the transistor differential amplifier jack w....
TRANSCRIPT
The transistor differential amplifier
Item Type text; Thesis-Reproduction (electronic)
Authors Blanchard, Jack Winfield, 1926-
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
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Link to Item http://hdl.handle.net/10150/319235
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 <,
T h i s i s d e s i r a b l e b e c a u s e t h e v o l t a g e g a i n of an e l e c t r o n i c
a m p l i f i e r i s ’e f f e c t e d by t e m p e r a tu r e s
V a r io u s t y p e s Of e l e c t r o n i c ^ DsG» 9 o p e r a t i o n a l a m p l i
f i e r s a r e c o m m e rc ia l ly a v a i l a b l e on t h e m ark e t t oday t h a t ; w i l l
f u l f i l l t h e need f o r most com m erc ia l com puting a p p l i c a t io n s ® '■
T hese o p e r a t i o n a l a m p l i f i e r s r e l y on t h e a m p l i f y in g a b i l i t i e s
o f t h e vacuum tu b e t o a c h i e v e th e d e s i r e d p r o p e r t i e s fo r- .com
p u t i n g e As a r e s u l t t h e y s u f f e r t h e d i s a d v a n ta g e s o f most
vacuum tu b e e q u ip m e n t | . n a m e ly ^ , h ig h s ta n d b y power co n su m p tio n ,
l a r g e s i z e and p o o r . r e l i a b i l i t y ® . . A
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o u t t h e c o u n t r y t o a d a p t p r e s e n t e l e c t r o n i c e q u ip m en t t o t h e i r :
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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
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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
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( l o 5 ) fBBSIS OBJECTIVE
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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
Xc
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* c t + % - Q - A ' ) + ^ -
L 2 £ 3
tf-A » /V — ■Z /
r / G U & B ( 2 . 1 )
/ILUSTJ24T/MG F lk l/T F /V P l/T /M P £r£W JC £r TO 77/2T D .C .4 A / F L / * = ■ / £ - £ ?
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A c s )
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B i - s )
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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 <, 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 c i r c u i t i s ch o sen a s th e
m ost s a t i s f a c t o r y b a s i c c i r c u i t t o use©
' ( 3 e 2 i mSCUSSIOH
The p r o c e s s of a m p l i f y in g Do,0® s i g n a l s r e q u i r e s t h a t
e s p e c i a l c a r e be t a k e n i n a l l p h a s e s o f a d i r e c t co u p led
a m p l i f i e r d e s ig n t o m in im ize b i a s l e v e l v a r i a t i o n s 0 T hese
v a r i a t i o n s $ r e f e r r e d t o a s d r i f t s c an n o t be d i s t i n g u i s h e d
from t h e d e s i r e d B«,Co s i g n a l a t . the o u tp u t o f t h e a m p l i f ie r®
The p r i n c i p a l f a c t o r ' s c o n t r i b u t i n g t o t h e d r i f t s i n a
t r a n s i s t o r d i r e c t c o u p le d a m p l i f i e r m ust be exam ined c a r e
f u l l y t o e s t a b l i s h t h e w e ig h t in g f a c t o r on th e o v e r a l l p r o b
lem = Once t h e d e g re e o f im p o r ta n c e o f eac h v a r i a b l e i s
e s t a b l i s h e d g m ethods o f a l l e v i a t i n g t h e e f f e c t s o f t h e s e
v a r i a b l e s must be c o n s id e r e d © Then a d e c i s i o n can be made
' . ' : ' : ' ' :: ■ ■ : ■ - ■ . : ' ■ ■ :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<, H u n te r '= Handbook o f Semi c o n d u c to r E l e c t r o n i c s - MeGraw Hill.p InCo 9 New Yorkp 1957®
5LOg E ndresp Zaw©lss W a ld h a u e r 9 T r a n s i s t o r E l e c t r o n i c s - P r e n t i c e H a l l g Inc® s New Yorkg 1956® ' • {
‘“T h e s e f i g u r e s a r e n o t . s t a t i s t l e a l a v e r a g e s b u t a r e , ,i n t e n d e d o n ly t o be r e p r e s e n ta t i v e ®
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 j:— + — — 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 <»
5) The a m p l i f i e r I d e a l l y a m p l i f i e s o n ly t h e d i f f e r e n c e ^
o r ou t o f phase# s i g n a l b e tw e e n t h e two I n p u t s «, T h e r e f o r e , ,
e q u a l l e v e l changes o f t h e two i n p u t s do n o t r e s u l t i n an
