. fh® matched iaput impadanoee now remain aoaawhat constant,
espeoially for poaitlTe feedfeaok. Shis is explained by the fast that
©ii ehwages oaly slightly with feedback and that th® variation in
input impedanoe is oootrolled primarily by (l-bfe)^^. On the other
hand, %j| iaoreasea sharply with ittoreaslng feedbaok. We would expeat
the output impedanee to deorease aooordiagly. fhia is shown by
Figure IT,
Power gain deoreases in both oases. Ihis is due to the rapid
inerease in as feedback is applied (see equation S4).
the approximtions made in ealeulating return differenoe and
sensitivity in eiuations {®8) and (fo) are good for ell Talues of
feedbaok eonduotaaoe used, fhe ourre for return differenoe represents
seasitiTity within two percent.
With H • 1, the oirouit is stable for all -Wkluea of feedbaok
resistanoe used. If I / 1, stability is represented by the condition
%i®«8 - ®ia%a.
where the network ooeffioients are those of Table IT,
S. fhe grounded emitter transistor oirouit
the matohed impedances for a typioal ;junotion transistor oon-
neoted as grounded emitter without added feedback can be calculated
4S
fro* ®q,ma%iom8 (43) aral (44). Subgtltwtioa of for the p'otinded
fitter eo@ffi@i«Hts trom II iato these «<iwationt gives
Siae • •«? oi»s . (73)
and
Mom » i6»600 ol^s . (74)
fhe transistor gains from efrntioas (46), (46) aad (47) are
imrn " -837 , (78)
^Sbm ** ""4»71 f (76)
aai
Aftae - mm , (77)
The r®t«ra differeaoe for r^ for the ateah-deriTei eqttiifalent
©ireuit ii
a»e (%*j'l»*re)(r0-r»#ra#i]t) - r^ir^'Tu) %e * T-y " 1-" - • v7i;
lAm (lg*r^*r«)(p©*ire*»i,) - r«
Patting itt the ooaditioa of misohsd tentinatiag lapeianses aad
aeglaoting the aesont tern ia the €®no®iiMitsr give®
?«= —= • (79) 1 j,
Svalttating eqwatioa (79) with the help of table II flv®8
oatbs . (80)
the eesaitivlty for r» mn b® writtea
*'-sx rax-pi#
(%*rh»re)(ro*rtt*re'»-l|,) - re(re"ra)
(%'«'ri)^re)(r0'hi.) (81)
iO
I®gl®etiag the first faotor and patting in the condition of matohsd
impedaaees gims
. (82)
whieh is the aame as eqtiation (7§),
zjw the retnna differei»e and aeniitivity for -^pj- for the nodal-
deriTed eiro«it oan h® lAiown to he
yne= sne
1 + gii
;ta
(8s)
fxi(i-fee)'
Withont added feedhaok, the gronaded emitter eonaeetion ia
stable.
the effeets of adding series feedbaek to the typical grounded
eraitter eircuit are shown by Figure 18. The dashed ©urves pertain to
the eireuit of Figure lS(a) and to the eireuits of Figures lS(b) and
lS(o) whoa 1*1 and when the transformers are oonaeeted as shown,
fhls represents added negative feedbaelc* the solid ourves represent
the olrouits of Figures lS(b) and lS(e) Aea the transformers are
reversed (I •• I). This represents added positive feedback,
'With positive feedback added, the grouaded-TOitter olroult
becomes unstable, the point of iMtability for the typioal Junotion
transistor with matshed loads can be determined from equation (48)
using the network eoeffislents froB labl® III,
51
10®
10'
10* —
10'
10'
10
, •* \ V
• •
• \
Mil
l 1
1 1
Positive F
Hegative F
teedbaek ~
eedbaok^>^'^
. -
^ —
\ ' H J)llfcbch
~ 1
/ ed Output / Impedance /
/
/ • • / / -
, 7-/ -
/ -/ -
/
/
r Oain y y
y -
oe y<^
/ / /
y
^eturn Differen
N e d Input ^ npedanoe N
\
\ \ -
\
\
— ' 1
—* vh|r-« ^=^1:2'
1 1 1 M i i n 1 I I 1 t i l l
\ _
\
s:
1 1 1 1 I N T
0.6
0.4
O.S
0.2
0.1
10 102 103 10*
Foodbftok reiiatftnoa Rx , Rs or E» (o)n«)
Figure 18. The typioal grounded witter junotlon transistor with series feedbaek added
m
(84)
Hare % r«pr«8«nt« fii, % or I9 dopeniiag upoa wfeieli eirmit is used.
Solvij^ «%m%ioB (84) for If md emluatiag by us® of fftbla 11 gives
With r®f®r®n0« to Figure 18, the oatehed input iapedaaac Sor the
p*ouBded emitter stage is geaerally higher th«ft that of the grounded
base staget the a&tehed output iapedaiaee is lower, fhis is highly
desirable irtiea MRtehing problems are ©oasidered,
fhe grounded eaitter sonneetioa produees higher power gain than
any oilier oonaeotioa.' Without added feedbaok, this power gain ap»
pronehes 4000. Wi'tti aegative feedbaek, the power gain deereases.
With positif® feedbaek, the power gain inereases.
fhe plot of Tetura differeme ©f Figure 18 represents sensitivity
within one peroeat. fhe ©urre shows that the eireuit is Inhererrfsly a
positiTe feedbaek elrouit when the olreuit parameters are written in
terms of the mesh-derived grounded base equivalent eireuit parameters.
The addition of negative feedbaek does aot raise F above unity.
Figure 19 shows the eharaeteristlos of the typioal grotaaded-
«ltt®r junstion transistor oireuit with parallel fesdbaok added.
The solid eurves pertain to Fifures 14(b) and 14(q) when tl® trans
formers are reversed for positive added feedbaek. the dashed' eurves
represent the eharaeteristiss of all three elreults of Figure 14
tf - 84.7 elms » (8fi)
53
O.S 10'
jPosltlTO Fe«db«ok
HsgatiT* Feedbftok - / •
0*4 Hitohvd Outpitt l»p«i/«no«
/X
0.3
rWmvf 6»in \ Return Dlffe renoe
0.2
x
0.1
Peedbeek eonduotanoe &x, On or Og (mieromhos)
Fig lire 19. The typical crounded emitter jui»»tion transistor with parallel feedback added
84
mkm %h® •tep»atfom®rs of Flgtir®s 14(b) ami l4(o) mr@ SiS
shoTsa, this rspressat# n®.g«tiT® aMsi fssdbaok. la all oas^s III
trajM!f^ra®rs ar» asswasd-.
th« ©irouit beoomes mnstabl® wIwb^ th« aided fwdbaok Is
posltiv®. fhe foint of ia«tabiHt|^ om be fouad ft*©® •qaatioa (60)
•usiag th« aetwark oQ#ffi©i®at« of fabl® If* for the typioal
transistor, this baeoaes
of •* i* nto®8 • (86)
It will b# aotai -ttiat th« aatshed Sapadaaeas dsoreai® for
a«gatlT9 addtd ftadbaelc aad iaereasa for pQaitive addad feadbatk.
fhiB is ofpofita to th« s@rlm f»adba®k ©haraeteristios of figura 18.
Ih® plot 0f ratmra differaae® f®r ths farallel faedbaok eirouit
rtpres^fets ssasitlvity withia oa« pareaat#
4. fh® growadad ©allaotor traasiator oirfttlt
fh® Mitohad impadanaea for the typisal Junetioa translator
eosuasitad as groaadad eollaetor aaa be aaleulatad from aqaatioaa
(43) aad (44), Wlthoat addad faadbaek, thay are
Rim® * i2,4£» ohms , (87)
aad
» I860 ohm* . (83)
&« traa«i»t©r galas, ©alealatad fro® afaatioas (4S)» (46) aad
(47) are
S6
4|te0 - 0>9n t (8f)
Alas - ll.i , <90)
ftiid
kfm ' ll.i . (91)
E%«atl®tt (Sl) skews ttiat tfe® growttdtd eelleeter stage does sot
produe® as audk powsr gala as tfe® oth®*- twa eoaasetions. However,
equations (S7) and (8S) show that the oireuit oaa be used to iaprow
aatehlng feetweea two ^oaaded emitter @r two grounded base stages,
this will be disoussed ia Sestlon f-B.
the expressioaa far retwa dilfere»ee aod smslti-ri^^ for the
grouMed oolleetor stage oMer aat^ed eoadltioas* oan be shorn to be
)*rxx^i 1-^® l"*o ^•raa. {ra-rgx )
(92)
and
ffficpii-ria) • rixra(l-a0)t
for the mosh-deri'red oiroait . For the aodal-derlTed oireuit, they
are
•no ^Sxx$mm [l*^e (^>•*1^0)'^]
]^s89*s«a. )^] -gsi)
(S4)
and
Bi
SfiQ • •" • """ . {Bb}
"ifj- {sms^saa.) • s«« -jpp (1-^c)
Putting mlues tut© these etaations shows that return iifferene© is
not ft a9«8ure of seailtiTity for the grouBuled eolleotor. this is
Bttbstftntiated by the large amount of direst traasraisBion present^.
