THE TRANSISTOR DIFFERENTIAL AMPLIFIER Jack W. …arizona.openrepository.com/arizona/bitstream/10150/319235/1/AZU_TD...3*7 The Transistor Differential. Amplifier 23 Chapter 4 ANALYSIS
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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® '
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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 ,
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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 :
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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
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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
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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
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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 =
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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 "-
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t h e o v e r a l l f u n c t i o n ^ t o ' . 7 .
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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
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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 . ■ • '
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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
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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
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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 ^
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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
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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 ® '■
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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
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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
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- ^ 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
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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
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; 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 . .
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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®
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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>
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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 .
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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 £ — =
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/ 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 -*—*
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, q : m w =! 1 i j
H +H J
t J s S L t i
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^ : l / o m , £ c
Y £ 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=
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