u n b a la n c e b e tw ee n t h e two o u t p u t s 0 T h i s c h a r a c t e r i s t i c may b e ,
•put t o . good use i n c a sc a d e d d i r e c t c o u p le d a m p l i f i e r s where t h e ■
I n p u t s must work a t v a r i o u s DeC=> 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 c
d 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 <?Z + c e j=r o ( 4 .1 9 )
I f th e above e q u a t io n s are so lv e d s im u l t a n e o u s ly f o r the
current i b i , and the r a t i o V i / i b i i s o b t a in e d , the f o l l o w i n g
e q u a t io n w i l l r e s u l t :
Z / m = J / l s + + * + A z t + £ i A z x )c b /
+ £ z ( f a x k x t k x x + l ♦ A a i t < ? i h t x + i j f R l i Kh + l )
( f cuK ii> ki i +1 +-&%,( + I2 ik ii) im R x(£ L ik tt* ljrA ti + ( /d u k ix + 0 1# e e ( 4 .2 0 )
When the assum ptions p r e v i o u s l y made in d e r iv i n g the v o l
tage g a i n are a p p l i e d h e r e , namely t h a t :A-ZZ £* Aa/o A t t yCz << I , /&*/ = %
e >} o * £z.
the e x p r e s s i o n f o r Zin may be reduced t o ,
Z it i i ^ A / / A // ^ 5*2 — Z A * t +( 4 .2 1 )
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 << A t / , than e q u a t io n ( 4 .3 2 ) s i m p l i f i e s t o
Ro = -J- +■ R e e f / + i i i ------------- 7 (4.33)/ ^ i - ( K b + h i , f K e e ) J
The e q u i v a l e n t r e s i s t a n c e ob ta in ed by u s in g a t r a n s i s t o r
as a c o n s ta n t current source may be s e v e r a l megohms with o n ly
a nominal v o l t a g e drop a c r o s s the c i r c u i t . R ep lac ing Ree in
the d i f f e r e n t i a l a m p l i f i e r w ith a t r a n s i s t o r as a c o n s ta n t
current source w i l l prov ide th e h ig h e f f e c t i v e r e s i s t a n c e r e
quired f o r sym m etrica l a m p l i f i c a t i o n .
+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 <,
B ecau se o f th e l i m i t e d t im e a v a i l a b l e on t h e a u to m a t i c
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
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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 "
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: 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
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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)<, The
v a lu e f o r h g g , w hich i s o n ly c r i t i c a l i n c a l c u l a t i n g th e o u t
p u t impedances,’was 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 s c The ■
t r a n s i s t o r p a r a m e te r s f o r th e 2N167 were m e a s u re d -o r t a k e n f ro m
th e o u tp u t c h a r a c t e r i s t i c s i n a s i m i l a r mannero The t r a n s i s t o r
p a r a m e te r s u se d f o r t h e c a l c u l a t i o n s a r e a s f o l l o w s :
■ T o l l 2E117 -
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, ' ' - - . ■ ■ • . " 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
t r a n s i s t o r
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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
a nce Eg* T h e r e f o r e , i t i s n e c e s s a r y t o m easu re t h e o u tp u t
im pedance o n ly u n d e r one o p e r a t i n g c o n d i t io n * The m e a su r in g
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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 (5<>8) © 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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b i n a t i o n s e v a l u a t e d a r e d e sc r ib e d - a s f o l l o w s r
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f o l lo w e d t h e same g e n e r a 1 t r e n d a s p l o t t e d In f i g u r e ( 5 0 8 )
e x c e p t t h e m ag n itu d e o f t h e v a r i a t i o n s was a p p r o x im a te ly tw ic e
t h a t o f t h e f i n a l v e r s io n ^ The r e s u l t s o f c o m b in a t io n (3 ) a r e
h o t c o n c lu s iv e b e c a u se t h e l i m i t e d s u p p ly o f 2N117 t r a n s i s t o r s
p r e v e n te d t h e Use o f . s i l i c o n t r a n s i s t o r ' th r o u g h o u t 0 ' However^ . :
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a b l e ■ were v e r y p o o r a n d i n d i c a t e d t h a t th e e m i t t e r f o l l o w e r
h a s p o o r fVC-o s t a b i l i t y , compared w i th t h e s t a b i l i t y of t h e : .
