design of a transistor operational amplifier...
TRANSCRIPT
Design of a transistor operational amplifier
Item Type text; Thesis-Reproduction (electronic)
Authors Ozdes, Demir, 1929
Publisher The University of Arizona.
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DESI GN OF A TRANSISTOR OP E R A T I ON A L
AMPLIFIER
by
D em i r Ozdes
A Thesis Submi t t ed to the Fa c u l t y of the
DEPARTMENT OF ELECTRICAL E N G I N E E R I N G
In Pa r t i a l F u l f i l l m e n t of the Requ i rement s
For the Degree of
MASTER OF SCIENCE
In the Gr a d u a t e C o l l e g e
THE UNI VERSI TY OF A R I Z O N A
1 963
STATEMENT BY AUTHOR
This frhesis has been s u b mi f f e d i n p a r t i a l f u l f i l l m e n t o f t he
r e qu i r e men t s f o r an ad v a n c e d degree a t The U n i v e r s i t y o f
B r i e f q u o t a t i on s f rom t h i s t hesi s are a l l o w a b l e w i t h o u t
s p e c i a l pe r m i s s i o n , p r o v i d e d t h a t a c c u r a t e a c k n o w l e d g m e n t
o f source is made „ Requests f o r pe rmi ss i on f o r e x t e n d ed
q u o t a t i o n f rom or r e p r o d u c t i o n o f t h i s ma n u s c r i p t i n who l e
or i n pa r t may be g r an t ed by the head o f t he ma j o r d e p a r t ”
ment or t he Dean o f t he G r a d u a t e C o l l e g e when in t h e i r
j udgmen t t he proposed use o f t he m a t e r i a l is i n t he i n t e r es t s
o f s c h o l a r s h i p * In a l l o t h e r i n s t a n c e s , h o we v e r , permi ss i on
must be o b t a i n e d f rom the a u t h o r .
A r i z o n a and is de p o s i t e d in t he U n i v e r s i t y L i b r a r y to be
made a v a i l a b l e to bor r ower s under r u l es o f t he L i b r a r y ,
S I GNE D
APPROVAL BY THESIS DIRECTOR
This thes i s has been a pp r o ve d on t he da te shown
b e l o w :
Dr , G r d m n o A , KornDr , G r d m n o A , KornProfessor o f E l e c t r i c a l E n g i n e e r i n g
Date
A C K N O W L E D G E M E N T
The a u t ho r is i n d e b t e d f o r e v e r to his a d v i s o r . Dr .
G r a n i n o A . Kor n , whose t e a c h i n g s , p a t i e n c e , g u i d a n c e ,
and v a l u a b l e c r i t i q u e s made th i s thesi s poss i b l e .
The a u t h o r is g r a t e f u l to M r . Henry Ko e r n e r , whose
i n c o mp a r a b l e e n g i n e e r i n g k n o w l e d g e and s up e r v i s i on was
the i n s p i r a t i o n and f o u n d a t i o n of the d e v e l o p m e n t .
A c k n o w l e d g e m e n t is due to the Bur r - Br own Research
C o r p o r a t i o n and M r . Thomas R. Brown, Pres i dent f or sup
p o r t i n g th i s p r o j e c t .
The a u t h o r thanks M r . John Vanc za of Bu r r - B r own
Research C o r p o r a t i o n who e n t h u s i a s t i c a l l y assi sted in
t e s t i ng and b r e a d b o a r d i n g .
Much c r e d i t is due to Mrs . L. Ozdes who a b l y
t yped the thesi s and Mr . Howard Ha nd l e r o f The U n i v e r s i t y
of A r i z o n a for his co n t i n uo us suppor t and enco u r a g eme n t .
P a r t i c u l a r a c k n o w l e d g e m e n t should be made to Drs.
R. L . Wa l k e r and G, R . Peterson of the E l e c t r i c a l E n g i n e e r
ing F a c u l t y and Dr . R . E . Br iggs of the Agr onomy Depa r t men t
who s u b j ec t ed the e n t i r e manus c r i p t to c l ose s c r u t i n y and
who suggested i n n u me r ab l e ways o f mak i ng the p r e s e n t a t i o n
more u n d e r s t a n d a b l e .
P R E F A C E
O p e r a t i o n a l a m p l i f i e r s f i n d n u m e r o u s a p p l i c a t i o n s i n
b o t h m i l i t a r y a n d c o m m e r c i a l f i e l d s . T h e f l e x i b i l i t y o f
s e l e c t i n g f e e d b a c k c o m p o n e n t s p r o v i d e s a l a r g e v a r i e t y o f
a c c u r a t e , l i n e a r a n d n o n l i n e a r t r a n s f e r c h a r a c t e r i s t i c s . In
t h e i n s t r u m e n t a t i o n f i e l d , w h e r e p r e c i s e g a i n s a r e r e q u i r e d ,
t h e o p e r a t i o n a l a m p l i f i e r b e c o m e s an i n d i s p e n s a b l e t o o l .
M a n y a n a l o g a n d h y b r i d a n a l o g - d i g i t a l c o m p u t e r a p p l i
c a t i o n s r e q u i r e o p e r a t i o n a l a m p l i f i e r s w i t h v e r y h i g h g a i n
a n d I ow d r i f t .
