The transistor differential amplifier

Item Type text; Thesis-Reproduction (electronic)

Authors Blanchard, Jack Winfield, 1926-

Publisher The University of Arizona.

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THE TRANSISTOR

DIFFERENTIAL AMPLIFIER

by

Jack W. Blanchard

A T h es i s

submitted t o the f a c u l t y of the

Department o f E l e c t r i c a l E n g in ee r in g

in p a r t i a l f u l f i l l m e n t o f the req u irem en ts f o r the degree o f

MASTER OF SCIENCE

in the Graduate C o l l e g e , U n i v e r s i t y o f Arizona

1957

Approved: P U cu iZ i* - £ • , gD i r e c t o r of T h e s i s * Date

T h is t h e s i s has been submitted in p a r t i a l f u l f i l l m e n t

of req u irem en ts f o r an advanced degree a t the U n i v e r s i t y of

Arizona and i s d e p o s i t e d in th e L ibrary t o be made a v a i l a b l e

t o borrowers under th e r u l e s of the L ib ra ry . B r i e f q u o t a t io n s

from t h i s t h e s i s are a l lo w a b l e w ith o u t s p e c i a l p e r m is s io n , --

provided t h a t a c c u r a te acknowledgment of source i s made.

Requests f o r p e r m is s io n f o r extended q u o t a t io n from or r e p r o

d u c t io n of t h i s manuscript in whole or in par t may be granted

by the head o f th e major department or the dean o f the Grad

uate C o l leg e when in t h e i r judgment th e proposed use o f th e

m a t e r i a l i s in th e i n t e r e s t s o f s c h o l a r s h i p . In a l l o th er

i n s t a n c e s , however, p e r m is s io n must be obta in ed from the

a u th o r .

SIGNED:

TABLE OP COHTBNTS

Chapter 1 ̂ THE PROBLEM x - - . , ' ’ V . Page ;

l o l I n t ro d u e t io n 1

log The O p era tio n a l A m p lif ie r 3 •,

loS T hesis O b je c t iv e ; ■ 7

Chapter 2 ' DESIGN RE#IREMEETS OF THE OPERATIONAL

' AMPLIFIER : ' : vV 9. 'I

■ :2S1 . I n t ro d u c t io n : ■ / . ,: ' - 9

2*2 Design Requirements ; v; 9

2o3 Summary ; " • : ' 12 . ;

Chapter 3 THE DIRECT COUPLED TRANSISTOR AMPLIFIER 14' ■ - ̂ . • . .

5*1 In t ro d u c t io n ' 14

V " ;v3o2 : " -^pL acuss loh^ ■' : ; r : 14

3*3 The E f f e c t s of Temperature on T r a n s i s to r

' • : C h a r a c t e r i s t i c s ■ 15

- ;3o4 ■ : .•.SNegatlve ■Feedback f o r S t a b i l i z a t i o n - 18 /

3*5 S t a b i l i z i n g Techniques ; 21 ■

'’5 06 : , . Summary of P re v io u s 'E f f o r t s 22

3*7 The T r a n s i s to r D i f f e r e n t i a l . A m p lif ie r 23

Chapter 4 ANALYSIS OF THE TRANSISTOR DIFFERENTIAL • ■ ■'

AMPLIFIER; - ' : 27 V

• 4 o l I n t r o d u c t io n 27

7,4 *2 " The E q u iv a le n t C i r c u i t - ' 1'; 27 - -

4 63 S o l u t i o n f o r t h e V o l ta g e G a in o f th e '

D i f f e r e n t i a l A m p l i f i e r ' 50

4 e4 S o l u t i o n f o r the. I n p u t Im pedance o f t h e

D i f f e r e n t i a l A m p l i f i e r 55

4o5 S o l u t i o n f o r th e O utput Im pedance o f th e .

D i f f e r e n t i a l A m p l i f i e r /. 37

4®6 A n a ly s i s o f t h e T r a n s i s t o r a s a C o n s ta n t .

C u r r e n t S o u r o e - . - 40

4o7 Summary : 45 -

C h a p te r : 5 v ? ; : 44

5«1 : . I n t r o d u c t i o n , '' yf-: ' ' f - - , 44 i

5»2 . ;. C i r c u i t D es ig n , ’ : . ' 44

5o5 T r a n s i s t o r C h a r a c t e r i s t i c s : •' “ 47

5 0 4, •. D i s c u s s io n = C a l c u l a t i o n and E x p e r im e n ta t io n 50.

5o4ol Operating Point 50' . 5*4o2. Voltage Gain 53

; . 5o4 o3 Input Impedance 555e4o4 . Output Impedance . 55

, ;; 5e4s5 Drift' Characteristics ; : 575 = 5 Summary v 61 ■-

C h a p te r 6 S T3MARY'■■M'©..''.!® C OMIiEIIDATI ONS f 63.

6 01 - T h e s i s Summary 65

6 o 2 . Hecommendation f o r F u t u r e E f f o r t . . 65

6 6 3. : C o n c lu s io n ' 6 6

BlBLIpGRAPHr 67

' Ciaapter lo : ; ' -

'. THE PROBLEM ; •

( l o l ) : IirRODHCTlOH. '

' G oaow ren i; -with th e b e g in n in g o f W orld War I I a new e ra

a p p e a r e d I n e l e c t r o n i c s o T h is p e r i o d saw th e dev e lo pm en t of; ;

v a s t sy s te ta s o f e l e c t r o n i c and e l e c t r o - m e c h a n i c a l d e v ic e s h a r=

n e c e s s e d t o p e r fo rm t a s k s which ware h e r e t o f o r e im poss ib le® '

The f i r s t sy s te m s o f t h i s t y p e s such a s f i r e c o n t r o l s y s te m s s

r a d a r 9 and gun b e a r i n g c o m p u te rs w e re n a t u r a l l y awkwards un»

r e l i a b l e 9 . and in a ecurate.c, These sy s tem s had g r e a t - p o t e n t i a l ,

b u t t h e i r u s a b i l i t y a s b a t t l e f i e l d equ ip m en t was c o m p a r a t iv e ly

poor® T h is r e s u l t e d i n a l a r g e e x p e n d i tu r e o f e n g in e e r i n g t im e

i n r e d e s i g n / o p t im iz in g sys tem p a ra m e te r s and p a c k a g in g th e

: sy s te m f o r ' .m an u fac tu re 6 ' 1 ■

The p r o c e s s o f sy s tem a h a l y s i s , r e - e v a l u a t l o n s r e d e s i g n /

and o p t i m i z a t i o n o f c o n t r o l p a r a m e te r s t o a c h ie v e th e op tim um '

, o v e r a l l sy s tem was p o s s i b l e o n ly a f t e r d e t a i l e d and t e d i o u s

n u m e r ic a l com puta tions® The p rob lem was even more s e v e re when

I t . w a s n e c e s s a r y t o e v a l u a t e th e a f f e c t o f p r o d u c t i o n t o l e r a n c e s

on sy s tem p e rfo rm an c e o Som etim es t h e n u m e r ic a l r e l a t i o n s were

i n t r i c a t e and I n v o l v e d | b t h e r t im e s , t h e s h e e r q u a n t i t y o f e e l - :

G u la t io n s was enough t o seem in su rm oun tab le®

The s o l u t i o n t o p ro b lem s of t h i s ty p e was fo u n d i n i n t r i

c a t e and com plex a u to m a t ic com puting e q u ip m e n t / w hich h a s s in c e

fb een e x p l o i t e d t o f i n d u t i l i t y th r o u g h o u t m o d e rn ' i n d u s t r y e

Two p r i n c i p l e t y p e s were ad v an ced from t h i s w a r tim e e ra t o .

h a n d le p ro b lem s o f t h e ty p e i n d i c a t e d ; t h e d i g i t a l and a n a lo g

com pu te rs o' Each t y p e o f com pu te r h a s i t s d i s t i n c t a d v a n ta g e s

and d i s a d v a n ta g e s ^ . • ,y :

E s s e n t i a l l y ^ d i g i t a l co m p u te rs c o n s i s t of program m ing

u n i t s d r i v i n g c o u n te r s t h a t r e g i s t e r and add i n d i s c r e t e s t e p s G

M a th e m a t ic a l o p e r a t i o n s a r e p e rfo rm e d by c o m b ir ia t io n s of a d d i

t i o n 0 The a c c u r a c y o f staeh m ach ines i s l i m i t e d o n ly by t h e

space a v a i l a b l e t o house t h e com p u te r b e c a u se t h e c o m p le x i ty

and s i z e a r e in' d i r e c t p r o p o r t i o n t o t h e a c c u r a c y and sp e ed

desired-o' T J n f o r tu h a te ly s t h e p r o c e s s o f r e d u c i n g th e m a th e

m a t i c a l p ro b lem a t hand , t o a r i t h m e t i c o p e r a t i o n s ' and i n p r e -

p a r i n g th e i n i t i a l p rog ram i s v e r y t im e consum ing and r e q u i r e s

g r e a t ex p erience® Once program m ed 9 h o w e v er# t h e speed of com

p u t a t i o n i s t rem endouso D a ta h a n d l i n g . s p e e d s o f 50 th o u sa n d '

b i t s p e r second a r e r e l a t i v e l y e a sy t o a c h i e v e «, C om puters o f

t h i s ty p e f i n d g r e a t e s t u t i l i t y w here ex trem e a c c u r a c y a n d / o r

r e p e t i t i v e ty p e p ro b lem s a r e e n c o u n t e r e d =

The a n a lo g com puter on th e o t h e r hand u s e s p h y s i c a l quan

t i t i e s su ch a s l e n g t h s vo ltages , and s h a f t r o t a t i o n t o r e p r e s e n t

t h e v a r i a b l e s i n t h e p ro b le m » By c o n t r o l l i n g t h e s e a n a lo g s i n

t h e p r o p e r m anner t h e y can be made t o p e rfo rm i n an a n a l o g o u s "-

-manner t o th e o r i g i n a l e q u a t i o n b e in g a n a ly z e do C o - e f f i c i e n t s '

,o f th e v a r i a b l e s may be r e a d i l y v a r i e d t o o b t a i n t h e e f f e c t on

t h e o v e r a l l f u n c t i o n ^ t o ' . 7 .