. . d i f f e r e n t i a l a m p l i f i e r o ' .
f 5 &5) : , • . i , . •
T ab le S o l shows a r e a s o n a b l e d e g re e o f a g re e m e n t b e tw ee n
c a l c u l a t e d and m easu red v a l u e s o f th e c i r c u i t p a r a m e t e r s a P a r t
o f t h e d i s c r e p a n c y . that;: a p p e a r s I s b e l le v e .d t o - O r i g i n a t e i n ' t h e
m easurem ent o f h]_3 _ and; hg^ w i t h t h e v a r i a t i o n , o f The m e te r
used t o m easu re l b - be tw een 100.. and 200 m ic ro - a m p e r e s s I n c l u s i v e ,
had a f u l l s c a le ' r e a d i n g o f 1200 m ic ro -am p ere So The v a lu e s , o f
l b were r e a d i n the . low p o r t i o n o f th e m e te r s c a l e where l a r g e
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 .
in g ,1s v e r y p o o r 0 The o p e r a t i n g b i a s c u r r e n t s were . l a t e r r e a d
-w ith th e same m e te r and t h e v a lu e s o f u sed t o o b t a i n t h e
v a lu e s o f h -^ a n d hby. f ro m th e g r a p h 0 These, . r e a d in g s may b e i n
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 .
"po in t i s on a r e l a t i v e l y s t e e p p o r t i o n o f t h e h ^ y and hg%
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c u rv e 8 5 , a sma 1 1 e r r o r i n b i a s c u r r e n t r e a d i n g can c au se a
l a r g e e r r o r i n t h e - v a l u e s o f and used t o c a l c u l a t e
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
e r r o r when th e i n p u t im pedance i s assum ed t o be h-^® T h is i s
e s p e c i a l l y ;t r u e when th e g a i n o f t h e a m p l i f i e r i s ' l a rg e > The
p r i n c i p a l so u rc e o f t h i s e r r o r . i s a t t r i b u t e d t o t h e a f f e c t o f
th e v o l t a g e f e e d b a c k f a c t o r h i s w hich was assum ed t o be s m a l l
i n t h e d e r i v a t i o n s o W hile i t i s t r u e t h a t h^g i s s m a l l , i t s
e f f e c t a p p e a r s i n t h e in p u t c i r c u i t m u l t i p l i e d by t h e g a in o f
t h e a m p l i f i e r ® W h e n t h e g a in i s l a r g e t h e e f f e c t , may be
a p p re c ia b le ® However , i n g e n e r a l , t h e - c o r r e l a t i o n b e tw een t h e .