If sensitivities Are saeeded, they mst be ealeulated from e^aations
(SS) or (9B). For the typical traasistor under matched oonditions,
the sensitivity for saa be stown to be
s - oasi . (96)
fader mtehed eoaditions, all single stage grounded oolleotor
oirsuits of Figures IS and 14 are stable nfeea I • 1. If I' /
i»oint of instability my be detemined flrom eqaatioa (49) or
equation (§6) using the network edeffieients of fable III (xt
fable If respeetively.
D. 4nalysi8 of Cireuits Containing Both Series and 'Rurallel Feedbaek
All of the oirouits diseussed so far have been two-loop or two-
node networks, Wiea both series and parallel feedbaek are used ®n
^Bireot transmission here refers to the voltage or aarrent gain ®f the eiroait when % is made Eero.
S7
©n» translator, a thrse-loop or three-aods wtwork results. It
would be very desirable if Itie preeediag methods aad fomulas oould
be applied t® those oirouits where both types of feedbaek are
present, ?wo methods irhi«^ aake this possible will now be diseussed.
Consider the et»ations for any assh-derived transistor equiva
lent eirouit given by equations (97) aad (98).
Sx • TxtU * rxm^» » (97)
% - • rggia . (98)
the equations for the oorrespondiiig nodal-derived equivalent eirouit
are
II - 8. . (»9)
I. - • t B. , (100)
where
|r| " rxxTm ' . (lOl)
If parallel feedbaek is added to the eirouit as in Figure lg(a),
equations (99) and (lOO) beome
ii • • a.] Si - • a.] 1. . (102)
- [irf' * ®«] * [W" * ®*] • <1°®^
&iavertittg froa the nodal-derived equival^at eirouit baolc to a mesh-
derived equivaleat oireuit, the corresponding equations oan be
68
written as
(104)
(105)
where
p - i 4. sacrii+rab-rib-rai) . (106)
the eqttiTftleat oirowit oorrespoaiiag to etuations (104) aad (lOi) is
shown in Figure 20. The additioa of parallel feeit»ok to the meth-
derived equi-mleat airouit adds a resistaaee of Ga|r| ohms in series
with the shuat leg aad deereases all parameters (laeludiag the added
reststaaoe) hy the faetor p* Series foedfeaok «ay now be added in
the usual manner.
Figure go. Mesh-derived eqwiimlent eiretiit with parallel feedhaek
If a nodal derived equivalent eirouit is desired, •Wie oiarouit
o-vw
if
of Plg«r« 21 should used* lere» the additloa of aeries feedbaolc
to -teie swdal-derived equifaleat elreuit adds a ooaduotanoe fi® |gl ahos
Ss2aM ' ' S
aaa^
Figure 21. lodal-deriired efuiimleiit elreult with series feedbaek
la pirallel wi% the shuat hranoh aad reduoes all the |».rameter8 hy
the faetor s where
|g| " iiigibb - » (107)
and
s • 1 • Ia<gii*Saa-gi»-i«i) • (10®)
Parallel feedhaek may now be added ia the usual naaaer.
the above »ethods for handli]^ sireuits with both parallel aad
aeries feedbaok have been illustrated for ©ireuits without traas-
formers, fhla does Hot aeaa that traasformers eaaaot be used. With
proper laterpretatioa, the above equivalencfe ©ireuits eaa be modified
%@ iaolude traasforwsrs.
60
?. SASCABIU fmwisfot CllCUIfS
jk. Staifmleat 0ir«wit8 for Cuaeadsd IraaBistors
la ©uses 0f ao added fsedback or wh«ro feedback is applied to
iadivldual stages, oaseaded traaslstor eireaits may be aaalysed
stage by stage, fhe aaalysis aaaast begla with the last stage aad
proeeed backwards aatil all stages ha-re beea treated,
la eases of added feedbaok itoere the feedback paths iatflolve two
or more stages, stage by stage aaalysis eaaaot be ased. A method
which caa be ased ooasists of deri^iag aa eqaiTaleat oiroait to
replace two or aore traasistors. Psedbaak caa thea be applied to
th® aaiw eqmivaleat ©iroait ia the asaal way.
Ooasider two traasistors ooaaected la cascade. JUt each
traasistor be represented by a mesh-derived eqaimleat oireuit. If
the iapat curreat aad wltog© to each traasistor are ooasidered to
be the issiefwadeat mrlables, We aatrix efuatioas for the first
traasistor caa be writtea as
rlx
m*
rl%
psi
(109)
where
61
ir'l = r|irvi«r4« • (119)
fii9 efttfttlons for th® sstoad transistor ®aa fee written as
8j 1^ % 8j
m
rgi rm.
X
%
i
^«x £25
wkere
|r*( = riira»-^Mi • ("2)
lore, the &mmm voltage ant ©nrreat at the Jimetioa between the
transistors has been given the sabs©rift J» fhe earrent Ij is
assnaed to flow into the first transistor.
fpon elinftinatian of Ij and Ij by natrix methods, the following
aatriac is obtained t
Si riir^i+|r»| rii [r"| *r«a |r»| Ba
^ I X i"" rjiiraa.
X
Ix |r"| •ra»r«« -I.
(lis)
It is mm fossibls to find a a«* *esh»d«riTed e«iuivalent ©ireuit to
replaee the oaseaded pair. Sla®« the »Rtrix for any q»8 mesh-
derived eirouit takes the t&m Qt (lOi) or (111) we ©an write by
inspeotion
62
nx , riirix*Jrj
rkraa. (114)
kl „ rh Ir1 •fag kj . ^ rai rUrk '
(116) pjil
am
.»l £ffi.j£l!!Mss, (117) ^MX ^h.^m
wti«r«
|r| = rxir^'rxs^m. - (118)
SolTiag thess sxpressioaB for r^x* '^x»» network
0o«lti<ii®ttt8 for tl« B®w oqaivftlejat eirawlt lire
1-13. - "'s'—i' » (119)
rxa • £2£- , (120) rxx*rm
(121) ^xx*^am
mi
r^lji • ' "" ""m ""•'"""i" . {,Ad£/ ^'xx*fMm
If tfe® first transistor i« represaatad by a. mah-derivod
efaiTal«at eireuit aaA the seoond traaslster is repreaeatefl by the
aoial-fierliret 9q,a,iTftleat airsait, the mesh-t.eriwd equiTaleat eiroult
represontiag th® pair is fe»ad fr0» the following aatri®ea»
63
mA
i.
Jll
(12S)
m ssa
€mx
1
m
m ssa
€mx tt~
, • g«3.
X
m «
fa3.
If sxi rr-s83.
"•^8
(124)
Ij asd Ij aiud selTiag for tlio astwork ooeffioients
glirei
rxx ••ll8i!«*|r'l It'
gmmsi'm '
* i mi i » $»»* s"! rm
W I g*i f Sm* s"! 88
(x2s)
(It©)
(127)
aad
^ma s»«*|k i *•»«
(128)
la th«8# •xpr«s»lo»8, w® dsflae
(129)
€4
* »
5 u 0 a
f
1
ill u 1 §
il I
1 •? t :l •
•3
I i
I -I % r-
s s« '*•8 •S'S
i i?
p
+ en % tk
•s I
I
-i
•8
.§ -5
4
.1
4 (L* r*.
*i4 •j
**•
-| i •! • t
•1 -f
^ -3 •a
"1 •
t
•1 -f m
4 •A **
5 *"1 (tS M ha
*/*
m *r< *{8 •a s
_6B
It m n m
4 u 1 «h 60
4 -5i i~~ 1-4
— *1
4 -I •1 :l f -1 :!
-3 t*
W 8W
-a
1
1 i
€ s
r-l
f I
I « 4»
I i t(
s 5 6
5 •§ a
4» «
I
II •H a ^ § ol »« <n S "2
ii 11 0
If §1
II » »« II
fable f (ooBtiatt®d)
tmnsijtw l®pr®s eatatloa
I®%90rk Cos ffielasfes*
l®ial-deriTeii resultaat
Ist fr*a- Zw& frm" 8i«tor sister Szx Sxm §81
ssb maah ir^lrli+lt'lrl
» « ^xi^xm
t « rmx^mx riirlitlr'!
|r"|rl,i-|r-|rj, |r-|r£i«|r'|r;. lr"|riit|r'| rj
wsh
m^skl
no^l
mssh
'^im6xx*^
rli+|r*|gji
^taasla.* |r*|3t|g*|
rii* Em
9 ^ rlmUm
rk+l^-'l dx
rlmSxm
^mxsix
^mx&kx
r^*|r"|«k
h3.g8a*l'^*n|s''|
rh+|r*| gfi
aedftl msal. gla.gii*lg'l m • f
&xx*Sm
gia8f«
s3.3.^s»l $xx*&^ 6xx*%m
*Sli:^l® primes desigaat© aetsork eseffieis^s of the tirais traasistor. Double priaes d«8iga»te the aet?K>rk ©osfflei«nts of the saeoad tramsistor.