To p rogram a p rob lem i n t o att a n a lo g com puter i t i s o n ly

n e e e s s a r y t o i n t e r - o o n n e o t t h e v a r i p u s com puting e le m e n ts

w i th p a t c h .conds and e s t a b l i s h t h e p r o p e r s c a l i n g f a c t o r s t o

c o m p le te ly s iB m la te t h e e q u a t io n o f i n t e r e s t o

A c c u r a c i e s i n t h e ra n g e o f oS^. t o lO^ a r e a d e q u a te , f o r

t h e s o l u t i o n o f m ost p ro b le m s e n c o u n te r e d i n e n g in e e r i n g

a p p l i c a t i o n S o . T h is r a n g e o f a c c u r a c y i s r e a l i z a b l e w i th t h e

a n a lo g com pu te r and b e c a u s e t h e t im e n e c e s s a r y t o se t= u p a

p ro b lem i s much le s s > t h e s e c o m p u te rs f i n d g r e a t u se i n t h e

e n g in e e r i n g f i e l d a :V . ■ • '

The ty p e o f com puter t h a t f i n d s g r e a t e s t a p p l i c a t i o n I s

t h e a n a lo g com p u te r w h e re in D~ 0 v o l t a g e s a r e u sed t o r e p r e

s e n t b o th t h e c o = e f f i c l e n t s and th e v a r i a b l e s o When used a s .

t h e l a t t e r t h e y may be made t im e v a r i a n t o ' W ith a f u n c t i o n

g e n e r a t o r 9,: p o t e n t i o m e t e r s s D-G a m p l i f i e r ' s p. and p a t c h - c o r d s j,

com plex m a th e m a t ic a i , p rp b lem s may; be a n a ly z e d ; w i th r e l a t i v e

e a s e » P a r a m e te r s and c o - e f f i c i e n t s ' o f t h e p rob lem a s w e l l a s

i n i t i a l v a lu e s s e t i n t o t h e - s o l u t i o n by p o t e n t i o m e t e r s can be

v a r i e d w i th e a s e t o o b t a i n t r i a l and e r r o r s o l u t i o n s » I n t h i s

m anner i t i s p o s s i b l e t o o p t im iz e d e s ig n p a r a m e te r s And to .

o b s e r v e th e e f f e c t s o f p a r a m e te r v a r i a n c e o '

t l o 2 ) : THE :OPERATIQHAI, AMPLIFIER . ; .

The h e a r t o f t h e D-C a n a lo g com pu te r i s th e D-C a m p l i

f i e r o W hen.used w i th a p p r o p r i a t e f e e d b a c k n e tw o r k s s an .am -

p l i f l e r 1 s c ap ab le ; o f ■perf orm ing v a r i o u s " m a th e m a t ic a l ' o p e r a - ' . •

t i o n s w h e re in t h e o u tp u t v o l t a g e i s made t o b e a r a d e f i n i t e

ma t'hema 11 e$ 1 r e l a t i on s h ip t o t h e I n p u t v o l t a g e 0 A d d i t io n ^

s u b t r a c t i o n ^ d i f f e r e n t i a t i o n % I n t e g r a t i o n and m u l t i p l i c a

t i o n b y a c o n s t a n t a r e r e p r e s e n t a t i v e m a th e m a t i c a l o p e r a

t i o n s o When u sed i n a p p l i c a t i o n s o f t h i s t y p e , ;■ t h e D-0

a m p l i f i e r i s commonly r e f e r r e d t o a s an" o p e r a t i o n a l am

p l i f i e r «, ... :.V. * ■' ■. ." ' . _

T r a n s f e r f u n c t i o n s - o f s e v e r a l t y p i c a l com puting n e t -

.works g u s in g o p e r a t i o n a l a m p l i f i e r s i a r e i l l u s t r a t e d i n P i g -. ■ ■ ' ■ i a . - • : ■ •

u r e ( l o l ) » In t h e s e and o t h e r a p p l i c a t i o n s 0 th e v o l t a g e

g a i n o f th e B -0 a m p l i f i e r i s v e r y h i g h e As a r e s u l t 9 t h e

t r a n s f e r f u n c t i o n s a r e d e te rm in e d by s t a b l e f e e d b a c k n e tw o rk s

r a t h e r th a n th e fo r w a r d g a i n o f th e e l e c t r o n i c a m p l i f i e r

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t r a n s i s t o r v e rs to r io A ehange o f t h i s ty p e w i l l r e a l i z e a

g r e a t s a v in g i n w e igh ty s i z e 9 and power co n su m p tio n o v e r t h e '

vacuum tu b e v e r s io n s o . I n a d d i t i o n ^ where p r e s e n t e l e c t r o n i c

eq u ip m en t r e l i a b i l i t y i s s e r i o u s l y l i m i t e d by th e r e l i a b i l i t y

o f t h e vacuum tubeg th e t r a n s i s t o r v e r s i o n shou ld , s u f f e r no

such . l i m i t a t i o n s ' ;

; - fh e .DoGb o p e r a t i o n a l a m p l i f i e r i s one exam ple o f e l e e -

t r o n i c equ ipm en t t h a t can b e n e f i t by b e in g a d a p te d t o th e

t r a n s i s t o r v e r s io n ^ ■ :

( l o 5 ) fBBSIS OBJECTIVE

The need f o r a t r a n s i s t o r v e r s i o n of t h e DoCo o p e r a t i o n a l

a m p l i f i e r h a s b een r e c o g n iz e d by th e E l e c t r i c a l E n g in e e r in g

D ep ar tm en t o f th e U n i v e r s i t y o f A r iz o n a and a j o i n t g roup o f

t h r e e men w o rk in g to w a rd . . t h e i r MSEE.,have u n d e r t a k e n t o a n a ly z e

some o f t h e v a r i o u s a s p e c t s o f a c h i e v i n g a t r a n s i s t o r o p e r a

t i o n a l a m p l i f i e r v Work on t h i s p r o j e c t w i l l c o n t r i b u t e d i r =

e e t l y t o t h e t h e s i s . r e q u i r e m e n t ' f o f -'th® MSEBo -The w r i t e r ^ -

a s a member o f t h i s g ro u p was c h o s e n ■to a n a ly z e and s e t f o r t h

t h e d e s i g n r e q u i r e m e n t s f o r a t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r e

T h is p a r t i c u l a r e i r c u l f a p p e a r s t o have e h a r a e t e r i s t i e s t h a t

- ^ O th e r c o n t r i b u t o r s ) : ' \ % .. x

Do d- 6 H a v i l l e « C hopper s t a b i l i z a t i o n o f d i r e c t c o u p le d a m p l i f i e r s ~ T h e s i s - U n i v e r s i t y o f A r iz o n a ^ 1957 6

R o J ® B eck er n 'T h e T r a n s i s t o r O p e r a t i o n a l A m p l i f i e r - T h e s i s U n i v e r s i t y o f A r iz o n a P 1 9 5 7 0 . : . ■ ■ ■

w i l l s a t i s f y t h e r e q u i r e m e n t s f o r th e i n p u t s t a g e o f th e

t r a n s i s t o r o p e r a t i o n a l a m p l i f i e r 0

. The t h e s i s w i l l em ph as ize t h e DoGv o h a r a o t e r i s t l c s o f

t h e t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r o These c h a r a e t e r i s t i c s

a r e im p o r ta n t b e c a u s e t h e d r i f t t h a t n o rm a l ly o c c u r s when

t r a n s l a t o r s a r e u sed a s a m p l i f i e r s i s c o n s id e r e d t o be a

m ajo r p ro b lem i n d e s i g n in g a t r a n s i s t o r ©oCo o p e r a t i o n a l am pl

i f i e r * The o b j e c t of t h e t h e s i s i s t o o b t a i n a' s t a b l e DcGo

a m p l i f i e r s u i t a b l e f o r u s e ; i n t h e t r a n s i s t o r o p e r a t i o n a l •

a m p l l f i e r o • ■. . ' . / - • • .

CHAPTER - 2

DESIGN REQUIREMENTS OF: THE' D»C . ' OPERATIONAL AMPLIFIER

< 2 o l) TNTRODUCTICM ■ ̂ ' r '

The g e n e r a l desTgn re q u ire m e ii i is o f t h e DoCo o p e r a t i o n a l

a m p l i f i e r and a c o m p le te d i s c u s s i o n o f e a c h r e q u i r e m e n t w i l l

be fo u n d I n Ro SI B e ck e rs T h e s i s F o r th e sake o f c o n t i n u i t y ^

and t o p r e p a r e t h e r e a d e r f o r l a t e r d i s c u s s i o n ^ a b r i e f r e s u m e ;

o f some of t h e more im p o r ta n t r e q u i r e m e n t s w i l l be in c lu d e d

her© d : - ;; . . ; . v v .

( 2 .2 ) DESIGN".REQUIREMENTS OF D-C OPERATIONAL AMPLIFIER

2 02 01 DoOo c o u p l in g th r o u g h o u t a m p l i f i e r : :

I n a n a lo g c o m p u te rs t h e v a r i a b l e s o f th e e q u a t io n s t o be

s o lv e d a r e r e p r e s e n t e d by D .C . v o l t a g e s t h a t v a r y w i th time©

R a te o f v a r i a t i o n depends on b a s i c speed o f c o m p u ta t io n de«

s i r e d b u t h o r m m lly - i s v e r y low© P a ra m e te r s and c o e f f i c i e n t s

o f t h e v a r i a b l e ' a s w e l l a s i n i t i a l v a lu e s o f t h e f u n c t i o n m ust

be added t d ’a n h ie v e t h e s o l u t i o n o f t h e e q u a t i o n . T hese re-*■ -y:. 1 . .v f : ' ' :

q u i r e m e n t s . c a n - o n l y be. met by a d i r e c t c o u p le d a m p l i f i e r ©

2 02 02 I n p u t and o u t p u t a t t h e same D.O. l e v e l s

To a c h ie v e th e d e s i r e d d e g re e o f s t a b i l i z a t i o n and hav e .

t h e a b i l i t y t o i n t e r e o n n e c t t h e ■ v a r i o u s co m p u te r e le m e n ts t o

S l b i d .

;; ̂ ' ■■■ ■ ■ v ' . ; ' ' ' • - - ' ■ : ./ /

a .eh ieve th e eom puting a c t i o n r s q u l r e d s i t I s n e e e s s a r y t o

u se f e e d b a c k f ro m th e o u tp u t . t o t h e i n p u t o f th e a m p 3 . i f le r 0

C o n d u c tiv e f e e d b a c k w hich i s r e q u i r e d i n most com puting

a r r a n g e m e n ts 9 can o n ly be u sed i f th e i n p u t and o u tp u t o f . ;

t h e open lo o p a m p l i f i e r a r e a t t h e same •Dc.Co p o t e n t i a l o

To a c h i e v e t h e s e DC l e v e l s i t i s n e c e s s a r y t o u se a t l e a s t

two' pow er su pp lies -* More may. be r e q u i r e d i n c e r t a i n c i r

c u i t s t o e s t a b l i s h th e p r o p e r l e v e l s f o r I n t e r s t a g e coupling©

2o2©3 Ad ju s tp ie n t o f DoCj, o u tp u t l e v e l i

The d e s i r e d DaCe o u tp u t l e v e l can o n ly be a s s u r e d i f th e

a m p l i f i e r i s d e s ig n e d w i th p r o v i s i o n f o r c o n v e n i e n t ' a d j u s t ==■

ment o f t h i s l e v e l The p r o c e s s of a d ju s tm e n t i s c a l l e d b a l

a n c in g o r z e ro ad ju s tm e n t 0 ... ' .