c a l c u l a t e d and m eaaured r e s u l t s i s good enough t o p ro v e th e
v a l i d i t y o f , t h e a p p ro x im a te eq u a t io n s®
lb o l t .0 ’; page a 2 0 =2 2 ,
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s m r n n T & m recgm m ehda tio hs • ,
( 6 01). :THESIS SIMMARY. / ' : V V':' : ' • ;; ;
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d r i f t would be th e m a jo r p ro b le m e n c o u n te r e d i n t r a n s i s t o r ^
i s a d D o G o .a m p l i f i e r s f ' As a r e s u l t s a l a r g e s h a r e o f t h e
e f f o r t was d e v o te d t o th e d e s ig n o f a n a m p l i f i e r w i th m in i- ,
.mum d r i f t o The d r i f t . e h a r a c t e r 1 s t i e s a c h ie v e d w i t h th 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 w ere m ost g r a t i f y i n g o ' " ■
: The p e a h . d r i f t »of-. l e s s ; t h a n , one; m i l^ f o r a two and o n e -
h a lf - h o u r p e r i o d f a r s u r p a s s e s . t h e , f e s u l t s e x p e c t e d <, From V
t h e s e r e s u l t s i t may be c o n c lu d ed t h a t a t r a n s i s t o r BoCo -
a m p l i f i e r can have " d r i f t e h a r a c t e r i s t l c s e q u a l t o , o r b e t t e r
. t h a n , t h e vacuum t u b e v e r s lo n o ; •' ■
'The v o l t a g e g a i n a v a i l a b l e w i t h 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 h i g h e r t h e n t h a t a v a i l a b l e when u s in g
h ig h mu vacuum tu b e t r l o d e S o C o n v e r s e ly , th e a b i l i t y o f
t h e t r a n s i s t o r a m p l i f i e r t o a m p l i f y o n ly t h e ■ .d if fe ren c e
s i g n a l d o e s n o t a p p e a r t o be q u i t e a s good a s th e a b i l i t y .
o f th e vacuum tu b e v e r s io n e ' .- ;
The i n p u t im pedance t d t h i s 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 tw ic e t h a t a v a i l a b l e w i th th e common e m i t t e r a m p l i
f i e r w i th o u t e m i t t e r d e g e n e ra t io n ^ . T h e .im p ed an ce of th e
seeond d r i v i n g sour-e© ad ds t o t h e imp e da nee s e e n a t th e f i r s t
i n p u t s The v o l t a g e g a in i s s h o w e v e rS: re d u e e d by th e impedanpe
of t h i s seco n d g e n e r a t o r 0 To r e a l i s e maximura v o l t a g e g a in i t
i s n e c e s s a r y to d r i v e t h e a m p l i f i e r from a low im pedance source®
Where h ig h i n p u t im p e d a n c e ;and h ig h v o l t a g e g a i n a r e d e s i r e d i t
i s n e c e s s a r y t o u se e m i t t e r f o l l o w e r s von each input® I f i t i s
d e s i r e d t o u s e t h e d i f f e r e n t i a l a m p l i f i e r a lo n e a compromise
b e tw ee n v o l t a g e g p in and i n p u t ' im pedance m ust be made 0
Some d i f f i c u l t y may b e e x p e c te d i n t h i s c o n n e c t io n when
d i f f e r e n t i a l a m p l i f i e r s a r e c a sc a d e d f o r D«,0® o p e r a t io n ^ The '
. c o l l e c t o r . o f t h e f i r s t s t a g e m ust be d i r e c t c o u p le d t o t h e
in p u t to , t h e seco n d s ta g e o A v o l t a g e d i v i d e r r e t u r n e d t o t h e
n e g a t i v e s u p p ly v o l t a g e i s n o r m a l ly used, t o r e d u c e t h e q u i e s c e n t
DoC® l e v e l t h a t i s c o u p le d t o t h e second s t a g e » The d i v i d e r
sh o u ld be made up o f r e l a t i v e l y . ' l a r g e r e s i s t a n c e s so I t ' w i l l
n o t io a d th e c o l l e c t o r o f t h e f i r s t stage® I n t h i s e v e n t 8 t h e
d r i v i n g impedance, t o th e secon d s t a g e w i l l be large® The:, g a in
of; t h e second s ta g e w i l l h e r e d u c e d b e c a u se o f t h i s h ig h d r i v ^
in g Im pedance» Z en e r d io d e s can be Used I n p l a c e o f th e to p .