66
for til® flrit transistor aad
Is"! = fiigVsiefaa. » (ISO)
for th® seeoad transistor'.
Imljle ? i«»ari«es th® aatwork eoeffleicats for caseadsd pairs
iBQluding all posalbl® owttblmtloas* faramsters for the first
transistor ar» indioatsd hy singl® prSmas, I^raasters for the seooad
traasistor ar® Indioated by double prl»®8.
fhe prooess of e«ablaii^ transistors as swaarieed in Table f
is aetmally oire«it reduotioa of aotiT® networks, fhis proaess of
rsduetioa oaa be applied to any amber of transistors la easoade}
after two trasasistor oireaits haTe been c«blaed, the resultant
oireuit M&y be toabiaed with the ISilrd and so oa. fh# amownt of work
retaired is -tiie only limitation.
The eftilTmlent eirouits oorrespoading to the network ooeffioieats
of fable f are not showa. fhey «ay be obtained by the methods
outlined ia Seetioa Ill-i,.
i. Analysis 'Of Oasoaded Ciro-uits Coatainiag Series or Parallel Feedbaok
Without the use of impedaaee laatehing deviees, aatehed conditions
ar® not obtaiaad ia oaeeaded transistor eirouits. the most desirable
ooaaeotioas, eonsidering pow«r gain only* are the grounded base and
the ijroaaded eadtter ooaaeotioas. these ooaneetions have low iaput
iapedanoe and high ontpat impedaaoe. If transistor sirewits of these
67
are @ftf®aded, *uoli power gala *11,1 be loai dae to miia*t®hiag^.
Oa the other Mad, -fee grsraaded ©olleotor etage hae relatlfely
high, input i39^edftaee e&d Im output jspedamee. Using a gromded
©olleetor staige alteraateljr with t,he grotti^ed base or greunded
emitter stage produeea a better match* loweTer, the iasrease ia
fower gain obtaiaed trom the grounded base or grounded wiitter atmge
ts offset by the law power gain of •l;^e groaaded eolleetor stage'.
the aboTe @m be easily deaoaetrated for a two-atage translator
amplifier# Soasider two grouiaded em,itter stages eonaeoted in easeade'.
fhe network ooeffioleats for the pair, obtained froa equations (110)
through (122) using values ft-oa'INiible II, are
*•11 • (s7i)^ * •m.z X 1#
• i'Si ohas (131) ®.S,400
(24.s)2 ria • •
6® ,400 • 0 *00804 ohms , (1S2)
• 7,800,900 ©has # (ISS)
^.2 X 108 4.gg X Iq9 • ®i,so0 obmw (1S4) rm - 6@,400
iquatieas (4S) a&d (44) east um be used to fiad "iie laage iapedaaees
of the oaseaded pair, fhey are
slate • 6w * (13s)
@@
«01w8 • ««,»q ®i»« . (136)
?h« pswsr f«la from 9t««ti@a (47) i«
^9mm • s8,8<» • (137)
If tli« BoaoM st&ga war® r«pl«.®«a by a grQwadtd oolleator atage#
®t^»attoas (isl) tbroufb (isf) ibaawe
**1.1 •
ria « 1.9 atet .
spjm. • -®6t»0'00 *
ra« * 6,1®0 ofe®a , (i®e)
k|a«& ** alms ,
^mm • »
aad
** •
If %li« first 8t«f• vara «. gro«mdad aallaator stags and tba
saaomd a grouMad amlttar staga* aqn&tiaai (131) -terattgh (1S7) |}aeo8ia
r%% • S,040 otais ,
ri.a " 24»4 ©Jha® »
«*«3. • -8,iOO,Q0O otai# ,
I'ais •" S«,SC» olua« , (189)
^i]®taa * ,410 albma
S@aa,e - 84,SO0 otos ,
aad
aftooa • 41,»§0 ..
IqmatioiMi (15S) aM (ISf) that th« groaadad eolleotor stag#
is vary aaefttl as a mteMag ddvlsa. Th®y show that hi^sr gain «ay
obtaitted froa a combiaatioB of gromadad ©ollsator aad grounded
^ittar itagas thas saa b« obtained fro» a oiro'ult aad® up of all
grottndad e»itt»r stages.
When fesdbaek is addad to ©asoadad traaaistor oirauita, it ia
vary easily handled by oirsuit reduetioa taoteiques. If the added
feedbaok is applied to iadividual stagesas shown in Figures 13 aad
14, thott the 0@rre«f0adjyQf network ©oaffiaieata #f fables III mad If
are used in flaea of the r*s and g's of fable T. If the added
feodbaek involTss «ore than one stage, suoh as shown by figures
21(a) and g2(b)» the faadbaek alsttants Sg or a«a be added after
(a) Series faedbaek (b) Parallel feadbaek
Figure l!2. easoadad transistor pair with added feedbaak
70
the oirouit ims beem redueed. the additioa of tkeee feedback elements
to the redweed eirotilt is id«atieal to the additioa of feedback to
single stage® in that adds direetly to rg and @| adds directly
to ga *ii#re and gg are parameters of tfe® two-stage eqiai-wlert
oir®uit (see figures-2 awi S). Sh® iadividwal traasistors of Figure
21 0aa be represented by either mesh- or nodal-deriTsd equiiraleat
©ireaits. loweirer, for ease of handlist, the resaltaat two-stage
eq«iTal®nt oirouit «ast b® a »esh-deriv®d eqaimleat oirouit for
Figure Eg(a) aad a aodal-deriTed equimleat oireuit for Figure 22(b).
this is indioated by the type of feedback preseat.
4 aore eomplidated series feedback oirouit, inoluded merely for
illustratioa,. is shows in Figure 2S. lere oirouit reduetion, oan be
Figure 2S. fhres-stage traiasister feedbaok ©ireuit
11
applisd to th« fSrst 'two sttgss wi'lto % aM % iiwjladed. Itth %
ftdd«d to tke rmultmM two-stag® ®%uiv*l®Bt ©irouit aad witb I4 add®d
t© the ©tttiwlettt oiromit of th® last stage, tb® sijreuit ©aa
redaeed to ©as ataivaleat oiroait fbr %h@ tfer®e stages, fiaally
0*a b® &dd«d t© th® ti*re®»8tRg® etuimlsat eirowit to ooaplete life®
problesi
Siailarly, «as®ad«d olrsaits with parallel faedbaek ®an b® easily
rsdaeed witk tli® ms® of aodal-derivad aftiitmlaBt ©iraaits. . lo- farther
explanatioa of this seeos aeeessary,
fh« sqaatioas dewlopsd is Seatloa If-C for applioatioa to siuglt-
stag® transistor eireaits oas be applied t3 oasoaded transistor
oireaits wittoat additional mrk. the sfai-waleiit oirsuit repressntiag
a oasoaded traaasiator eir®mtt is i» ao way differsat froa th® ©qairn-
leat ©ireait ®f a ®iagl® stag® axeept ia the imla# of th® parameters,
ffing the aetwork oo«ffiol®Brt»s of th® oasoadad ©ireait, eqaationa {4S),
(44), (60) and (SI) will yield "itoe matehad iapat «ad oatpat temi-
ijatioM for the 0as«ad®d oir®ait. Sfaatioa (4?) or (S4) will yield
th® power §aia ©f th® easoaded ©irsait. Itoe ©faatiaas fer wltag®
gala, earreat gala amd stability also apply*
C. Analysis of CSasaaded fraasiitor aireaits CoBtalniag Both Series and I^rallel Peedbaek
lo illastrate the method of handling eiroaits eontaiaiag both
series aad parallel feedbaek, figure 24 is shown. Ciroait redaotioa
72
on
Stage Stage
Piguro 24. 0a«0a€ed transistor eirouit with series and parallel feedhaek
oaa be applied to this eireait ia the follswiag iwiy.
I<8t the first stage be represeated by a jwdal-derived equiiraleat
oireuit. % »ay be added direstly to this eirottit, I»et the second
and third stages be represented by a aesh-deriTed equiiraleat oiromit.
Rlj aay be added direotly to the third stage, fhe last two stages eaa
now be oombiaed by use of the relationships of fable V, liae 6, ais
resultaat two-stage equiwlent oireuit is of the aodal-derifsd type,
therefore my be added direotly. Sow, the equimleat oirouit of
the first stage (with 0^ iaeladed) om be oombiaed with the two-stage
equivaleat oiroait (with % aad Kb iaolmded) resultiag ia a three-
T3
itaga eireulti it my b® of eitiier the assh- or nodnl-
d«piT®d typ«.
Xf th« thr««-8tag® sfmiTOleat oiroait is obtainexi by use of tha
r«l«.tlo»6feip8 of labia liae 4, a a«8h-d«riv®i cireait rtsalts. Sj^
aay a©* b« adied to tfeie oiarsait by methois outliaad ia Seatioa IT-D.