2©24 R eq u irem en t f o r h ig h open lo o p v o l t a g e g a in s

I n iP lgu re (1® 1) t h e co n f i g u r a t i o n o f s im p le RC com puting

n e tw o rk s and t h e more e l e g a n t v e r s i o n u s i n g t h e DC o p e f a t l o n a l

. a m p l i f i e r a r e i l l u s t r a t e d » ‘ Accompanying t h e s e i l l u s t r a t i o n s ; •

a r e t h e e x a c t and sim p1i f l e d e x p r e s a lo n s f o r th e o u tp u t v o l ta g e ©

The 'fo rw a rd ga in j, As o f t h e D0C0 o p e r a t i o n a l a m p l i f i e r i s c o n - ‘

s i d e r e d much g r e a t e r t h a n u n i f y s An a n a l y s i s on th e am ount o f

e r r o r "in v o lv e d i n u s in g t h e s i m p l i f y i n g e x p r e s s i o n shows t h a t

i n g e n e r a l s g a in s b e tw e e n lo® and 10^ a r e s a t i s f a c t o r y w i th th e

h i g h e r g a in s o b v io u s ly p r o v i d i n g th e g r e a t e s t a c c u r a c y o f com-' .

p u ta t io h © ■ v - -

SoS'oS Feed f o r D d o s t a b i l i t y ? ■.

O o n d u c tiv e c o u p l in g b e tw een s t a g e s o f a h a m p l i f i e r .means

t h a t t h e o u tp u t o f t h e a m p l i f i e r i s s e n s i t i v e t o DoC© l e v e l

11

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F / G C / G ’E ' ( 2 . 2 )

B A S IC /fA & dL L B L B B B O B d C k ; s A M F L /f /B 'S

c h an g es i n t h e in p u t a s w e l l a s w e l l a s v o l t a g e l e v e l

c h an g es w i t h i n th e a m p l i f i e r i tseX S o Changes o f t h e " l a t t e r

ty p e a r e ' te rm ed d r i f t and c o n s t i t u t e e r r o n e o u s i n f o r m a t i o n

o r u n h a la n c e i n t h e o u tp u t o f t h e a m p l i f i e r = F o r a c c u ra c y

o f co m p u ta t io n ^ t h e s e d r i f t s m ust m in im izedo

2o2«>6 High i n p u t im p e d a h e e z ; '

■ A f i n i t e i n p u t im pedance t o t h e DoCo a m p l i f i e r i n c r e a s e s

t h e com puting e r r o r o ' The m ag n itu d e o f th e e r r o r depends on

t h e c o m p u ta t io n b e in g p e r f o r m e d » R e f e r r i n g t o F ig u r e ( 2 o l ) ».

i f t h e g a in o f t h e open lo o p a m p l i f i e r i s h ig h and th e r a t i o

o f t h e com puting im p e d an c e s t o t h e i n p u t im p ed an ce 9 Zg?

i s made s m a l l 5, t h e e r r o r w i l l a l s o be sm a llo On t h e o t h e r

h a n d , where I t i s n o t p r a c t i c a l t o make t h i s r a t i o s m a l l , t h e n

th e open lo o p g a i n . A, m hst be l a r g e r -to r e a l i z e a g iv e n e r r o r »

2 o 2 67: l e e d f o r h ig h f r e q u e n c y s t a b i l i z a t i o n ? ' ,

A b a s i c p a r a l l e l f e e d b a c k a m p l i f i e r "with ah open loop,

t r a n s f e r f u n c t i o n A (s ) and B (s ) i s shown i n F i g u r e (:2 e 2 ) I f

t h e p h a se s h i f t : i n h e r e n t i n t h e open loop t r a n s f e r f u n c t i o n

A (s ) B (s ) r e a c h e s 560 d e g re e s f o r some f r e q u e n c i e s w h i le t h e

.ga in |A B | i s g r e a t e r t h a n u n i t y , t h e - . a m p l i f i e r w i l l b r e a k i n t o ;

s u s t a i n e d o s c i l l a t i o n s « I n th e d e s i g n o f t h e a m p l i f i e r w i th '

two o r more s t a g e s o f a m p l i f i c a t i o n s , i t w i l l be n e c e s s a r y t o

i n s e r t co m p e n sa tin g n e tw o rk s t o oyercome t h i s d i f f i c u l t y *

C2o3) SUMMARY- - ' v .

The . .des ig n r e q u i r e m e n t s t h a t h av e b e e n l i s t e d c o n s t i t u t e

t h e m a lo r f a c t o r s t h a t m u s t-b e t a k e n i n t o c o n s i d e r a t i o n i n t h e .

d e s ig n o f th© t r a n s i s t o r v e r s i o n o f t h e D&Go o p e r a t i o n a l

a m p l i f i e r o T h is t h e s i s s however> w i l l be c o n c e rn e d w i th

o n ly t h o s e c o n s i d e r a t i o n s w hich e f f e c t t h e p®Co p r o p e r t i e s

of •■the ,amplifier a.,"' « / ■

14

CHAPTER 5

: '.THE DIRECT COOPIED TRAHSISTQR AMPLIFIER :

. ' :i3 o . l ) i THTROBIICTION , : ....

. I n t h i s c h a p t e r we c o n s i d e r t h e e f f e c t s o f t e m p e r a tu r e

v a r i a t i o n s on t h e t r a n s i s t o r when u sed i n a d i r e c t co u p led

a m p l l f i e r o P r e v io u s work shows t h a t 1) S i l i c o n t r a n s i s t o r s

2 ) : A b r i d g e - t y p e c i r c u i t and 3) n e g a t i v e f e e d b a c k sh o u ld be

u sed t o a c h ie v e a s a t i s f a c t o r y d i r e c t c o u p le d a m p l i f i e r

' . ' : ' : ' ' :: ■ ■ : ■ - ■ . : ' ■ ■ :15

t o u se the . b e s t m ethod o f a t t a c k t o m in im ize t h e l a r g e r

v a r i a b l e s and s t i l l m eet t h e end o b j e c t i v e ^

(SoS) THE EFFECTS OF TEMPERATURE'OH TRANSISTOR CHARACTERISTICS.

• ^The j u n c t i o n b r a n s i s t o r may be r e p r e s e n t e d a s shown i n

f i g u r e (S o l)o The c i r c u i t i l l u s t r a t e s a p e r f e c t t r a n s i s t o r

w i th an a d d i t i o n a l c u r r e n t s o u r c e Ieo> The c u r r e n t so u rc e

r e p r e s e n t s t h e c o l l e c t o r c u r r e n t t h a t f lo w s th r o u g h a r e v e r s e =

b i a s e d c o l l e c t o r j u n c t i o n w i th z e r o e m i t t e r c u r r e n t * The c u r^

r e n t I G 0 h a s two co m p o n en ts j t h e s a t u r a t i o n , c u r r e n t o f a p e r

f e c t d io d e and t h e l e a k a g e r e s i s t a n c e due t o c o n ta m ln a t io n o f

t h e c o l l e c t o r ju n c t io n o The l a t t e r i s n o t a l i n e a r f u n c t i o n

o f th e a p p l i e d v o l t a g e f o r l a r g e c o l l e c t o r v o l t a g e v a r i a t i o n s o

B oth com ponents a r e s u b j e c t t o t e m p e r a tu r e v a r i a t i o n s o The

r e s u l t i s a n e x p o n e n t i a l b i a s c u r r e n t t h a t v a r i e s w i th t e m p e r a

t u r e and c o l l e c t o r v o l t a g e and i s i n d e p e n d e n t .o f t h e a p p l i e d

b ia so : 'h ’ ' ; ' ̂ ̂ ' : : f . . 'v?' i

■ I n th e common e m i t t e r t r a n s i s t o r a m p l i f i e r t h e e f f e c t o f

I co a p p e a r s i n th e c o l l e c t o r c i r c u i t a s I co ( l ' - h hg ^) s® where ,

hg]_ r s p r e s e n t s t h e dynam ic c o l l e c t o r t o b a s e ' c u r r e n t t r a t i s f e r •

r a t iO o ""For th e a v e r a g e t r a n s i s t o r hg^ may h a v e a v a lu e o f

P

16

^ A C T U A L

I T R A N S I S T O Rco

P E R F E C T T R A N S / S T O R

F I G U R E 3.1 - EQUI VALENT T R A N S I S T O R CIRCUIT W I T H X co

v

N O A t A h L T £ f A P £ 1 L A T U * i

£Le'/ATi£D retAPE*.* ruee

FIGURE 3 . 2 - T H E A F F E C T OF TEMPF/SATORE ON T H E TRANSISTOR. / N P U T C H A R A C T E R I S T I C S

" • ' ■ ' V - V : 17;a b o u t f o r t y o The m ag n itu d e o f XGo a t room t e m p e r a tu r e i s

o f t h e o r d e r o f O d m lcro= am peres f o r s i l l e o n t r a n s i s t o r s

and 3 LD m ic ro -a m p e re s f o r germanium t r a n s i s t o r s c ■ The varla™ . x

t i o n o f I GO w i th t e m p e r a tu r e i s o f t h e o r d e r o f f l y e p e r c e n t

p e r d e g re e c e n t i g r a d e f o r s i l i c o n and e i g h t p e r c e n t p e r d e

g r e e c e n t i g r a d e f o r germ anium » Even t h e s e s m a l l I eo v a r i a

t i o n s a however,, when m u l t i p l i e d by (14=* hg^) c o n t r i b u t e

a p p r e c i a b l e e r r o r i n t h e c o l l e c t o r c i r c u i t o f a d i r e c t coup

l e d a m p l i f i e r i f I f s e v e f a l s t a g e s ' o f a m p l i f i c a t i o n a f e c a s

c a d e d , t h e e r r o r i s a m p l i f i e d and added tO , b y e a c h s t a g e ,

c a u s in g a ,much l a r g e r e r r o r a t t h e o u tp u t o f t h e a m p l i f ie r®

Means m u s t, t h e r e f o r e , be t a k e n t o s u p p r e s s t h e e f f e c t s o f ;

I co i f s a t i s f a c t o r y DoG® s i g n a l a m p l i f i c a t i o n 1 s t o be

a c h ie v e d o ' , ■;

The fo r w a r d b i a s e d d io d e j u n c t i o n Of t h e b a se to e m i t t e r

c i r c u i t i s a l s o s u b j e c t t o t h e e f f e c t s o f tem p era tu re© I n

c r e a s e d t e m p e r a tu r e r e s u l t s In. a r e d u c t i o n -in H u , t h e dynam ic

i n p u t r e s i s t a n o e and Vbe> th e b a s e t o e m i t t e r v o l t a g e $ see

f i g u r e :(S© 2)© S i l l d o n t r a n s i s t o r s e x h i b i t l e s s p e r c e n t a g e

v a r i a t i o n o f V'be t h a n germanium t r a n s i s t o r s © However, t h e ' .

m ag n itu d e o f Vfea i s h i g h e r f o r s i l ic o n ® As a r e s u i t , te m p e r

a t u r e e f f e c t s on t h e i n p u t c i r c u i t a r e o f t h e same o r d e r o f

m ag n itu d e f o r b o th t y p e s o f t r a n s i s t o r s ® The n e t r e s u l t s o f f ,

any changes i n byy o r V^e a r e s h i f t s i n t h e o p e r a t i n g p o i n t

b i a s c u rre n t® T hese s h i f t s c an n o t be d i s t i n g u i s h e d a t t h e

o u tp u t o f th e a m p l i f i e r from a DiC© s i g n a l l e v e l o h m ge a t f

t h e i n p u t ® '■ ; ' • :