r e s i s t o r i n th e d i v i d e r t o d r o p . t h e Dad® q u i e s c e n t l e v e l w i t h
o u t r e d u c i n g t h e s i g n a l a p p re c ia b ly ® T h is w i l l r e d u c e th e
d r i v i n g im pedance t o a v a lu e l e s s t h a n th e o u tp u t im pedance o f
t h e f i r s t stage® S a t i s f a c t o r y v o l t a g e g a in c an be a c h ie v e d , b y
t h i s method® I n th e e v e n t ; t h a t h i g h e r g a in i s r e q u i r e d s e m i t t e r
f o l l o w e r s can b e i n s e r t e d b e tw een t h e c a sc a d e d a m p l i f i e r s to - '
good a d v a n ta g e o I n g e n e r a l a l t e r n a t e l y c a sc ad e d e m i t t e r f o i "
- . ' ;; : V' •- : . ' ■ 65 :
lo w e rs .and g rounded: e m i t t e r a m p l i f i e r ' s p ro v id e t h e most ' .
s a t i s f a c t o r y o v e r a l l c a sc a d e d a m p l i f i e r s o I n t h i s case t h e
a f f e c t o f d r i f t i n t h e e m i t t e r f o l l o w e r i s r e d u c e d by t h e
g a in of th e , f i r s t s t a g e of, a m p l i f i c a t i o n when th e a m p l i f i e r
•cascad e i s u sed i n c lo s e d lo o p o p e r a t io n o
The .s in g le s t a g e c i r c u i t d e s ig n e d by t h e w r i t e r was con - >
n e s t e d t o a c h o p p er s t a b i l i z i n g sy s tem d e s ig n e d by Do Go
H a v i l l e 0 An e m i t t e r f o l l o w e r was added t o t h e o u tp u t and t h e
f e e d b a c k lo o p c lo s e d t o s i m u la t e t h e o p e r a t i o n a l a m p l i f i e r e ■
The sy s tem f u n c t i o n e d a s i n t e n d e d a l t h o u g h some com puting e r r o r
was e v id e n to T h is e r r o r was b e l i e v e d t o be c a u se d by th e l a c k
o f s u f f i c i e n t open lo o p g a i n and th e h ig h o u tp u t im pedance o f
t h e e m i t t e r - f o l l o w e r , used® A more c o m p le te r e p o r t on th e re=>
s u i t s: w i l l be, f o u n d l l n t h e t h e s i s o f DoGv H a v i l l e 0^
( 6 e2) RECOMMENDATION FOR FUTURE EFFORT
The work c b m p le te d t o d a te on 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 does n o t c o n s t i t u t e a c o m p le te e v a l u a t i o n o f t h e c i r
c u i t „ P u r t h e r e f f o r t i s s t i l l n e c e s s a r y a lo n g two l i n e s , a s
f o l lo w s % . : •
1). A n a ly ze 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 th e c i r - ' ■
c u l t and d e r iv e an e x p r e s s i o n f o r t h e c u t o f f f r e q u e n c y i
2 ) R e a n a ly z e th e i n p u t im pedance t o t h e d i f f e r e n t i a l .