1® a»y ba aided diraetly.
If th® tlir««-stag® eqaiwleat ®ir©uit ia obtaiaad by usa of th®
rslatioaships of f&bl® V, lias S, * aQdal-darivod eiroait results,
lar®! May be added to th® ©ireuit by aetliods outliaed ia
Se®tioa I?-D, aad 0^ way be' added direstXy.
Regardless of lAiat method is used, the oirouit of Figure 24 oaa
be redueed to oae aotiTe aetworlc defiaed by four parameters. This is
afplioable to. ©aseaded sireaits in geaeral.
74
A large seleotioa of traaaistor equi-mlent oiroaits Is available
for us® ia transistor ©ireuit aaalysis. In partieular, those tquira-
l0iat eirouits which fit on® of two gsaaral typss ar® ®sp®oi&lly useful.
fh®s® ars'tii® mesh-ierived I aM tb® aodal-derived if oquiTOlent
oirouits. To radtto® the nwbar of stttiiraisttt oirouit parasiaters aM to
greatly siapli^ th® aotation, all parim9t«r8 can be writtan ia terms
of the grouadad baa© ffissh-dariwd etuiYalant oirouit paramataras Tg,
%•
Th© natwork ooaffioiaati partainiag to the aMal equations tmj be
fairly easily aaasurad by bridg® methodsj the mesh eoefficients are
oomparativaly diffisult to measure with existing equipment. Any one
of the three traasistor oomsotioas aay be used. Thea, by means of
mathematioal relatioasMps, th© equiiraleat cirouit parameters eaa be
fouad froffl th® aetwork coefficieat®. lesults obtaiaed ia the actual
measuremeat of ooBimeroially amilatble P-M-P Juaetioa traasistors show
that for ideatioal bias eonditioas, the equimleat ©irouit parameters
v&Tj greatly betweea traasistors.
The traasistor is iahereatly a feedback deTioe. Feedbaok may be
added to single-stag® transistor oirouits with or without traasfonaers.
Weight, spaoe aad eost aake traasforaers uadesirable but their use
permits more -rersatil® ©irouit desiga. Ia either ease, feedbaok aay
76
b® ia om at two ways? series faedMolc.whieh eoatrols th®
ahiiat resistor of th® T ©qai-ralent oirouit aad parall®! f«0il»ok
wfeieh oontrol# th® sbmt rsaistor of th® « aquimleat eirouit.
eircaits ar® b®«t analyzed on th» Msis of aatehad eonditions at
•feh« iaput aad output S«a«ral ©quatioas whloh hold for any
typ« eoaneotioa mn used la arasfe of th® analysis* i. oompreh^asiv®
study of 9®ri«i8 or parslltl feadMek oa single-stags traasistor
Qire«it0 shows that matohed laput impedan©®, »»tohed output iKpedanee,
•roltag® gala, ourraat gaia, power gaia, ratura dlffepaaea, saasitlvity
and stability are wry mmh dapeateat upoa faadbaok aM oaa be eoa-^
trollad by fsadMolc taohaltu®®. laoh type ooaaaetloa is uaique aad
must l>e studied'separately. Stagas with series aad parallel faadbaok
eaa also b® aa'slly handled,
•Caaoadad traasistor airouita prasaat ao particular problem whaa
eireuit raduotioa of the aotlw aatworks ia employed. Ihis method
ooasists of obtaiaiag a f or « equivaleat oirouit to raplaoa two or
aara trsasistors. It is wry versatile aad eaa be used with sarias,
parallel, or both ssries aad parallel feadbaek. Feedbaok aeed aot ba
limited to oaa stage but »ay iaTolw aay atmbar of stages. Of most
sigaifloanoa, after-the oaseadad eiroult l»8 beaa raducad, the
aaalyals la idaatioal to siagle stage aiMilysls. All BUithoda aad
formula® applicable to siagl® stage eirouits.are applicable to
reduced oaaoaded slrouita.
7$
fii. siuefi® iikiwcis
Al.«xftni«rs0s, 1^* F. W. Coatfol applleatims of tlia treaslstor. Pro®. ®f the IBl. l»S-liU, 1»S2.
AM9r»0U, A, Bttgaua* franalstors in 8vlt@hiag eirotaits. .Ball Sys. fash. 4qw, ill 1107-1243. 19S2.
Aagello* S. J. S«l0oaitt©tor rattifiars. Slae. ia«. ®ii SS6-872. 194S.
iaabti*^, P. 0. Bottljle surfaaa laad gulphita traaaiitor. Proe. Phya, Soo. (toadoa). ©Sl» 2S6. XfS2.
aad Baalsah, I. I. Oa tlia frataaaay raseoaaa of PW traaaiit^a. .Pre®, ftiya. So®, • (I<®Moa}. 63Bi 6^-541. IfSO.
Bardaaa, J. Sarfaee atatas aai raatifiaatioa at a »8tal awnl-0oai«@tor soataat. fkja, la*. 71t fl7«f8T. 1047.
, Oa tha thaary of tfea a-© Imfadaaoa sf a ©sataet r«®tl.fl®r. Ball Sys, fa^. 4mT, 28* 4g8*4S4. If48,
, -ffeao'ry of ralatioa batwaaa feola ©oaetatratioa aai okaraotaristios of ganwialm potat ©oataets. Ball Sys. laoh. J0«r. 29I 4Sf-4te, 19S0.
aad Brattala, *. I. fraaaistor, a swaieoadaetor trioda. fbya. »eT. 74i 2»-gSl. 104S.
aad . Fbysieal frla@iflaa iawlvad ia traaslstor aotioa. Pkys. lav., fii 1208-122g. 1949.
aad Pfaaa, W. §. iffaets of alactrioal fominf oa tha raetifyt^ barriars of H- aad P-garwialua traaai^tors, Pfeya. ieir. 771 40l*«52. li».
laoker, 4. A. Photoaffaott la a^deoadaotora. Ilae. lag. ©Ss 9S7-94E. 1949.
. trwisiators. lie®. Sag. ®9s ®8-®4. 1960.
n
l®ek«r, J. A. »ni SfeiT®, J. H. th« trantistor* a &m swalcoodustor a»plifl®r. Il«0. Sns- 6$t tXi-221. If4t.
Beokar, 1. and Itot, 1. ¥. IRfeotoroltal® ®f f»I ttaotlosi 4b f9wmh^a»« fhy», !«•?•, fsi 301-s&2. 1060»
s
Ball, l>» A. Bml olretilt of a faedtoetc «ffl.flifl«r. Wlrelass t®t 40-4S.. F«fer. If§2.
Bed®, laadrlk W. »®%work attalyils aad f9®dtwi«Sc aaplifiar dasiga. 1st ad. M. T«« B. Tan Xostrand tm^, 19^.
Brattain^, W. 1. and lardeea, J. Satar® ©f th® forward aurrent la gara»aiw« potat soata«ts« Wkf»* lev# ?4t 2gl-2S2. 1948.
and . Surfae® prop«r%i^ @f gamaaiiaii. Bell Sys. ' ' feeli. Jowr. 121 l-4l. ItiS.
aad Irlgfs, 1. B, fhe Qptleal ooaataat® of gonaaalam ia lafra«-r®d aad Tialbl®. Fhys*'!®-** TSt 170&-1T10. 194®'.
aad Shoeklay, W, Dsaalty ®f s'sirfae® 8tat«s oa ailieoa dedaeod from @oataot p»t®atial Masttrvmaats. fhys. Rev. Ut MS. Ii4f.
Iray, lalph. Dapeadea©® of r«8istiirity @f garwittlm oa «l®0trie fiald. Piiyf. R®t. ?6i Igg-lfJI. 1949.
irigga* B. B.. Optieal'«ff®ots la bulk sillooa and germaalm. Fiiys. la-r. ff j 287. 19S0.
. lafiia»r®d absorption in silieoa. I^ya. lav. 7t! 72f»fft. 1#S0.
Brow, e. B. Mftgaatieally biasad traaslstors. ftoya. tav. 76 J 173S-1737. 1948.
. llghi fV9<imea0y ©peratloa of traasistors. ll®etroBlo8, 2it gl-8:3. ^ttly 19S0.
* Iryaa, ®. W.» 4r. Applloatioa of traasistsrs to lilgh-Toltag® low-eurr«at supplies. Pro®. @f th® III. 40t 1821-152S. 19§2.
f8
OiiFtttliers, 1* S. &&WM sjs^m &f|)ll@atioas of trimslstor enflifi^rs* la lell Tslephoa® lAboratorlss,. Ia®. fke tr«3asistort .S0l«0t®d ref@r«M« aiit«irlal oa efearaoterlatles «M applt* sfttiea*. p. 3Si-S7S-. I«w York. fh« laboratories. 10S1.