( 3 a4) ' NEGATIVE FEEDBACK FOR STABILIZATION

18

The u se o f a n e g a t i v e f e e d b a c k i n a h ig h g a i n d ir -ec t

cou p led a m p l i f i e r ‘i s mandat o r y 0 N e g a t iv e f e e d b a c k im prove s

l i n e a r i t y ^ p r o v id e s g a in s t a b i l i z a t i o n and a c e r t a i n d e g re e

o f DoCo l e v e l s t a b i l i z a t i o n * I t i s n o r m a l ly n e c e s s a r y t o

p r o v id e f e e d b a c k a t e a c h i n d i v i d u a l s t a g e o f a m p l i f i c a t i o n

a s w e l l a s o v e r a l l f e e d b a c k a ro und t h e c a s c a d e d s t a g e s e ®The

d e s i r e d c h a r a c t e r i s t i c s o f t h e o v e r a l l a m p l i f i e r d i c t a t e t h e

ty p e o f f e e d b a c k t h a t sh o u ld be usedo N e g a t iv e c u r r e n t f e e d ”

b ack r e q u i r e s a n open lo o p a m p l i f i e r w i th -g low i n p u t imped™

an ce => The e f f e c t o f n e g a t i v e c u r r e n t f e e d b a c k i s t o make t h e -

i n p u t and o u tp u t im pedance o f t h e a m p l i f i e r h i g h . N e g a t iv e

v o l t a g e f e e d b a c k r e q u i r e s an open lo o p a m p l i f i e r w i th a h ig h

i n p u t impedanceo The e f f e c t o f n e g a t i v e v o l t a g e f e e d b a c k ■i s

t o make t h e i n p u t and o u tp u t im pedances lom» 0 The o v e r a l l ;

a m p l i f i e r f e e d b a c k sh o u ld be t h e " d u a l" o f th e i n d i v i d u a l s t a g e

f e e d b a c k o To i l l u s t r a t e j , i f n e g a t i v e v o l t a g e f e e d b a c k i s t o b e

usedj, t h a n th e i n n e r s t a g e f e e d b a c k sh o u ld be n e g a t iv e c u r r e n t »

fee d b ac k o T h is p r o v i d e s t h e h i g h i n p u t im p e d an c e 9 d e s i r e d i n •

t h e .open lo o p a m p l i f i e r o % h e n Used a s an o p e r a t i o n a l a m p l i f i e r .

f o r com putings t h e i n i t i a l h ig h i n p u t Im pedance s e r v e s to '- r e - . : ' ;;

duoe t h e com puting e r r o r * v' . ‘

The u se o f n e g a t iv e f e e d b a c k on each s t a g e o f a m p l i f i c a t i o n ;

©Ho Bo H u r le y “ D e s ig n in g T r a n s i s t o r : C i r c u i t s - Do Co , ; > ...a m p l i f i e r s E l e c t r o n i c E qu ipm ent “ B a re h 9 . 19571

. '^OPo C ito > Ro I® B eck e r " ' ' " . .

19

p r o v id e s s t a b i l i z a t i o n , but does t h i s a t the expense of g a i n .

Where s e v e r a l s t a g e s of d i r e c t coupled a m p l i f i c a t i o n are cas

caded t o a c h ie v e an o v e r a l l h igh g a in a m p l i f i e r t h i s s a c r i f i c e

may not be d e s i r a b l e in a l l c a s e s .

^Figure ( 3 . 3 ) i l l u s t r a t e s t h r e e cascaded d i r e c t coupled

a m p l i f i e r s w i th g a i n s A^, A'g and A3 . V oltage d r i f t s in h er en t

in each s ta g e are r e f e r r e d t o the in p u t s as o f f s e t v o l t a g e s

e l> e 2 a n ^ e 3 * I n the p r e sen ce of and input v o l t a g e and

o f f s e t v o l t a g e s e j , eg and 6 3 th e output v o l t a g e ,

vE'o = £ t A % A \ A * + G i A \ A ' t . A % + € \ A \ A 3 ^ € 3 ^ 3 fI —A t Ax A * *0

w i l l be brought back t o zero i f

- — /e , i- f — )x /4 i A i A t A i A x A s J

From t h i s i l l u s t r a t i o n I t can be seen that n e g a t i v e feedback

red u ces the d e s i r e d s i g n a l E% by the same amount th a t the un

d e s i r e d d r i f t v o l t a g e e% i s red uced . S u c c e s s i v e d r i f t s i n th e

a m p l i f i e r , however, are reduced by the g a in o f the p ro ceed ing

s t a g e s . Because th e d r i f t v o l t a g e 6 % i s not reduced by f e e d

back i t w i l l appear i n th e output as an error i n the a m p l i f i e d

s i g n a l . P a r t i c u l a r a t t e n t i o n must t h e r e f o r e be devoted to

a c h ie v in g an input s ta g e of d i r e c t coupled a m p l i f i c a t i o n w i th

low d r i f t and h ig h g a i n .

®0P. G i t . - Korn & Korn

20

FI GUR E 3 . 3 - CASCADED D I R E C T C O U P L E D A M PL IF IE R W I T H D R I F T

Dtnoout-Aroe

F I G U R E 3 . 4 - C A S C A D E D D I R E C T C O UPLEDA M P L I F I E R W I T H S T A B / L I Z A T I O A I

O

21

( 3 . 5 ) STABILIZING TECHNIQUES

S t a b i l i z i n g t e c h n iq u e s have been developed®' ^whereby

h igh g a i n A . c . a m p l i f i e r s may be used to minimize the e f f e c t

of d r i f t i n a d i r e c t coupled a m p l i f i e r . The most w id e ly used

scheme, i l l u s t r a t e d in f i g u r e ( 3 . 4 ) employs a chopper t o con

v e r t the input B . C . s i g n a l t o an A . C . s i g n a l . A high g a in

A . C . a m p l i f i e r f o l lo w e d by a demodulator c o n v e r t s the v o l t a g e

back t o B . C . at a much h ig h e r s i g n a l l e v e l . When t h i s c i r

c u i t i s added t o the p r e v i o u s l y a n a lyzed d i r e c t coupled am pli

f i e r , a s i l l u s t r a t e d , th e output v o l t a g e

£ o = £ ’t ^ A ! ' H ) A l A z A 3 + C t A t A i A } r e x A * A 3 + C y A ? + € < * I — (4 , + I ) Ai A t As

w i l l be brought back t o zero i f

t i i — — r . §?»— + — i ĵ:— + — — 7L ( A \ ^ l ) ( A l H) A* ( A \ + l ) A i A x ( A l * * ) A i A x A 3 J

As c o n t r a s t e d t o th e p r e v io u s case the e f f e c t o f the

d r i f t v o l t a g e e^ i s reduced by (A^-#-1 ) , a p p ro x im ate ly the g a in

of the A.C. a m p l i f i e r .

9The bandpass c h a r a c t e r i s t i c s o f the s t a b i l i z i n g a m p l i f i e r ,

demodulator and f i l t e r are g e n e r a l l y r e s t r i c t e d t o a bandwidth

of l e s s than one c y c l e . In t h i s way the c o n t r i b u t i o n of A d o e s

not a f f e c t th e h igh freq u en cy s t a b i l i z a t i o n r e q u i r e d . I t does

®0P. C i t . - Korn & Korn

90P. C i t . - G. B. H a v i l l e

: ; : ' : :: ■; ; : . 'v " . ' @ 2

p r o v i d e h i g h g a i n a t v e r y low f r e q u e n c y t o m in im iz e t h e l o n g

t e r m DoC® . d r i f t I '

The o u t p u t o f t h e s t a b i l i z i n g a m p l i f i e r must be added

I n t o t h e I n p u t s t a g e of t h e d i r e c t c o u p le d a m p l i f i e r i n t h e

p r o p e r p h a se t o a f f e c t an a d d i t i o n w i t h t h e i n p u t s i g n a l E q 0

T h i s a d d s one more r e q u i r e m e n t t o t h e i n p u t a m p l i f i e r c i r c u i t

d e s i g n where t h i s s t a b i l i z i n g t e c h n i q u e i s usedo

( 3 0 6 ) SUMMARY OF EREVIODS BDPORTS ̂ : '

Many t e c h n i q u e s have b e en u sed t o r e d u c e t h e e f f e c t of

t e m p e r a t u r e v a r i a t i o n on t h e o p e r a t i o n o f a d i r e c t c o u p le d

a m p l i f i e r * Some o f t h e t e c h n i q u e s ha ve i n c l u d e d t h e u se o f

b i a s e d d iod esg t h e r m i s t o r s s t r a n s i s t o r and r e s i s t a n c e br idge ,

c i r c u i t S p com plem en ta ry symmetry t r a n s i s t o r s a n d v a r io u s - com

b i n a t i o n s of n e g a t i v e feedback*. A l l o f t h e s e t e c h n i q u e s have

r e s u l t e d i n ' s a t i s f a c t o r y d i r e c t c o u p le d a m p l i f i e r s s b u t i n : -:;

g e n e r a l g s p e c i a l s e l e c t i o n o f t h e c o m p e n sa t in g components were

n e c e s s a r y V F u r t h e r s v e r y c r i t i c a l c i r c u i t a d j u s t m e n t s were

n e c e s s a r y t o a c h i e v e t h e s e r e s u l t s * •

The p r e v i o u s e f f o r t s , i n t h i s l i n e a r e n o t t o be i g n o r e d

a n d t h r e e c q h c l u s i d n s . may he .drawn- t h a t , w i l l l a i d , t h e p r e s e n t ; 1

. e f f o r t n r . % 1 .1 ',,' . ' . - l ' ' ' ; 1

1) S i l i c o n t r a n s i s t o r s a r e t o be p r e f e r r e d o v e r germanium

t r a n s i s t o r s * • v- ■:>. ■. ;V"l' r ' . f .

2 ) The u se o f n e g a t i v e f e e d b a c k i s m a n d a to ry and p r o v i d e s

c e r t a i n d e g r e e s o f s t a b i l i z a t i o n * Howevers n e g a t i v e f e e d b a c k

a ro u n d s e v e r a l ' s t a g e s , o f c a s c a d e d d i r e c t c o u p le d ' a m p l i f i c a t i o n

does n o t a i d i n c o m p e n sa t in g f o r d r i f t s i n h e r e n t i n t h e f i r s t

s t a g e * A d d i t i o n a l s t a b i l i z i n g , t e c h n i q u e s : m u s t be u se d t o r e

duce t h i s e f f e c t * : . ; V-

5) A b r i d g e c i r c u i t u s i n g t r a n s i s t o r s w ho se . t e m p e r a t u r e ; \

c h a r a c t e r i s t i c s ^ a r e s i m i l a r a p p e a r s t o o f f e r t h e s i m p l e s t and ■

most s t r a i g h t f o r w a r d s o l u t i o n t o b a l a n c i n g ou t t h e f i r s t o r d e r '

t e m p e r a t u r e , e f f e c t So I n a. c i r c u i t o f t h i s t y p e s t e m p e r a t u r e

v a r i a t i o n s t h a t change t r a n s i s t o r c h a r a c t e r i s t i c s by e q u a l

amount s do n o t r e s u l t i n a n o u tp u t , s i g n a l * Only t h e second

o r d e r e f f e c t s , whereby t r a n s i s t o r s ' o f t h e same t y p e ha v in g d i f

f e r e n t r a t e s o f change o f t h e v a r y i n g p a r a m e t e r „ c o n t r i b u t e t o

t h e o u t p u t s i g n a l * " , , ■

(2*7) .THE-; T MHS 1ST OR: DIFPEREHTI A i AMPLIPIER:.; , .