a m p l i f i e r w i th e m i t t e r d e g e n e r a t i o n added t o e a c h t r a n s i s t o r <> v
^ O P o C it» - T h e s i s - © 5 : Go H a v i l l e ••
' - - ' • . . ' . : 6 6
She e f f e c t o f t h i s added r'e s i s t a n c e w i l l be t o r a i s e th e
i n p u t im pedance and. d e c r e a s e th e v o l t a g e gain*- / However# p r e - '
l i m i n a r y t e s t s i n t h e l a b o r a t o r y i n d i c a t e t h a t t h e r e may b e a
l a r g e r i n c r e a s e i n t h e i n p u t im pedance th a n l o s s o f g a in f o r
s m a l l am ounts o f d e g e n e ra t io n o An e q u a t io n r e l a t i n g i n p u t
im pedance and v o l t a g e g a in /cou ld be d e r i v e d and ch eck ed f o r a
maximum t o s e e i f su c h a p o i n t does e x i s t » -
5). The DeGo s t a b i l i t y of t h e c i r c u i t o f f i g u r e ( 5 01)
sh o u ld be checked w i th S i l i c o n t r a n s i s t o r s u se d a s e m i t t e r
f o l l o w e r s on e a c h i n p u t f T h e , h i g h i n p u t im pedance and lo w :
d r i v i n g s o u rc e im pedance d e r i v e d w i th t h i s m ethod w i l l be v e r y
a d v a n ta g e o u s i n t h e o p e r a t i o n a l a m p l i f i e r d e s ig n o A c e r t a i n / :
amount o f d e t e r i o r a t i o n ’i n th e d r i f t c h a r a c t e r i s t i c s can be/
t o l e r a t e d # e s p e c i a l l y i f th e ch o p p er s t a b i l i z i n g , u n i t i s u se d
i n c o n ju n c t i o n w i th th e f i n a l d e s i g n 0 . ' -
X6e5)tiO H G H JSIO H ' : / / /.%
■ 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 a n a ly z e d and e v a l
u a te d i n t h i s t h e s i s sh o u ld p r o v i d e t h e b a s i c b u i l d i n g b lo c k
f o r any c a sc a d e d 1)^0® a m p l i f i e r o The d a ta i n d i c a t e s t h a t t h e •
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 a r e s u f f i c i e n t l y good t o 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 t h e a m p l i f y in g s t a g e s i n a t r a n s i s t o r
DoGo o p e r a t i o n a l a m p l i f i e r » ■
The e s t a b l i s h m e n t o f t h i s : c o n c lu s io n f u l f i l l s t h e b a s i c
o b j e c t i v e o f t h e th e s is ® , ' ’ '
67
v v BIBLIQGHAPHr,
T e x ts
Kor-n' and Korn ~ ^ E l e o t r o n i o A nalog C om puters '1, = McGraw - HI 11^ I n c e s Hew Tork> 1952 0 ■
■ Lo-@. E ndresg Z aw e la s W aldhauer a n d Cheng ^ ^ T r a n s i s t o r Elect™ ■' r o n l e s 1' = P r e n t i c e = H a l l .P I n c »s Hew Y ork , 1956<, •
.. S h e a s Ro P e - ^ P r i n c i p l e s o f T r a n s i s t o r C i r c u i t s ' 5 « John W iley . and S o n ss I n c Q g 1954», 1 . r
Jo M llltnan and Ho Tauh = " P u ls e a n d 'D i g i t a l C i r c u i t s ”: * McGraw -: .. H l l l p Inco 9 Hew York.s" 1956 e ,
Thomas Lo M art I n p' J r 0 = " E l e c t r o n i c C i r c u i t s ' 5 - P r e n t i c e - H a l l> Incog Hew Y o rk $ 1955o ; : .
. Do - Po H u n te r = " S e m i-c o n d u c to r Handbook^ •=■ McGraw = H i l l , In c 6 5- ; Hew Yorkp 19 579 ■ , < ' - . .
L i t e r a t u r e and P e r i o d i c a l s
R an ishp H& = ?fA T r a n s i s t o r I n t e g r a t i n g A m p lif ie 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 s 1956» .
Hurleys, Ho B0 = "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 - DoCo -A m p l i f ie r s " ■ E l e c t r o n i c E quipm enty M archs 1 9 5 7 0 ■ :
To Lo M a r t in and A s s o c i a t e s - T r a n s i s t o r " E q u iv a le n t C i r c u i tC r i t e r i a " - R e p o r t - U n i v e r s i t y o f Arizona's, A u g u s ta 1 95 6s .
Ae J® W h ee le r - ’-T h e rm is to r s Com pensate T r a n s i s t o r A m p l i f i e r s ,$ » E l e c t r o n i c s J a n u a r y s 19570 - ! ' ;
D$ As R o b in so n => " O p e r a t i o n a l A m p l i f i e r Has Chopper S t a b l l l z a - t i o n 111 ^ E l e c t r o n i c s > ' S e p te m b e rs 1956<,
, Go M:»r E t t i n g e r => " T r a n s i s t o r A m p l i f i e r s f o r A na log C om puters" = E l e c t r o n i c s “ J u l y s 1955o