. So»« «.xp0ri»9srtal asi frastioal applieatioas of traa-aistor oaelllators. Ia B®ll f«le|AwS'a« Laboratories, lae. fh« traasis'tert seleotei refereate aaterial oa ©iiaraoter-lsti®8 aai applieatioas. p., S®?-4l4* Sm fork. The lAboratories# 10SI.
Cobleag, Altrahaa aai •Qmemt Wktrj li. Variatioa of traasiator far«oter8 witla. teaperatwre. fro®, of the 1®. mt I4f2-I4f6. l»Si.
aai . fraasistorst titeorr and applioatioa. lleetronios. g@i t8-l02. Mar. liSS.
m& . l^rgy lewis ia transistor eleotroaioa. " Ileotronios. 2$s IS8-141. Apr. 1$$$.
————. • ^ysisal properties of eleotroas ia soliiis. Ileo^rottios. ESi iSll»l$i. Iky 19S3,
aai . transistor a»tioa ia gemaaim aad silieoa. " Ileolirottios.. 261 Mi-l?l. imm liSS.
^ . ?oiBcfe«i«®oataet traasister operatioa. Bleetroaios. 2ii liS-lSS. (fely liSS.
aai . Operatioa of Juaotioa traasistors. lleo^roaios. 26i lSi-l#l. Atig. 19SS.
aM . liwivaleat traasiator oiroaits .aad etuatioas. ^ lleotroaioB. Ut ISS-lil- ' Sept. ISiS.
Coawell, lather M. IVoperties of siliooa and gersMaium. Froo. of the m. 401 istf-mf. it®2.
. ligh field mobility la geraaaiw® with imparity soatteriag •ioaiaaat. Biys. ler. 801 7St-T7E. ItSS.
and Waisaitapf, V. F. theory of impttrity ae&tteriag in s«»ieoBdtt®tors. Hiys. lev. 7fi SS8-W. 19S0.
Baeey., ®. G. ipaoe^otairge 'limited hole oarreat ia germaiw. Phys. t«T. 901 liw.
7i
I^0«y, ®. C. m& loss, I. M. Mipolftr "fliM-sffeet* tmasistor. Froo. of tli« IIB. 411 ff0-f7®. ItSS.
S» F» aad SerMoM, 1, 4. friat®«S ciremitry for tmnsistorB. Proo. of %hm Hi. «i lS24-li2a. ISSE,
Dttalap, W. 0rawf®rt, Jfr* Imporfeaat mm s«ai60.aiu@tor. S. g. lair. Sgi 9-17. fabr, im.
Mrl^, J* M. Iffaets &t spR®a-®h«rg« lnyar wtdaaisBf In ^unotioa tr%aslit®r8* frot. of tiia Ill» 40i I'^l-14D6. 1982.
Itears, 3* J. F<>w«4©miiwil traaslatora. Pro®. ®f tha IIS* mt IS61-1I64. If§2.
Ipstalii, iaraM S.» .Msh, ioim Jk* mA Stealhorn. transistor iilag ©©JMamiea-lioas etwipawlf* llaotroaias. Eit 8S-102, mj 1®S2.
Buhaastook, teaas D. fiepapSMaalsa illttstrata traaaister appll-0«tioaa» Klaatraaiaa* tii llt»ll3. Mr* 10S®.
. fraa»l8t®ris5a4 Jiaarlag aids, llaatroaies. 2Si li4-16©. Apr. ISSS.
Paa* 1. T. taagaratwra 4apaadeaoa of tha aaef^y gap ia samiaoa-'dmtors. I^ys* lair. $tt WO-»tOS. 18S1.
Farlay, i. S. Syawiios of traasistor aagatiire-rasistaaee eirouits. fTo6» of ^8 im, «l 1417-1108. 19SE.
Flak, 0. «Bd Jwgwi# 1. I. fha jaaatioa traasistor. lleatroaies. 141 Sg-8S. lov. ISSl.
aM tsaicat^ F. 1. Iha traaslster, a oiyetal trioia. Slaotroaies. Zlt «S-7l. iaft. lf4S-
fallar, Gml-tln S» Mffuaioa of daaor sM aaoaptor al«®aafes iato garwiaiw. I^ys. lav. S«i IS6-137. 19S2.
aoid Strutliers, <3. D. Gopp«F as a» aeeaftor alaaaat la garaiaaiaa. fteys. tar. 87s S26-S27. 1S62.
, 'ffeatiarar, I. C. aad vaa Boesferoaok, W. Prapartias of "bkariMtlly froiaeai aeaaptors ia gammlaa. fliya. Ibt. §Sj i7i-87f. If&E.
io
§8%bl,0| !• 4.# Mmfcwy, P. G. aai logarth* 0, A. 0ry«tal iied# aai trio4« aotioa ia Isad iwlphiii. Pro©. Phya. So©, (toaioa)* iSBi 371. urn*
Seaapal laiio fampaay. Opepatiag iastrae-fcioas for typa- S«l-D Taeutw-tatoe liriiga* 07S laaaaohaaettea CsAbridga if, Maisa^hasatts. ^aa. 10IS.
§ia©©l®tto, t* 4^. Jaaotioa traasistor «haraeteriatio« at hm aai aaiiaa fSraqaaaoias, lat. llaflrtsroaioa Goaf. Pro®. 8t Stl-ia®. 1SS2.
. ^etioa liraasistor afuiwlealf -tirouits aafi •aaaaai-tab® analogy. Pro®, of th® ISI, 4S« I4i0-I4i3, 1®S2,
. ferminology and efwatioaa for liaaar a®tiir« foar-taraiaal natworfcs iaelaiiag traasislfopi. EGA. Sariw, l4i g8*4§.
. Iquipaasts for aaasariag Jaaetioa transistor a&iittan©« |iar«wt«r8 for a wide rang® of firtqaeasl®®. I0A l«irlafw. Ui 2S®-2iS. 196s.
ioM®a» I. and Hielsaa, I. Osoilloseofio display of traasistor stati® el«0tri®al ®J3«.ra®t®ri8ti@g, Pro®, of tfe® IH. 401 l4S7-14Sf, imt.
Soaeher, P, S. Pfesfoa yield of elaetroa-bol® fairs ia geraania®. ;^s. !«•. 78 s Sli. ItSO.
. MeataraBSi^ of Mole diffusion ia S-typ® gersaaitm. Hiys. ler. Sit 4ffi. IfSl.
, Paarsoa, &. L., Eparks, M., foal, S. K. and-Shooklsy, W. theory aad. emperimaat for a gamaaiwia ?•» Janet ion. Phys. &®v. flj 637-688. liSl*
anA Priae®, M. B. latsrfratatioa of a-wla«8 ia P-M' jaaetioa traasisters* Ibys. Ssir. Si i ®®l-tSS. 19S.3.
Sraniill®, J. W. and Bardsley« W. Soma profartiaa of silioon poijacfe'-eoatast transistors. Pro®. Phys. io®. (leadoa). SSB> 42®. 19ES.
®aill««in, Iraat A. Co»iaai®ati®a aetworks, ?ol, II. Ist ed. ». f. jrohamiey and Sons, la®. l9Si.
daan, 4, S. ladiatiT® transitions in gtnaaaiaa. Pro®. Pfey®. So®. (London). i6B» SSO-gSl. 19®S.
SI
ai,«g8l0, a. W» Crystal tatrod® aixar. Ilaetronios. tit 80»gl. Oat. I94f,
lall, I, I* ll«6troa-h®l9 raaoabinatloa in g@rmmlm., Phya. lav. B7i S8T. ItSi.
.. fowar reatiflara aai traa«istsr«. Fro®, of tha IB. " m$ islg-lsie. if62.
aad Ottttlap* W* •§. ?-I Jmotiaas preparad by impurity dlffmaisa, ays, l®ir, mt 467-4eS. 19S0.
laynea, J, 1, and Shookley, W, ' Ikwatigatios of hole lajaatioa ia transiat©r aetioa. Btys. tar. Tgi 6fl. 1940.
. &e aobility sad life of lajaatad holaa aad alaatroaa "ia garaaaim. Phya. lev. 8t ®3S»843. 10il«
Barriag, Oaayara. theory ®f traaaleat ia the traaif»ort of holes ia aa axeasa aamiaoadaetor. Ball Sya. faoh. our*. 281 «l-4af. 19^.
Ittatar* fl@yd P. fmiteiaal aaalysis ®f traaaistar aharasterlstios. of the m. mi 1387-lSfl. If SO.
laater, I#* P* Physteal iaterpretatioa of type A traasistor oharao-teristias. Wiys. lev, 77$ iJI8-Sg9. %mo.
aad ireum, 1. i» fradaatioa tester for traaslators. lleatroaiaa. Ut Oat, It&O.
Iellay» ilarvia i. She flrat Ave years of the traasistor. Bell tale. »g. Si I fS<-86. ItiS.
leaajiaa, 1. aad Sehaffaer, 4. i. Aa experimeatal iavestigatioa of traaaiatar aolsa. Pros, of the liEB. 401 l4Sg-14S0'. liM.
aad , lolse ia transistor amplifiers. Ileatroaioa. • 261 lQ4-l0f. Fehr. IfSS.