The doub le ended o r d i f f e r e n t i a l t r a n s i s t o r a m p l i f i e r c i r

c u i t - i l l u s t r a t e d i n f i g u r e (3*5) a p p e a r s t o o f f e r a f i r s t o r d e r

s o l u t i o n t o t h e m a jo r p ro b lem s a s s o c i a t e d w i t h DoG* a m p l l f l c a -

' t i b n o T h e . f o l l o w i n g cpmbined a d v a n t a g e s a r e , o f f e r e d 2 ' ,

. 1) I n t h i s c i r c u i t t h e t e m p e r a t u r e c o m p e n sa t in g a d v a n t a g e s .

of t h e b r i d g e c i r c u i t a r e a c h ie v e d * To t h e e x t e n t t h a t t h e t e m

p e r a t u r e c h a r a c t e r i s t i c s o f t h e t w o . a r e a l i k e 9, d r i f t i n t h e ' -

t r a n s i s t d r does n o t c a u s e a n o u t p u t s i g n a l s

: ■ 2 } Two i n p u t s and two o u t p u t s ' a r e a v a i l a b l e f o r t h e .s t a g e

o f a m p l i f i c a t i o n * The two i n p u t s make t h e c i r c u i t a d a p t a b l e

f o r c h o p p e r s t a b i l i z a t i o n * A z e r o b a l a n c e a d j u s t m e n t t h a t does

R u

O ^ol

s /' ] V/^CC

F I G U R E 3o5" ~ T H E BASIC T R A N S I S T O R DIFFERENTIAL AMPLIFIER

to

' 8 5 ' ;'

n o t i n t e r a c t w i th t h e I n p u t c i r c u i t can a l s o be a d d e d l e v e l s i f c r i t i c a l c o u p l in g

c i r c u i t a d j u s t m e n t s a r e t o be a v o i d e d ^ /

4)' The symmetry o f t h e c i r c u i t r e d u c e s t h e e f f e c t o f

power s u p p ly v a r i a t i o n s , b e c a u s e v a r i a t i o n s a r e a p p l i e d t o

b o t h s i d e s of t h e b r i d g e e q U a l l y 0 '

5) The i n p u t impedance o f t h e t r a n s i s t o r d i f f e r e n t i a l

a m p l i f i e r i s a t l e a s t t w i c e t h e i n p u t impedance o f a s i n g l e

comm;on-emit ter s t a g e of a m p l i f i c a t i o n i f Bee i s l a r g e enough

t o p r o v i d e good d i f f e r e n t i a l c o u p l in g o : T h i s r e s u l t s f rom t h e

f a c t t h a t t h e i n p u t s i g n a l i s e q u a l l y d i v i d e d b e tw ee n t h e two

b a s e ' . t o e m i t t e r c i r c u i t s e Because t h e s i g n a l i s d i v i d e d be

tw een t h e two i n p u t s t h e v o l t a g e g a i n t o e a c h c o l l e c t o r i s

o n ly o h e - h a l f t h a t a v a i l a b l e f r o m ,a s i n g l e common e m i t t e r am pl

i f i e r ^ The f u l l g a i n may be o b t a i n e d # however# by u s i n g : t h e

d i f f e r e n t i a l s i g n a l a v a i l a b l e frbm: c o l l e c t o r t o e o l l e c t o r o - ,

6) S i g n a l s o f e i t h e r p h a se . a r e a y a i l a b l e a t t h e o u t p u t o f

t h e d i f f e r e n t i a l a m p l i f i e r 0 As' a r e s u l t i t i s n o t n e c e s s a r y

t h a t an @dd num ber1 o f s t a g e s be' c a sc ad e d t o o b t a i n o v e r a l l .

n e g a t i v e ' f e e d b a c k ® /• .■ . 't. - '

1 E x a m in a t io n of a l l the- a v a i l a b l e l i t e r a t u r e : on d i r e c t

v ' ' - . ' ■. > . - : . . 26

c o u p le d a m p l i f i e r s h a s f a i l e d t o r e v e a l any c i r c u i t o r com

b i n a t i o n o f c i r c u i t s t h a t o f f e r s t h e a d v a n t a g e s Of th e d i f

f e r e n t i a l a m p l i f i e r =- T h i s c o n c l u s i o n e s t a b l i s h e s t h e j u s t i f i

c a t i o n f o r t h e a n a l y s i s and e x p e r i m e n t a t i o n c o n d u c te d i n t h e

f o l l o w i n g c h a p t e r s o

27

„ ' ■ • ' v;: V ' ; " • ■ GHAPTBR' 4 ' ' - ' ' ■ ̂ ■ : : •

AHALYSIS OP THE TRANSISTOR DIFPEREHTIAL AMPLIFIER

{ 4 * l j INTRODUCTION . ; / • ' ; : -

; I n t h i s c h a p t e r t h e t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r ,

i s a n a l y z e d u s i n g t h e h y b r i d p a r a m e t e r ' e q u i v a l e n t c i r c u i t Q :

E x p r e s s i o n s a r e d e r i v e d f o r t h e v o l t a g e g a i n s i n p u t imped”

an ce and o u t p u t impedance* The dynamic c o l l e c t o r r e s i s t a n c e

o f a t r a n s i s t o r i s shown t o r e p r e s e n t a v e r y h i g h r e s i s t a n c e . .

Use o f t h i s dynamic r e s i s t a n c e f o r Ree i n t h e a m p l i f i e r i n ”

c r e a s e s t h e e f f e c t i v e c o u p l i n g b e tw ee n t r a n s i s t o r s * W ith

t h i s method t h e l o s s t h a t would be e n c o u n t e r e d i f an e q u l ”

v a l e n t r e s i s t a n c e were u s e d i s . avoided®

f loB ) ' THE BQUIVAIENT CIRGUIT >/. ■ •

Ii i t h e f o l l o w i n g a n a l y s i s o f t r a n s i s t o r c i r c u i t s t h e

m ethods o f a n a l y s i s ' - a n d ; - t h e e q u i v a l e n t c i r c u i t s u se d - w i l l be

t h o s e d e v e lo p e d by To fo M a r t i n and h i s a s s o c i a t e s ® ^ .

T he t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r , f i g u r e ( 3 o 5 ) s i s

i l l u s t r a t e d i n i t s e q u i v a l e n t f orm i n f i g u r e ( 4 61) =, H e r e . t h e

tw o ” t e r m i n a I m p a i r h y b r i d p a r a m e t e r e q u i v a l e n t c i r c u i t i s ' r e p r e

s e n t e d i n i t s v a r i a t i o n a l f o r m | i g n o r i n g t h e q u i e s c e n t l e v e l s ®

i p T ® M a r t i n s and a s s o c i a t e s - T r a n s i s t o r E q u i v a l e n t C i r c u i t C r i t e r i a .=■ R e p o r t s U n i v e r s i t y o f A r iz o n a ? A u g u s t s 1956>

h n

■AAAAi b t

6 z

o t

F I G U R E 4 . / - L O W F R E Q U E N C Y E Q U I V A L E N T CIRCUIT OF

THE T R A N S I S T O R O / F F E R E N T / A L A M P L I F I E R

29

The problems i n v o l v i n g q u ie s c e n t l e v e l s f o r i n t e r s t a g e

co u p l in g and b i a s i n g w i l l be t r e a t e d s e p a r a t e l y . Their

i n s e r t i o n a t t h i s p o in t o f the a n a l y s i s would s e r v e no

u s e f u l p u rp ose .

The v a r i a b l e s used t o d e s c r ib e the o p e r a t io n o f the

common-emitter d i f f e r e n t i a l a m p l i f i e r are as f o l l o w s :

vb = v a r i a t i o n a l component o f the base v o l t a g e

ib « v a r i a t i o n a l component o f the base current

vc * v a r i a t i o n a l component o f th e c o l l e c t o r v o l t a g e

i c = v a r i a t i o n a l component o f the c o l l e c t o r current

ve = v a r i a t i o n a l component o f th e e m i t t e r v o l t a g e

i e = v a r i a t i o n a l component o f the e m i t t e r current

h u =

a

' " ■ = - § 5 5 :

h i I —

d c b

h i o . —- d c cd sir'c

a S q

Lb

' X f z

Lb

~ T r a n s i s t o r input impedance

V o ltag e feedback r a t i o

n Current t r a n s f e r r a t i o

— T r a n s i s t o r output adm ittance

The v o l t a g e feed b a ck r a t i o , h^g, i s a v ery sm a l l q u a n t i ty ,

When i t i s in c lu d e d i n the a n a l y s i s i t does no t m a t e r i a l l y

e f f e c t th e f i n a l r e s u l t s . I t d o e s , however, add a g rea t d e a l

o f c o m p le x i ty t o the e q u a t io n s developed which obscures the

u s e f u l r e l a t i o n s h i p s . T h e r e f o r e , throughout t h i s a n a l y s i s th e

30

q u a n t i t y w i l l be c o n s id er ed n e g l i g i b l e . F ig u re ( 4 . 1 )

was der ived us ing t h i s s i m p l i f y i n g assum p tion .

( 4 . 3 ) SOLUTION FOR THE VOLTAGE GAIN OF THE DIFFERENTIAL

AMPLIFIER

The v o l t a g e g a in o f th e d i f f e r e n t i a l a m p l i f i e r i s

d e f in e d a s th e r a t i o o f the s i g n a l e Q a t e i t h e r output t o

th e d i f f e r e n c e between the two input s i g n a l s . To d e r iv e

the v o l t a g e g a in o f the e q u i v a l e n t d i f f e r e n t i a l a m p l i f i e r

o f f i g u r e ( 4 .1 ) i t i s n e c e s s a r y to f i n d the output s i g n a l s

e 0 i and e 0 2 due t o input s i g n a l s Vj and Vg. For purposes

of the d e r i v a t i o n , I s assumed g r e a t e r than Vg.