Ilahr, Oarl I. aad luater, Ii* ?. leasarwaeat of seaiaoadaator impwrity aoateat. Phya. lev. Sli 10S®-1Q60. 1961.
Kaight,' ©eoffray, r.,, J<s^aioa, liahard A. sad lolt, lolaad 1. Measaremaat of smll sigaal parameters of traaaiators. Proa, of the Ilg. 41« ®SS«#8t. IfSS.
S2
Itoeli, W. !• «mA Walla®#, I, L., Jr. fto soaxlal transiitor* Bl®e. Sag. 68i lf4t.
lursliair, J., lotaan, 1, f, aad Israof, f. B. Cathoda-ray tttba flotS'traaslst^r eurcrat. ilaetroaioo. 2Si 12t-lt7. P«br, lifii.
Iaw, 1. R., laailsr# 0» W.fankof®, J. 1* aM Amatroag, i, B. A-ieTelo^aa-bal garaamlw P-I-? Jwae-lioa transIstor. Pro0. ®f the i», mt imt'im, i$m,
he^Ut frank V* fraBsist«r osoillat^r t^r tslamatarlag. Sleetro&ios. Ut ®0-»l. Aug. It4®.
I.#ioT«8, I, Oa hoi® attrraat la gaimaiaa transistars* Phys. !«•, TSt UOQ-llOl, lf4S,
. fastiBE traaslstors, llaatroal®.®. 121 8S-89. 184®.
. Km fliotoaleatrle davlets mtillatag oarrier injaetioa. Fro®, of %h« li®. 40s 140T-I«f, ltS2.
Utt4l>9rg» Olof. lall ®ffaa%. fro®, ©f the IIS. 40i 1414-1419. imi,
tlnvill, «y. i. fraaslstor m«fatlv«-iaf®daa0® ao«T«rtsrs. Fro®, of th« III. 41I T2S-Ttf. IS6S.
lotaiaa, lo^ert D. eaapl«a«atary sjamatry trwislstor ©ireuits, Il®®troaies. gfii 140-14S. Sej>t. iSSg.
MoAfs®, E. 1., ]^d«r# I. 4., Shofkiay, W. aad Sparks, M« Obtsr-vatioas ©f aeaer e«rr®a%« ia gsimailw P»I Jwaotioas. Hiys. I®ir. SSi eS0*@6l. ISil.
, ihosklsy, W. and Sparks, M. Mfaswamsnt of ilfftisloa in s@ai®oBdttetorB a aafi^ltaa®® sietkod* Phys. R@r, mt IS7-1SS. i»si.
lelay, I«in®%h S. 1^® *-F-» Jtiaetion as a .»i»d®l for seeoadary iii®%o«oad«®tivity. Fkfs* lev. ®4i 8SS-SSS. IfSl.
M»rrlttoe«r, 1. F. Vois® aaalyssr for transistor produotion. llastroaios. 26j Miy 1®SS.
Meafegoaery, H. 6. Baaiiirottad noise l» traasistors. Boll lafe. I®e. 281 mo-ms. 19S0.
ss
Wiubgomryt S» C. ll.e@tri0sl mtm ixi smiooaduetori* Bell. Eys. t®eh. Jomr. Sli iSO-tfS, IfSt.
. fr*asiit«r aois® la «trcwi"l ai>fli«atioa«« Pro©« of tli« ^ !».. mt I461-14n, I98t.
lortoa, -I. A* Pr®8«ttt statms of tmnsiitsr <i«irtlopieat. Proc, of tht X», mt ItiE.
8aT(m« ®. #• ip*y, 1. «39^' Rija, 1» f. •W.fatiae of iajeete€ oarriera lift gurm&imstb mil, mm0r, fkya* sos. 27} 30, 1062.
0*lsill, i» 4, ftsoA iatteima, Arlshar. Methoii mA «fwipwat for traa-»i8t®r tOBtiag. Il«®%yoale#. 2Si 172-lTS. #uly 19SS.
Ptarsoa, 6. I»» fh® fMyti®8 of el«otr©aie 8«®deoaa«0tors• traa. of Am. 3®I ItiT.
aaft Bardaea, J. Sl«©trleal frop«rti0« of para silieoa aM illi®oa alleys eoatalaiag bsroa aai j^oasboroua. Ifeyi* Be-r. Ui SSS*8SS. l»4i.
t teaij W. t. aai Shoeklay, W« Pi^bi^ the spaoe eharg® layar %m a ?-» »y». »«•. SSi 10iS»10i7. I»i2.
aaS Sawyar, 1. Sllts^a F-* juaetloa all^ iiodaa* Bpoe« of the m, «I li4S-lS8t. Ifii,
fataraoa, I.. 0, I^ttiTaleat olrsutts ®f llaaar a«tlT« fowtarmlaal astworka. Ball Syt, laefe. Jour, 07• iSS-S22. 194S.
PetritE, Siafefkri L. 0« -Ifea •^ao,!^ ®f aolaa to P«I Joaotloas aai relata«l i«Tiae«. fro#, of tha !»• 40i 144iO«14®g. If SI,
Ffana, W. ®. aat Soaff* 0* 1. F-garwialwa traaaiator. Pro©, of %ka 111. ®Si llil-ll©4. 1S».
ftot«Ep©l, W. J, P-I aaetloa raotifiar aad fto©t@»oell. f4iya» leir, g^i ito-ltl. mi.
ft-itehari^ 1, I., ^afaaaoy mrlatloat #f ©ttwraat-ampllfioatlm faetor f®ar Jaaetloa traasiatora. Pro®, of tfea III. 401 1476-1481. Um,
i4
laisbeok, S, A mm lim&r «aflifter usiaas a tran-s if tor «ni ft 'mewn In B#ll felophoiiQ laterfttories, Ino, the trftaslstori lalsetsd refertoee mterial on etora.at®ri8l!i®8 aad applloatioa#. f. Sff-Mf* Wm Icark. fh« XA'tK»r«tori@8. ItSl,
. A high"0ttl&l9my «»pllfi®r. la B«ll felsphoa# ^borat©ri«Sg tm* fht traaslitort s»la®tei rafsraao® BMiterial on almraettrii'teiaa mi apfllsttions. p. S8S-S9f. Mm fork. Hi® lafeomtories. 1061,
. friaslffcQr eiremlt a®sig». il@0troale8. t4i 128-lM. B«®. ISSl.
MaBttfaettiriag Goxpaay, Sermmitm trausister data shsats K0. m*m$l aad Wo. 0i*t884. i§ Ohaftl Street» Hmrtan SS, laisaohmsetts* Wqv. 19fE.
lead, W. I. and Shaekley* W, ©Itlseatioa aadels ®f oi^tal grala hottudaries.. Phys. R®t« 7$t "tfi-tSi. 1®©9.
0» M. aai Slade, ». I. fraailitor* oseillate at K)0 W,. il«etr©ai®B* iSi 116-ll«. »oir. imZ.
jfejth, tiDttise and taylor, 1. 1. Profaratlon of germaliewt sii^le orystals. Pro®, ©f the I», 40t ISSS-IMI. If82.
Koaattlt, C. L. aawl lall, t« I. A. high wltag«» meilm-fower reetlfier. l^roe. of the III, 40i lllt-lSgl. XSi2.
lydar, 1. #. *>hility of holes aai eleetrons la high eleetrle fields. Biy«. lev. 901 Tti-fSS. ms.
aad ihe®]eley> W. laterpretati^a of defeadaaoe ©f reslB-tlvity ®f geraaal'm-©a eleotria field. Kiys. lev. 7si sio. 194?.
aad . 'Mahillties ®f «l«#troa» ia high eleetrio fields, fkjs* Mm* Sli l§t-'l40. Ifil.
%der, 1. 1. the tfiie A traaiistor. lell lah. I^e. 2fi 8i»f5. lt4i,
, Agiag Mid te®p«ratar® resfoase of iseiat-eoataet traa-sisters. Ia lell felei^eae tabomtories, la®, the traaalstan seleeted r«fereiM»e Material oa oluaraQteriatios and afflieatioas. p. lES^lSS. Mm fork, fhe . lAbarat©ries. ItSl.
s§
IE^«p, 1« 1. iiiii I.lrdim«r* 1. -J. ®oms •,sp9«ts.@f ttai traa-siitQf, lull Syg* t«©h. JF0tir, Z$t mf-mi* IS4&.
Sm%f» ^@bn S. iapurity P-S-P Jimetlam traaslttop. Proo. of th« 111. 401 lSSS«lSiO. 18S2*
SoJiialthaist, f. 1. aa4 Isleh, 1. #. Sow Isrsuislator trigger tlroutts. Jfeo®. of tfc» J®* SSt @Ef-65g» l»Sl.
S©Qtt, f. I» Crystal trio4«8. Il«e. eoa®. 2$t lfS-t08. Itil.
lidfeari F. fr*ail«tor Qf«ratl0ai stabilisatioa of of«ratiHg potati. frao. «f tJi® IM. Mt mz.
. Priaeiplea of traiaaistor ©Iroalta. l«t ad, H» T. John Wiiay mA Boms, lae* IfSS*
ihalcal, J!m0h* latri* rafrea-aatatiQH of traaa-istor oireulti. Proo. of the 111. «•! l40S-l4if.. lfS2.
Sfeiire, Jo'ha M* The 4oaW« aurfa®^® traasiator. lev. TSi 68f-iiO. 1940.
, fk« lAototraasiitor. lAb. l«o. 281 SST-'Sii. i»g0.'
, Properties ©f tii® Jl-lf40 P-I Jwastioa traaslator. Bro©, ®f th® ,111. 101 1410-x41s. iteg.
SJio®kl«y, W. fh® theory «f P-I J«a®tio»« la semleoadaotors mi. P-I ^aaetiaa traaalitora. iell Sys. feoh. jQur* 28i 43S»4S9. 194S.
llaotroae aad holas ia s^miooaittotora. lat ed. ff. f.* ©. faa' Bostraai Co., la©. MiO.
. Saargy aad atraetarea la a«tleoB<la®t®r8. Phya. lev. ^ f$s lf$. i$m»
, lot «3.e®treas ia. fomaaim and «Ata*a Mw. i®ll Sya, feeh. oar. mt 9®0-10S4. Itil.
. traaaiator •laotroaieat iajperfaotioaa, aaipolar aai m&%og traaaiatora. Pro®, of the 181. 40« 128i«lSlS. ItSE.
. A mipolar "fielt-effeet* traasiator. Pro®, of tii® IH. 401 l»S-iSfi. l9St,
m
Sliooklej, W. aad Bi,rd@«n« J. Bn.«rgy bands and mobilities in aoaatomio s®mi0oadia«tor8> Phys. Ist. fft €57-€>8. 19®).
and Pe&r8©a, S. L. Modulation of thin eoaduetaae® filas of saai-^saduetors 'by surfa®® ©barge®. Pbys. lev. 74s 2Sg-2S8, IS4S.
» _ and aiynee, J. E. lol® injeotion in germnim, qiSttflfaflTe stadiea and ftlaaenfeary transistors. Bell Sys. feoh. imr, 28t S44-S66. 1949,
and Pria, 1. 0. Spaee-obargs limited eaisaion in semioon-duetors. Phys. lair. 90j ?SS-Ti§. ISSS.
and lead, W, f., Jr. Statistioa of raoomblnations of boles and eleetrona. fhys. leo, S?i 8S6-84E. 19S2.
, Spirks* 1» and Teal» §. I. fhs P-* Juaetian transistors, fhys, ler. 8Ss lSl«li2. 10SI.
Sittner, W* 1. Current multiplioation ia the type A transistor. Pro®, of the IH, mt 448-464. 1982.
Skalnik, leish, I. J., iibson, J, 1. and Flyan, f. Auxiliary ourreat alters transistor oharaeteristios, Ileotronies. 24i 142, 22S» gS2, 2M. Sept. ItSl.
Slade, B. H. A high-perfoimnee transistor with wide s^oing between oontaot®. ICA leTiew. IIi ilT-626. 1960.
• fhe eontrol ©f frequeney response and stability of point-ooataet transistors. Proe. of tha III, 40i IS82-IS84, 1962.
. faetors in the design of polttt»®ontaot transistors. RCA Review. I4t 17-27. 19i3.
Sliehter, *. P. and lolb, I, B, Impurity effects in the therml oonverslon of gersianiua. Phys. le-r. 87i gg7-§2S. 1952.
Spenser, llohard I. •transistor-eontrolled jMgnetio amplifier. Ileetronios. 2ii 13i*l40. Aug. IfSS.
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Stausel, F. 1. transistor equations. Bleotronios. 26t 1S6, 166 Mar. l»SS.
Sf
Ittrl L. fh®®ry of, al^a for f-S-P jttnetioa transistor's. Pro®, of the I®, 40i 1^4-1428, 1®S2.
Sta®t»®r, 0. -m. Srystal amplifier with high input iapad«nc«.. Pro©, of th« IIS. 381 8«S-int lt».
, transistors in airborne ®tttip#®at» Proo. of tl® IB, 40 J 1629-1630'. liSE.
Stthl, I. and thookley, 1. Conoantrating holos and ©Isetroas by wign®ti0 fields, fbys. &«t. ?Si 1S17«1018. 194t«
Sulser, P«t«r §. Junotioa transistor oiroult applioationa. Elaotronioi. 26i 170»17S, i»f. 19SS.
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thomaa, d. s. iLoW'-drain transistor a«dio oaoillator. Proo. of th« IIS. «)t 1M8-1S0S. ISSt.
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88
TaM®8, I». 1. • Iffaet of sleetrod# spaeiag on ©qmifaleat bas® resistaao® ©f foiat-eoataet transistors. Proo'. of the 111. 401 1429-14S4. 1952.
Taa loosbroeek, W. theory of the flew of eleetrons and holes i» gerawalm aad other swBieoaduotors. Ball Sys. Teoh, Jour, 29» 860-607. 19iO.
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89
fill. A,®IOTOiSMKrS
Ih® nutfaor wishes to express his appredifttioa to Rrefessor
W. I.. Oassell for his- ea-eelleat suggestions sad critioisiBSj to
i^ofessor M. S. Cower *feos» eneattrageaeat aod asslstasee aaia
this thesis fossiblei aiid to ^ofessors I*. W. Voa fersah tkM
B. L. ty for their .interest «Bd eooperatioa..
m
APPIHUICiS
A. ISAStJlBffiSf OF IIMSISTOS Ilf»K OOlFPmiEIfS
fh® eirsttit parsuse-feers for aa aetir® aetwork mn be
Jteaai 'through the network ®®«£flal«Bts. this aay be showa by eoa-
siieriaf th« gea«ral refreseatatioa ©f aa aetlT® artwork saoh as
ahowa ia Flgar® 1.
fh® a®8h eqaatioas f^r aa astiT® eirealt are
% " 3fii.ii * i«ia * (1^)
aad
• JTiSSill • **«»!* • (141)
If the sir©ait is irivea at th® iapat t®miaals aad !» is mad®
gero, these eqmtioas eaa b® witt®a as
rxi-~, (142)
aad
r»i. • . (us)
Itaatioa (l^) sh<m-s that rxx fcifat iRpedaae® of eirouit,
Sfiiatioa (145) shows that rm oaa b® fouai by takiag th® ratio of
output •©Itage to iaput ourraat. Similarly, if the iapat aai output
teraiaals ar® iat®rohiMag®4, th® a®twork eooffioieats rj.® aad rga oaa
b® fouai.
m
Al^hmgh thi» method em b® to traasistersi, It has on«
8«rio«8 dl«aimatag«, la oriar to »al£» Ii or !•« aero anl. atlll
maiatala tha i-e bias oarraat, a hi^ fttallty ©arraat sowre® is
a««i«d. fcr tt«« witk Juaetioa traaslstwr-s, tMs otirraat »ouro« »u«t
haf« 'a0re thaa tea mgQhm lataraal lapedaaoa.
fhe aatwork e^ffieiaats pertalaiag to tke aodal-darivad
atttiTOleat airamit eaa also be swasttred. Itola provea to be mare
aaaTeatmt far traaalatere wMieh are ateort-olrealt etabla.
The aodal tfaatioaa Ibr aa aativa aatwarlc aaa b® wrlttaa aa
% * * §xsfim » (144)
aad
I* " S8X% • S«)!^a • (14S)
If the airauit is irivea at the iapit tamiaala aad Bg ia made
aara, ataatioae (144) aad (148) may ba writtaa aa
sii • f (1^)
aad
Sai " %
Sg afty be made aero by sapflyiag %e d*® biaa wltage by maaas of a
battery# Ifnatiea (14i) aJiawe -feat gn, it the iapat adaittame of
the airauit. fftiatiaa (147) sktowa that ggj, aaa be fouad by takl;^
the ratio ®f ©utpat aarreat to lapat wltage. Slailarly, if the
iafttt aad. outpat tamiaala are interahaa^ed* .gj.^ aad aaa be
Baaaarad.
n
Wmuj brMg®»-bn« ©irmits My® bean «««d to nsasure the aatwork
©oeftioleatg psrtminiag to tli« no€«l «ta*tioa8* Ib purtioalar, tli«
®«n«rAl ftntiO' fyp« Tusatm-fob# Brlig#^ it well suitttd. @im»s
this briiga was destgati primarily fysr'fmmm. tub@», all eoEtrola
ar« labeled with memw-tmba paramwtern. tt li thewrfor® umemmry
to ©oi^ar# mottwtwb® and traiasisttr tte%w©rk eoelTioiwats.
fh« asdal sfttatioa for th« grouoaded eathod® miowa® tmbe aador
mrmi ofsratioa oaa b« wrltt«n aa
ii - c0)bi + (0)1« . (148)
aad
im - mx • gpb. • (1«)
I«r« % 1« the grid to aathed* wltag® lad 1, la tha plat® to ©altood®
•oltage. Sfe® aetworlc Qo#ffi®l0at8 ar® deflwd as follow® i
1^ — mtual ©oadaotaao® ,
am
gp — plate asMuetaao® .