The K ir ch h o f f v o l t a g e loop and current node e q u a t io n s

a s s o c i a t e d w ith the e q u i v a l e n t c i r c u i t o f f i g u r e ( 4 . 1 ) are

r e p r e s e n t e d by e q u a t io n s ( 4 .1 ) through ( 4 . 5 ) .

i c t ( f o t + r L - ) - cb* A zjl + i t * k*LL — c c z / # Lz +-L- ) = O ( 4 .1 )

i b t &i — c b z £ 2 c V/ - V a ( 4 . 2 )

where — X// & s t /kMD — A / / v- £ s a

c b t & , — c C & c C = V/ ( 4 . 3 )

(4 . 4 )

31

Lbt -+ ibz. + i c / -t i c z + c e. ^ O (4 .5 )

The c o l l e c t o r c u r r e n t s i c ^ and i c 2 are now obta ined in

terms of and Vg by the s im ulta n eo u s s o l u t i o n o f the above

e q u a t i o n s . I f the c u r r e n t s - i c ^ and - i c g are m u l t i p l i e d by

and RLg r e s p e c t i v e l y , the produ cts are e q u a l t o E0i and

Eo 2 ‘The s o l u t i o n of t h e s e e q u a t io n s y i e l d s ,

= - L c t R u ~ ( R l 7 k x i *- / t k x i + G li

V / £ j k n " R\)kit - k z z Rz f KLikxi + ij t G* ku 2 k™ +1)1

( R u Kxi i-1 Ait + 1 + k z i 4 R z k w J + R x ( P u i k n + 1 } £ / ? * > / k x i + / + J i z i + R i k z i J

>?e e

(4 . 7 )

32

and,

E o z — - CC 2 R lz - ( V t - S / z ) A i t ( kzx + I * Ail 4 f c ihzx j R i.i

— V t J ^ A z i f Z i - E i J A z i - A n E x A n f / A . i

t \/z j^E i k i t A x i + j ) ( J - _ A z . i g j . l

Ei(£^iAn +l)J&i.z A n f / >* A i / +‘£ \ k x x j + A*i Axx +J/-Ax/ -t E tA z i^

Ex B z ( & i f A x i + l ) ( E h Azz + l ) >?ee

( 4 . 8 )

The d e s i r a b l e s i g n a l s a t th e output o f the d i f f e r e n t i a l

a m p l i f i e r are the p o r t i o n s o f e q u a t io n s ( 4 . 7 ) and ( 4 .8 ) t h a t

are m u l t i p l i e d by (V%- V g ) . The o th e r c o n t r i b u t i o n s to t h e

output s i g n a l due t o the c o e f f i c i e n t s o f Vj and Vg a lone may

be c a l l e d common mode e f f e c t s . In the case o f th e vacuum tube

d i f f e r e n t i a l a m p l i f i e r the common mode e f f e c t s are reduced by

making th e mutual c o u p l in g r e s i s t o r , d e s ig n a te d here as Re e ,

very l a r g e . In the t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r t h i s i s

33

o n ly p a r t i a l l y t r u e . I n c r e a s in g Ree d e c r e a s e s one term of

the c o e f f i c i e n t o f i n one output v o l t a g e and one term o f

th e c o e f f i c i e n t o f Vg in the o th e r output v o l t a g e ♦

by the d e s i r e t o have equa l c o e f f i c i e n t s of the common mode

v o l t a g e s a t the two output t e r m i n a l s . Making Ree very la r g e

w i l l accom plish t h i s r e s u l t .

The s i g n s a s s o c i a t e d w ith th e common mode terms in

e q u a t io n ( 4 . 7 ) and ( 4 . 8 ) show th a t t h e y appear w ith the

same p o l a r i t y i n each c o l l e c t o r c i r c u i t . The d e s i r e d s i g n a l ,

(Vj - V g )* appears w ith o p p o s i t e p o l a r i t y in each c o l l e c t o r

c i r c u i t . General eq u a t io n s w r i t t e n f o r th e output v o l t a g e s .

The requirement f o r a la rg e Ree i s e s t a b l i s h e d , however.

a r e :

Eoi rr —Aft! ( \ / i ̂ \/i) V# -h Ki V* ( 4 . 9 )

and

E g z = A R - i - l / t ) * kV ^ V z ( 4 . 1 0 )

where :

A&i =* v o l t a g e g a in from input t o c o l l e c t o r o f T

A j S i v o l t a g e g a in from input t o c o l l e c t o r o f Tg

K, i K,' c o e f f i c i e n t of terms

Aft ̂K x c o e f f i c i e n t o f Vg terms

34

I f the t o t a l output s i g n a l i s taken as th e d i f f e r e n c e

s i g n a l between the two c o l l e c t o r s t h e n .

r o r * L = o z — ( 4 .1 1 )

S u b s t i t u t e e q u a t io n s ( 4 . 9 ) and ( 4 .1 0 ) i n t o ( 4 . 1 1 ) and

assume Ar l z Ar 2 ,

o r o r / 94. — Z ( I/51 + l/i ( K t ~ J + \ / t ( Kx — K t ) ( 4 .1 2 )

Equation ( 4 . 1 2 ) shows t h a t i f th e d i f f e r e n c e s i g n a l

between E0g and E0i i s used the t o t a l g a in w i l l be tw ic e t h a t

a v a i l a b l e from one inp ut t o the c o l l e c t o r • In a d d i t i o n , com

mon mode e f f e c t s are c a n c e l l e d t o the e x t e n t th a t th e c o e f

f i c i e n t s o f th e common mode v o l t a g e s are made e q u a l . Cascaded

d i f f e r e n t i a l a m p l i f i e r s accom pl ish t h i s r e s u l t by a m p l i fy in g

o n ly the d i f f e r e n c e s i g n a l .

For purposes of D.C. s t a b i l i z a t i o n complete c i r c u i t

symmetry w i l l be m ainta ined wherever p o s s i b l e . With the

assum ption t h a t z = j A t * & « I and i f

& e e » >£/ o * e q u a t io n s ( 4 . 7 ) and ( 4 .8 ) may be sim

p l i f i e d and then s o lv e d f o r th e u s e f u l g a i n .

A e / - _ F o i ( 4 .1 3 )( - l/t )

and

A u £ j . (4 . 14)

35

I f symmetry i s m ainta ined a t the input c i r c u i t a l s o ,

Rl = Rg = hn-t- Rg, and th e e q u a t io n s reduce t o .

E quat ions ( 4 .1 3 a ) and ( 4 .1 4 a ) are r e c o g n iz e d a s be ing

eq u a l t o o n e - h a l f the v o l t a g e g a in of th e common e m i t t e r

a m p l i f i e r w ithou t e m i t t e r d e g e n e r a t io n , as m odif ied by th e

a d d i t i o n of Rg t o h j ^ .

( 4 . 4 ) SOLUTION FOR THE INPUT IMPEDANCE OF THE DIFFERENTIAL

AMPLIFIER.

The input impedance t o th e d i f f e r e n t i a l a m p l i f i e r may

be found by r e p la c in g the input v o l t a g e Vg by i t s i n t e r n a l

impedance and s o l v i n g the K ir ch h o f f e q u a t io n s f o r the r a t i o

of V i / i b 1 . With t h i s change made t o the e q u i v a l e n t c i r c u i t

i n f i g u r e ( 4 . 1 ) , K i r c h h o f f 1s v o l t a g e loop and current mode

e q u a t io n s are then r e p r e s e n te d by eq u a t io n s ( 4 .1 5 ) through

( 4 .1 3 a )2 (hn + Rs ) ( Rl + 0

and

(4 .1 4 a )

( 4 .1 9 )

L b i h a — i b z ( h a + e s x ) - V / ( 4 .1 5 )

(4 . 16)

36

~ I hi k u + ib-L kxi - t o i ( £ u + J — ) + i a t Z u +JL ) = o ( 4 .1 7 )>tiL k i t x A n / 1 4&i/

Lb* A'S — c . e / ? € € ~ V/ ( 4 .1 8 )

i h * + c t > l + CC/ y- 4

37

Examination o f the e q u i v a l e n t c i r c u i t shows t h a t t h i s

e q u a t io n r e p r e s e n t s the s e r i e s r e s i s t a n c e as seen a c r o s s the

top l e g o f th e c i r c u i t . A l l o th er r e s i s t a n c e s are cons id ered

t o be l a r g e enough so th e y do not a f f e c t lo a d in g in t h i s c i r

c u i t .

Because symmetry i s m ainta ined in the c i r c u i t , i t i s

obvious th a t the inp ut impedance as seen from th e base of Tg

w i l l be i d e n t i c a l t o e q u a t io n ( 4 . 2 3 ) . T h e r e fo r e , the d e r iv a

t i o n o f Zing i s o m i t te d .

( 4 . 5 ) SOLUTION FOR THE OUTPUT IMPEDANCE OF THE DIFFERENTIAL

AMPLIFIER

The output Impedance o f the d i f f e r e n t i a l a m p l i f i e r may

be der iv ed by f i r s t r e p la c in g the input v o l t a g e g e n e r a t o r s

Vi and Vg by t h e i r i n t e r n a l Impedances. I f a v o l t a g e gener

a t o r V0 i s now a p p l i e d a t the c o l l e c t o r o f Tg, the r a t i o o f

th e a p p l ie d v o l t a g e V0 t o th e c o l l e c t o r current l e g may be

d e f in e d as the output impedance ZQg . The e q u i v a l e n t c i r c u i t

f o r t h i s d e r i v a t i o n i s i l l u s t r a t e d i n f i g u r e ( 4 . 2 ) .

The K ir ch h o f f v o l t a g e loop and current node e q u a t io n s

a s s o c i a t e d w ith the e q u i v a l e n t c i r c u i t are r e p r e s e n t e d by

e q u a t io n s ( 4 .2 2 through ( 4 . 2 6 ) .

(4 .2 2 )

- ( X// - t & s t ) - ( / i n

i i > z A j £ L K t i h t z

R u

FIGURE. 4 .2 - E Q U I V A L E N T C I R C U I T E O E T H E O U T E U T -I M P E D A N C E o r T H E T R A N S I S T O R

D I F F E R E N T I A L A M P L I F I E R

39

— i b z / Z z . O ( 4 .2 3 )

+ A l t J — — O ( 4 .2 4 )

1 6 / f t* — t € / £ e € ~ O ( 4 .2 5 )

i b i + i b i + LCt + CCZ t i € O ( 4 . 2 6 )

I f the above e q u a t io n s are so lv e d f o r l e g and the r a t i o

o f V o / i c g o b ta in e d , the f o l l o w i n g e q u a t io n r e s u l t s :

2 oz - V e - I n ^ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A.%* + 1c c t K.XI ■» g c i k x t 4 l ) t £x ( Zu k v x + I ) J

X e e

( 4 . 2 7 )

I f the p r e v io u s assum ptions are made once a g a i n , namely,

V- A/z r- % -f k t t

( h i / t ) k i i « J

and « /

then e q u a t io n ( 4 . 2 7 ) may be s i m p l i f i e d t o

*** ^ i t x z D * Z( ^4 . t kxv +1) +hxi J ~ ( 4 .2 3 )

40

Inasmuch a s symmetry o f the c i r c u i t i s m ainta ined the

e q u a t io n f o r Z0 i w i l l be i d e n t i c a l t o e q u a t io n ( 4 .2 8 ) and

the d e r i v a t i o n can be o m it te d .