For iHTsrted ssr-rlo®, th® aodal afttatloa® for tJ»« motim tab® ar®
H • i#3. • if## t (1®0)
aad
i« - (0)% • {0)% . (181)
teaaral iRdio Coapia^* Qparatiag iastriaatioas for typ® i@l-S we»a»*tttb« bridge. 2fS la««a^ttsett8 Avsam®, Cambridge Sf, lfossaotais«t%t. ^aa. 19§S*
94
fh® aetwork eoefflaieats of ©qm^lon (ISO) ar« <iafiaed m faXlowBi
gg •- grii mMmtmm ,»
®fS """ i*"''**'*® asttwal ®oadtt®ta«8« .
fh9 aatwerk aoelTieleats ®f atwitioEM (149) «ad (l§0) *r« tot all
»«as«jf«i Alraotly. Iteat is maasured direstly Is as fallowst
1 rg • t- — p*i4 rasistanise #
% ®fg — ittvepse atttwal ©oatuetaae® ,
-fffi •- iaversa Mispllileatioa faetor , ig
1. sp
ifp • *• plat® raslstaae® ,
aad
ftt *tttaal eoaiaetaa®® ,
jjt « & — aaplifieatiea fa©t®r . ®p
fafel® n
aai fraaaiattr letwerk Coeffieieats
Bridge Settiag ^ 0o«ffieieat Itoasiired
Tg l/fii
spg S%»
Sla/fia.
'•p 1/^aa
^ gai/g«8
: I
11
m
o m <fa 3
m -s
I i •o
I
8
©
§
I 4i»
f ^ f
' 1 f 4»
I M I
s
i
I I 48
WW I
« I ^ i
©
I t m m
e
I at s o
J k
1 «
s
•p»
1 1
s I ! I •
% i
I j « i ps
I I ® ^ *
I i 1 i
i« j 5 s» i
s 4»
I o«
s6
afmsbu 1, mvm dimsmcm amd smmimt ma. fmmmQm
Spseinl eoaiidtmtloa aast l>t gives to transittors' ia defial&g
r»t».ra 41ff®r®ao®^ «ai
fh« aodftl-d«rlv®4 oqwi"wileat ©ireiiit of Figur® 25 e®a Is® eoa-
siderad to b® dri-rea liy the irtiltae® tour®® at inhorml r®8ist®a®e
i es
WV o
E
o
Figttr® M§4 I©^l»d®rl'V«d etulvaleat eireuit
%. W* Bad®. I«t«r0rk Aaftlyci® ®ad F®®dte®l: Amplifi®r*'d®8iga. let ®d. D. Tstt loitraai e©mpwiy, lae. IS^W.
97
©r the ©wreat sour©® with ahmbing oondttstans# tg. fhe ttse of
«itli®i' 8oar©« will proitto# tha amm «Bd rssalt mtoea ealealfctiug
retwtt tiff«r«n0« if
This i» alao tra® f®r •aetwtwfe® sirettit# wJileli «aploy ©oadttetitao®
t>ttw9®a fiftt® aad grid amltgotis to gn ia fignr® IS. the faot ttuit
gala shades wh®a is irariM d6«8 aot a®<ia««arlly sigail^ faadbaek.
Jk ^jsioal ©xplaiMitioa of retttra dlff®r«be« oaa be giir®© by ub»
of tk® ®lr«ait of figwta £6. S«re it i« a8«mi«i that th® aodal
(lit)
• *#g (iss)
It aliottW b® aotei tMt for feeibaak to axist
»g /o . (1S4)
1 volt
Figmr® 26. *oial»4®iriT«d eirawit with r«tttra diffaraa®®
38
polat S© controls th« motive slflmeat ilmilar to the grid ia tlwi
Tsenaa tabe. It unit voltmg® is applied to this ooatroX poiat, the
©irauit etuatiotts are
9 • 8i<%*gi.*E«) - ijiia » (lfi8)
aiad
-84 • -%s« • • (1»6)
SolTing •qiutloos (16&) Bad (160) for Ei glTM
»l - - •== . (l«t)
AS
where AI is the »iml eii^ait detemiaiwit An $4 8®^
1 mm * St fsm be writtea as
aa "• <%•!*•««) cs«"^s«*%) - 4 • (2.88)
fhe voltage dilYereaeo between the eeatrol paint mi Wo aode at %
is
A, k, - bi - 7-2 • fn . (is»)
an
Where fn is the return tifferenee f^or the iwdal-derived eqttl-mleat
eirettit.
^he aor*,l eiremit detenainaat is ©htainei when the aroies at Ig aad Ml are ©oaaeeted together.
fii« ssBSltiTlty f®r g4 is as
ag4 ' i
(iso)
ler® voltaf® gala ©r. ourreat g*ia. #«a msed frovldiaf th®y *re
frop«rly • IsferriBig' to Figar® 2i, f©lt»t« gaia must b®
€« fitted as
fbis mkm it aeesssary us® ireltSLg® souitte ivkea ®@apttixig this
gain. If ®arr«at gain is used, it must be defined as
fbe euxreist sotaree must be used vliea eoaftitiBg Aj.
fim above expressisas t&r gaim s®« -very reasoHabi® when aoa-
sideriB^ nfe-at is lapliai by th® sensitiTity expression. Stated
is words, tb® rseiproeal of seasitifity is ratio of the percentage
ehaage ia gaia (dii® to a otoRB^e ia g*) t® -^e peroestage 0han«e in g4.
Eealisii^ that % or I|. does wt r«aiia aoBstant wfeea $4 -waries, gain
expressions amst b® written to iaeltide the souroe oharaeteristies.
Iqmtioas (l®l) and (Ifg) do this by takiag into aeeoaat the soaree
resistanee or oonduetaaee respeotiTely. I^laating eqaatioas (lii)
aad (li2) for the ciremit of Pigare 28, we hate
(161)
(les)
100
aad
%(g8'*g4)
aa
®ipcsi|**s4 )
an
(16s)
(164)
Us lag ®ith®p of tfh« aboT« e*pr«s«ioa», «i« seaalti-dlty d«fiaed l)y
©qmtiom (liO) l>®0oi«i«
W&»
u
A. -(US)
Similarly, for %h« a®th-d«riT«4 •<|ui"ral«a% eirauit of Figwra 27,
the as# of sittier sour©® irtll fpodao# ttw 8i«a« sxiirMBion for return
diffwromos whea 8qi«*ttoai (ise) aai (16s) liom.
r4li
Pigwr# 2T. l98k-deriV0d efittiTaleat ®iro«it
101
4 ,of ratura 4lff®r«ao« for -fch® W'8h-deriT9d
oireuit em h0 wwl® aaiag the oirsuit af Figar® 28. I«r« branch
earryisftg th® ewreat 3^ is assumed ta wsatrol the setiTe elemmt* If
wait mrrm% is Sfplied t© "tela braaeh as showa, the eireuit eqmtioas
<saa be wittea as
0 - (%*ri#rs)li • (Its)
•*•4 " (167)
eg ri
-vw-aaa/"
r4lc
1 ampere
Figure It. Mesh-deriired otaimlei^ oireuit with retura differeaee
Sel-riag efuatioas (16@) sad (lif) f&r Ii. gives
(168)
102
nfeer# Aa i^rml ©iroait datsmiaaat A a *ith r4 8«t to zor&^t
It ®aa be wlttea as
A» " ra^» (169)
Fro» this, the differeaee between the oarrents lo unfi Ii oaa be
writtea ma
a.
Ak le - ii - - fa » (ITO)
where is retwrn diffareaee for the aesh*deri'red e^tiitmlent
oirsult.
In ©alottlatiag seasitiTity, ei^er of ttte followlag gaias mast
be usedt
or
a, . Js. <rap5Si *g A-
a, - - . h a*
cm)
(172)
fhe seasitiTity for r4 #aa thea be writtea as
i • da '£4 dr4 a
r§ A (173)
%he ii©rwal ©irsait determimat is obtaiaed uteea the braaoh shortiag the earreat soarse is ©feaei.
103
Ih,® aboVQ dafiaitioBS of return differeaoe'and sensitivity ar#
Qonearnsd with th« aetive «l®»®at only. For the aoial-dsri-WBd
oireult, til® retura differeaoe and sensitivity for §4 was daflaed«
fhlB oorrasjpoads to th« return diff»r«B09 and sensitivity for ia
vaouwa-tube ©iroults, For ttie ma8li-d«riv®d olrouit, the retura
dlfftreaee aad sensitivity for r4 was dsfiasd* thsr® is ao analogous
ease f«r this ia mourn tub®#.