The output impedance d e r iv e d in e q u a t io n ( 4 . 2 8 ) r e p r e

s e n t s the output impedance of the t r a n s i s t o r a m p l i f i e r w ithout

ta k in g i n t o account the load r e s i s t a n c e RLg. In the f i n a l

form the e q u iv a le n t impedance seen a t the c o l l e c t o r w i l l be

th e p a r a l l e l com binat ion o f RLg and or ,

Z o i e y . — Zc i G l i ( 4 .2 9 )Zoi +- ft11

( 4 . 6 ) ANALYSIS CF THE TRANSISTOR AS A CONSTANT CURRENT SOURCE

The e q u a t io n s f o r v o l t a g e g a in o f the d i f f e r e n t i a l ampl

i f i e r e s t a b l i s h e d the f a c t th a t a h ig h v a lu e f o r Ree i s n e c e s

sary f o r sym m etr ica l a m p l i f i c a t i o n . I f ord inary r e s i s t a n c e i s

used f o r Ree the v o l t a g e drop a c r o s s th e r e s i s t o r due t o the

e m i t t e r c u r r e n t s o f both t r a n s i s t o r s would r e q u ir e a very h igh

power supply v o l t a g e . The t r a n s i s t o r i t s e l f , however, has th e

output c h a r a c t e r i s t i c of a c o n s ta n t current d e v i c e ; i t has th e

a b i l i t y t o supply a c o n s ta n t c o l l e c t o r current with la rg e

changes in c o l l e c t o r v o l t a g e i f the b i a s current i s held con

s t a n t . I f current feedb ack i s used so the b i a s changes i n

v e r s e l y w ith c o l l e c t o r c u r r e n t , a s t i l l b e t t e r output c h a r a c t e r

i s t i c i s o b t a in e d . The dynamic output r e s i s t a n c e o f the t r a n

s i s t o r used in t h i s manner w i l l be v e r y h ig h w ith o u t e x c e s s i v e

v o l t a g e drop a c r o s s i t .

41

F ig u re ( 4 . 3 ) I l l u s t r a t e s the schem atic and the e q u iv

a l e n t c i r c u i t o f the t r a n s i s t o r a s a con sta n t current sup

p l y . The K ir ch h o f f v o l t a g e e q u a t io n s f o r the e q u iv a le n t

c i r c u i t are w r i t t e n i n e q u a t io n s ( 4 . 3 0 and ( 4 . 3 1 ) .

CC ( ̂( AlL — =■ Vc ( 4 .3 0 )k n

and

Z6 ( R b +■ h a +■ R e e ) + c c / Z e e - o ( 4 .3 1 )

I f e q u a t io n s ( 4 .3 0 ) and ( 4 . 3 1 ) are so lv e d f o r the r a t i o

o f V c / i c , the r e s u l t i n g e q u a t io n may be d e f in e d as the e q u iv

a l e n t dynamic r e s i s t a n c e .

I f A z z R e e

+Ec.c Vc

ResRz

LC

SC H E M AT IC DIAGRAM E Q U I V A L E N T C I R C U I T

F I G U R E 4 . 3 - 'T H E SCHEMATIC AND E Q U I V A L E N T C I R C U I T OFT H E T R A N S I S T O R A S A C O N S T A N T C U R R E N T DEVICE

to

43

: (4 .7 ) SUMMARY , ; ' - . . .. . . :

The c o m p le te e q u a t i o n s t h a t have b e e n d e v e lo p e d I n t h i s

c h a p t e r p r o v i d e t h e n e c e s s a r y c r i t e r i a f o r c o m p le te a n a l y s i s

o f t h e t r a n s i s t o r d i f f e r e n t i a l a m p l i f i e r * Where a d e s i g n

p r o c e d u r e i s t o be de ve loped? o r s im p le i n t u i t i v e u n d e r s t a n d "

: i n g o f t h e c i r c u i t s i s d e s i r e d ? t h e co m p le te e q u a t i o n s a r e

n e a r l y u s e l e s s b e c a u s e o f t h e i r c o m p l e x i t y „ E q u a t i o n s f o r ,

t h i s need were p r o v i d e d by a p p l y i n g a s s u m p t io n s t h a t a l l o w e d

t h e e q u a t i o n s t o be s im p l i f i e d ® I n t h e s i m p l e r fo rm t h e

e q u a t i o n s p r o v i d e b e t t e r u n d e r s t a n d i n g o f t h e d e s i g n r e q u i r e

m ents and t h e m a jo r e f f e c t s o f p a r a m e t e r v a r i a t i o n s ® •

44

CHAPTER 5

- . ; CALCULATIONS AND EXPERIMENTATION

(Sol)- INTRODUCTION

I n t h i s ch ap tie r tihe t r a n s l a t o r d i f f e r e n t i a l a m p l i f i e r

d e s ig n i s e v a l u a t e do The t h e o r e t i c a l c i r c u i t p a r a m e te r s cal**

e u l a t e d by th e e q u a t io n s o f C h a p te r .4 a r e compared w i th t h e

a c t u a l c i r c u i t p a r a m e te r s m easured i n th e l a b o ra to ry ® The

LAC. c i r c u i t s t a b i l i t y i s checked by a two and o n e - h a l f h o u r

d r i f t , t e s t . . . .

X5o2) CIRCUIT DESIGN

A f t e r th e b a s i c ty p e o f d i r e c t c o u p le d a m p l i f i e r s t a g e

h a s b een c h o s e n s th e a c t u a l d e s ig n p ro c e d u r e I s r e l a t i v e l y ,

s im p leo \ ' ■ ' '■ - •;

I n b r i e f s t h e d e s ig n p ro c e d u r e i s d e s c r i b e d i n th e seo=

t i o n s t h a t f o l l o w . ; . ;; : ; ' - ■ v.

( 5 . 2 . I ) S e l e c t a . t r a n s i s t o r w i th t h e d e s i r e d c h a r a c t e r i s t i c s

such a s : " . . - A . • .v - •. ./ , ' : \

a ) T em p era tu re s t a b i l i t y { s i l i c o n }

Ab} H ig h 'h g l - ' ■■■ ,

:c i High h n . ; . ■ a ;

.d) High To maximum

e ) R e l a t i v e l y h ig h a lp h a c u t o f f

- . 45

(SoSoS) Choose th e s u p p ly v o l t a g e r e q u i r e d f o r th e

a m p l i f i e r b a se d upon t h e f o l l o w i n g c o n s i d e r a t i o n s g

a ) Maximum v o l t a g e sw ing d e s i r e d a t th e o u tp u t o f

t h e : a m p l i f i e r o

,b) 'maximum of t r a n s i s t o r s e l e c te d o

e) Power s u p p ly v o l t a g e s r e a d i l y a v a i l a b l e e

(SaSoS) S e l e c t th e o p e r a t i n g p o i n t f o r t h e t r a n s i s t o r «

The s e l e c t i o n i s b a s e d upons

a ) L in e a r o p e r a t i n g r e g i o n . .

b ) : Medium l o w .c o l l e c t o r and b a s e c u r r e n t s =

e) H igh lo a d - r e s i s t a n c e b -^- : - --w

d) ^Low o u tp u t im p ed an ce 0 ;

e ) R e q u ire d DoCa q u i e s c e n t o p e r a t i n g l e v e l s

The c h o ie p o f t h e o p e r a t i n g p o i n t i s a com prom ise b e tw ee n

s t a g e g a i h ? s t a b i l i t y ^ and o u tp u t im p ed an ce» Ho s e t r u l e s c a n

be e s t a b l i s h e d to . c o v e r a l l c a s e s o l n s t e a d g a n i n t u i t i v e

a p p ro a c h i s r e q u i r e d o f t h e c i r c u i t d e s i g n e r s w i th j u d i c i o u s

c o n s i d e r a t i o n o f t h e f a c t o r s l i s t e d above®

A f t e r th e o p e r a t i n g , p o i n t and th e su p p ly v o l t a g e a r e

chosenj, t h e r e s i s t a n c e v a lu e s n e c e s s a r y t o p r o v id e th e b i a s

c u r r e n t s and o b t a i n t h e p r o p e r q u i e s c e n t l e v e l s a r e r e a d i l y

c a lc u la te d ® . . "

The c i r c u i t d e s ig n e d by t h e . w r i t e r i s i l l u s t r a t e d i n

f i g u r e (5®!)® ' : : / ;

Coz oc> ""O

F I G U R E S . l - F / N A L D E S I G N O F T H E T R A N S I S T O RD I F F E R E N T / A L A M P L I F I E R

o>

A

47

(5o3)' TRANSISTOR CHARACTERISTICS

The t r a n s i s t o r s used f o r t h e a m p l i f i e r w e re t h e T exas

I n s t r u m e n t gNIXYc T h is t r a n s i s t o r p r o v id e s m ost o f t h e c h a r -

a e t e r l s t l o s d e s i r e d e x c e p t f o r t h e v a lu e o f hg^s which i s '

r e l a t i v e l y lowe The T d o 2 M il 8 w i th i t s h i g h e r v a lu e o f h g i

w i l l be a b e t t e r c h o ic e i n t h e f i n a l a m p l i f i e r d e s i g n 0 The

g e n e r a l c h a r a c t e r i s t i c s o f th e c i r c u i t g h o w e v e r$, can be e v a l

u a te d w i th t h e d e s i g n i l l u s t r a t e d o :

The, t r a n s i s t o r u se d fo r ; t h e c o n s t a n t c u r r e n t - s o u r c e i n t h e •

e m i t t e r ' c i r c u i t was t h e G e n e ra l .E l e c t r i c - 212.67s a germanium

t r a n s i s t o r o 'The c o n s t a n t c u r r e n t c h a r a c t e r 1 s t i c s s and h i g h e r

h g i o f ' t h e germanium t r a n s i s t o r make i t a more d e s i r a b l e c h o i c e •

f o r t h i s p o r t i o n o f th e c i r c u i t » • 2 ;

The g r a p h s o f f i g u r e ( 5 02) and (5o5) show th e o u tp u t c h a r

a c t e r i s t i c s o f -the 2N117' and 21167 t r a n s i s t o r e o The c h a ra c te r ; - .

I s t l C s : w ere r u n on th e a u to m a t i c p l o t t e r a t t h e U n i v e r s i t y - •

R e se a rc h L a b o r a to r y 0 The maximum c o l l e c t o r v o l t a g e t h a t c o u ld

be a p p l i e d w i th t h e power s u p p ly . c i r c u i t o f t h e a u to m a t i c '

p l o t t e r v a r i e d f ro m 1 0 v o l t s down and depended upon th e c o l

l e c t o r c u r r e n to T h e re fo re ^ i t was n e c e s s a r y t o l i n e a r l y e x t r a

p o l a t e t h e c u rv e s t o p r o v id e c h a r a c t e r i s t i c s t o t h e maximum :

c o l l e e t p r ; y o l t a g e o f th e t r a n s i s t o r 0 : Large e r r o r s a r e ' i n t r o - .

duced a t t h e h i g h e r c o l l e c t o r v o l t a g e s by t h i s p ro c e d u re o The .

o p e r a t i n g p o i n t o f t h e t r a n s i s t o r ^ however^ i s c h o se n i n a

r e g i o n w here th e d a ta a r e r e a s o n a b l y v a l i d

OUTPUT CPAMCTPP/ST/CS !, n p S i U f i — Z N i n - t f U C O N .

i * z J £ — =

jv 2.0

/ S = ! 2 o w: :

j f l - .lo o U A

I 'e, * s o q a

& j l € ° m

(£ /T # * P O U tT E O D A T A - - - - - - - - - - - - - - - - - - - - )

/O ! . 2 0

M LiCTO Je y o ir s

r B i i i m i4^ ? * - r—I- i -*—*

7 —"

, q : m w =! 1 i j

H +H J

t J s S L t i

f & *:/oH f t e f e :xm- h

^ : l / o m , £ cY £ X T # X /= > o L 4 r £ D & A T A + -

c o u F c r a— ) , : ' : n # : r-t'TTi rt

-i 1 -L I—| —P4 -I—t ii-j 1 -f-rr' 1 1 1

p l o t t e r 0: th e o u tp u t c h a r a c t e r i s t i c s f o r o n ly one 2E117 and one

2N16Y t r a n s i s t o r were o b ta in e d o The i n p u t c h a r a c t e r i s t i c s

c o u ld n o t be ru n d u r in g ' t h e t im e a v a i l a b l e o I t was n e c e s s a r y s '

t h e r e f o r e $ t o o b t a i n th e e r i t i c a l t r a n s i s t o r p a r a m e te r v a lu e s

h%% and h g i by o t h e r m e th o d s 0

^ T h e a - c s m a l l s i g n a l t e c h n iq u e was used t o m easure t h e

p a r a m e te r s h^Qj and h p i f o r t h r e e 2E117 t r a n s i s t o r s s a t v a r i o u s

v a lu e s o f b i a s c u r r e n t » The r e s u l t s a r e p l o t t e d i n f i g u r e ( 5 o 4 ) e

T r a n s i s t o r s # 1 and #5. had p a r a m e te r s t h a t w ere most n e a r l y

a l i k e and t h e s e t r a n s i s t o r s were used f o r th e d i f f e r e n t i a l ampl=

i f i e r e v a lu a te d ^

( 5 e4) ' DISCUSSIOl - GALdlEATlGH AHB BXPERIMB1TATI0I „

( 5 0 4V l) O p e ra t in g :P o ln t , :

The o p e r a t i n g ;p o ln t -and power s u p p ly v o l t a g e ch o sen ■"

f o r th e 2H117 t r a h s i s t 6 r : a r e a s . f o l lo w s s "

: ' ' - '. :' f 1 , f ' ',1-^ =: 1 5 0 ' m ic ro -a m p e re s - \ ", " " ' , -:

: I;0 ;: ;ft 2 : < , 0 m i l l i - a m p e r e s - "

.. . . - . J & , ” :15: v o l t s . ■ . ■ . " - /

W ith a n o p e r a t i n g c o l l e c t o r c u r r e n t o f 2 m l l l l - a m p e r e s t h e

c o n s t a n t c u r r e n t t r a n s i s t o r . i n t h e e m i t t e r c i r c u i t must c a r r y

tw ic e . t h i s .c u r r e n t / o r 4 m i l l i - a m p e r e s o The o p e r a t i n g p o i n t

3-3-OP * 01 to » M a r t in and A s s o c i a t e s ■= P ag es 19=27*

n o t lh U.S.*

\l£T£A\■ r t; : r u i

L j

riii u i i . ^ l a o

3MS£ CV./mENT ~Za-M.a F I G U R E 5:i.4-

52

f o r t h e 2M167 t r a n s i s t o r was c h o s e n s t h e r e f o r e 9 a s : . -

Ve = 12 05 v o l t s

I c 2 4 m i ' l l i - a m p e r e s

The c i r c u i t d e s ig n was b a s e d on th e above o p e r a t i n g p o i n t s

t a k e n from t h e o u tp u t c h a r a c t e r i s t i c : e u r v e s o I n a c t u a l o p e r a

t i o n th e o p e r a t i n g c u r r e n t s and v o l t a g e s were s l i g h t l y d i f f e r ^

e n to The v a lu e s a r e t a b u l a t e d i n t a b l e ( 4 o l ) a The d i f f e r e n c e

i n th e b i a s c u r r e n t s be tw een t h e d e s ig n o b j e c t i v e and t h e

a c t u a l c i r c u i t r e s u l t e d i n s l i g h t l y d i f f e r e n t v a lu e s o f h i i

and h g i* - T h e re fo r e ^ t o g e t a g re e m e n t be tw een c a l c u l a t e d and

m easu red c i r c u i t , p a r a m e te r s i t was n e c e s s a r y t o u se th e v a lu e

o f a c t u a l o p e r a t i n g b i a s c u r r e n t and o b t a i n t h e o p e r a t in g

v a lu e o f h % 2 and h g i from th e c u rv e s o f f i g u r e (5o4)

, ' ' - - . ■ ■ • . " S3". ; :: C5 o4 ®8 }.. ¥olfcage G a in . . ‘ - . , '

The v o l t a g e g a in o f t h e a m p l i f i e r i n f i g u r e (S o l)

m ust be e v a l u a t e d f o r two d i f f e r e n t o p e r a t in g c o n d i t i o n s o

C ase One O ccurs when th e a m p l i f i e r i s i n i t s q u i e s c e n t o p e ra

t i n g c o n d i t i o n ^ w i t h no s i g n a l s a p p l i e d o t h e r t h a n t h e q u i e s

c e n t b i a s c u r r e n tS o Case two o c c u r s ’ when th e s t a g e i s o p e ra

t i n g a s p a r t o f t h e o p e r a t i o n a l a m p l i f i e r ® I n t h e fo rm er c a s e

t h e im pedance 1 Rgy a t th e b a se . c i r c u i t w i l l be t h e e q u i v a l e n t

r e s i s t a n c e se e n lo o k in g I n t o th e b i a s c i r c u i t . I n th e l a t t e r

. c a s e , when o p e r a t i n g . i n c lo s e d lo o p c o n d i t i o n w i th a ch o p p er

s t a b i l i z e r u n i t a t t a c h e d ^ t h e n e g a t i v e f e e d b a c k a m p l i f i e r a t

.o n e b a s e and t h e c h o p p er a m p l i f i e r a t t h e o t h e r b a se w i l l

r e s u l t i n e f f e c t i v e l y z e ro r e s i s t a n c e f o r Rg.

C o n d i t io n o n e s m en tio n ed a b o v e P was u sed t o e v a l u a t e - t h e

DoCo d r i f t c h a r a c t e r i s t i c s o f t h e a m p l i f i e f 0 F o r t h i s c o n d i

t i o n RgX s Rs2' 8 3 K ohmse The m e a su r in g c i r c u i t i s i l l u s t r a t e d

i n f i g u r e (SoS)® The c a l c u l a t e d and m easured r e s u l t s a r e t a b

u l a t e d In T a b le ( 5 o l) o ' • ■ r .'

The v o l t a g e g a i n d e s i r e d o f t h i s p a r t l e u l a r a m p l i f i e r i s t h e

g a in m easu red a t DoOi I J n f o r t u n a t e l y s t h e equ ipm en t a v a i l a b l e • r

w ould n o t m easu re s m a l l fUC® v o l t a g e s t o a l l o w d i r e c t e v a l u a t i o n

o f th e D®Co .gain-,.- I t was n e c e s s a r y , t h e r e f o r e $, t o m easure t h e

v o l t a g e g a in a t a c o n v e n ie n t f r e q u e n c y where s e n s i t i v e a - e .

m e a su r in g equ ipm en t co u ld be u s e d e TO i n s u r e t h a t t h i s g a i n

w a s th e same g a in a s would be e x p e r i e n c e d a t lo w er f r e q u e n c i e s s

t h e f r e q u e n c y r e s p o n s e c h a r a c t e r i s t i c o f t h e a m p l i f i e r was

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m easured* The lo w e s t c o n v e n ie n t f r e q u e n c y a v a i l a b l e was f i v e

c y c l e s p e r secondo The f r e q u e n c y r e s p o n s e was f l a t from f i v e

c y c l e s t o a p p ro x im a te ly 2 0 k i l o c y c l e s b e fo r e i t s t a r t e d t o

r o l l o f f » T h ere i s no a t t e m p t i n t h i s t h e s i s t o a n a ly z e th e

h ig h f r e q u e n c y c h a r a c t e r i s t i c s o f t h i s c i r c u i t e The f r e q u e n c y

r e s p o n s e c u rv e i s - o m i t t e d b e c a u s e i t has no s p e c i a l s i g n i f i "

can ee i n t h i s a n a l y s i s 0 "

' V,; ( 5 o4*5.) - I n p u t ■ Im pedanceo . ; - / - ' • > v ;

The i n p u t im pedance o f t h e a m p l i f i e r need be eval=> :

u a te d o n ly f o r th e o p e r a t i n g c o n d i t i o n where Rs » 0 o Howevers

t o c h e c k th e v a l i d i t y o f t h e e q u a t io n f o r th e i n p u t impedanceg

i t i s m easured w i th two v a lu e s o f s o u rc e im p e d an c e | Rg s 0 and

Rs 's -5 Ko The e l f c u l t u sed t o m easu re t h e i n p u t im pedance i s

i l l u s t r a t e d i n f i g u r e ( 5 06 ) 0 .

The i n p u t im pedance t o one s i d e o f th e d i f f e r e n t i a l am pl

i f i e r I n c l u d e s t h e p a r a l l e l f e s i s t a h c e . ; o f t h e b i a s i n g netw ork*

I n t h e c a l c u l a t i o n s ' i t i s ■•necessary: t o t a k e t h i s f a c t o r i n t o

a c c o u n t t o f i n d t h e a c t u a l im pedance s e e n " a t t h e t r a n s i s t o r -

b a s e In p u to - • -

■ The co m p ariso h o f t h e c a l c u l a t e d and m easu red v a lu e s a r e

t a b u l a t e d i n T a b le (S*!)® •

( 5 o4 o4} O u tpu t Im pedance *

The o u tp u t im pedance o f t h e d i f f e r e n t i a l a m p l i f i e r .

i s n o t a p p re c ia b ly : : a f f e c t e d by t h e v a lu e o f t h e source , r e s i s t

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r e f e r r e d t o th e i n p u t by d i v i d i n g by th e m easu red g a in o f t h e

a m p l i f i e r© . . '

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i s p l o t t e d i n f i g u r e (58) © The r e s u l t s p l o t t e d h e r e r e p r e - . '

s e n t t h e d r i f t c h a r a c t e r i s t i c s o f t h e a m p l i f i e r i n i t s f i n a l .

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i n a c c u r a c i e s a r e e n c o u n te re d and th e a b i l i t y t o r e p e a t a r e a d y .

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e r r o r by a s much' a s 1 0 f o s th e e r r o r a r i s i n g from t h e i n a b i l i t y ;

t o r e p e a t t h e r e a d i n g s on t h e . m e te ro B ecause t h e •o p e r a t i n g .

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t h e c i r c u i t p a r a m e t e r s o . F o r th e p u rp o s e of c o r r e l a t i o n a ,

b e t t e r o p e r a t i n g p o i n t would have b e en on the. f l a t t e r p o r t i o n

o f c u rv e s where h a n d hg^ do n o t v a ry a s r a p i d l y w i th 0 -

i?he l a r g e s t e r r o r e n c o u n te r e d i s i n t h e c a l c u l a t i o n o f :

t h e in p u t , impedance.® The c a l c u l a t e d v a lu e s a r e v e ry much i n

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