T h e l o w p o w e r c o n s u m p t i o n a n d t h e c o n t i n u i n g
i m p r o v e m e n t i n t r a n s i s t o r m a n u f a c t u r i n g t e c h n i q u e s h a v e
e n c o u r a g e d v a r i o u s m a n u f a c t u r e r s t o d e v e l o p v a r i o u s t y p e s
o f 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 s f o r t h e e l e c t r o n i c
m a r k e t . D e s p i t e t h e p r o g r e s s m a d e i n t h e t r a n s i s t o r i z e d
o p e r a t i o n a l a m p l i f i e r s , t h e g a i n - b a n d w i d t h p r o d u c t
re.m a i n e d q u i t e l o w a n d d i d n o t s a t i s f y t h e r e q u i r e m e n t s o f
t h e m o d e r n i t e r a t i v e c o m p u t e r .
To d e v e l o p a n e w o p e r a t i o n a l a m p l i f i e r w i t h v e r y
h i g h g a i n - b a n d w i d t h f a c t o r , u s i n g f e e d f o r w a r d t e c h n i q u e s ,
wa s s u g g e s t e d t o t h e a u t h o r b y D r . G r a n i n o K o r n o f T h e
U n i v e r s i t y o f A r i z o n a i n T u c s o n , A r i z o n a . N u m e r o u s
IV
di scuss i ons w i t h Dr . Korn and e v a l u a t i o n of t he ve r y few
t e c h n i c a l a r t i c l e s w r i t t e n in the f e e d f o r w a r d methods
i n d i c a t e d the p o s s i b i l i t y o f an o r i g i n a l des ign . The au t hor
u n d e r t ook the d e v e l o p me n t and t es t i ng of t h i s a m p l i f i e r as
his Mas t e r ' s Thesis at The U n i v e r s i t y of A r i z o n a at Dr .
Kor n ' s sugges t i on . The a m p l i f i e r was des i gned in a summer
e mp l oy men t at Bu r r - B r own Research C o r p o r a t i o n , Tucson ,
A r i z o n a . In the course of t h i s e mp l o y me n t , t he a u t h o r was
p r i v i l e g e d to work under the gu i d a nc e of Mr . Henry Ko e r n e r ,
V i c e Pres i dent E n g i n e e r i n g , Bu r r - Br own Research C o r p o r
a t i o n . The progress made was f r e q u e n t l y r epo r t ed to the
thesi s a d v i s o r . Dr . Ko r n , who p e r s o n a l l y v i s i t e d the a u t h o r
at Bu r r - B r o wn , i n s pe c t e d his progress, and gave v a l u a b l e
a d v i c e .
The thesi s f i r s t deve l ops o n e - c h a n n e l s t ab l e a m p l i
f i e r w i t h s u i t a b l e p o l e - z e r o c o mb i n a t i o n s and l a t e r adds a
second channe l to c o mp l e t e the f e e d f o r w a r d a m p l i f i e r .
Demi r Ozdes
The U n i v e r s i t y o f A r i z o n a Tucson, A r i z o n a , 1963
V
C O N T E N T S
Pref ace
Chqp i ’er 8 I n t r o d u c t i o n „
Se c t i o n 1 Des ign S p e c i f i c a t i o n s o
1 o 1 „ 1 G e n e r a l „
1,1 ,2 D e s c r i p t i o n o f t he O v e r a l l De s i g n , 1
Se c t i o n 2 Design Problems and T h e i r S o l u t i o n e 3
1 . 2 . 1 The D i f f e r e n t i a l A m p l i f i e r . 3
1 . 2 . 2 G a i n and Impedance Pr ope r t i es o f
the D i f f e r e n t i a l A m p l i f i e r . 4
1 . 2 . 3 D r i f t S t a b i l i z a t i o n M e t h o d s . 5
1 . 2 . 4 The Ko e r n e r S t a b i l i z a t i o n M e t h o d . 6
1 . 2 . 5 Adva n t a g e s and Di sadvan t ages o f
the Koe r n e r M e t h o d . 1 1
Ch a p t e r 16 O v e r a l l Des i gn , F r equency
Response and S t a b i l i t y . 14
S e c t i o n 1 S i n g l e Channe l A m p . 14
2 . 1 . 1 I n t r o d u c t i o n and Componen t
S e l e c t i o n . 14
2 . 1 . 2 C h o i c e o f O p e r a t i n g Points and
Stage G a i n s . 14
2 . 1 , 3 I npu t Stage D e s i g n .
V I
15
2 „ 1 e4 I n t e r m e d i a t e Stage Des ign,
2 , 1 , 5 F r equency Response and S t a b i l i t y ,
2 o. l«6 O u t p u t Stage De s i g n ,
Se c t i o n 2 Fe e d f o r wa r d A m p l i f i e r ,
2 . 2 . 1 i n t r o d u c t i o n „
2 . 2 . 2 HF Channe l De s i g n ,
2 . 2 . 3 Co n s t a n t C u r r e n t Load C o n c e p t ,
2 . 2 . 4 N o i s e and I ts E l i m i n a t i o n ,
2 . 2 . 5 Some C o n s t r u c t i o n P r e c a u t i o n s ,
Ch a p t e r 6 81 Test Methods and Resul t s ,
Se c t i o n 1 S t a t i c Tests,
3 . 1 . 1 I n t r o d u c t i o n ,
3 . 1 . 2 Zero B a l a n c i n g ,
3 . 1 . 3 Power Supp l y V a r i a t i o n E f f e c t s ,
3 . 1 . 4 Temper a t u r e V a r i a t i o n E f f e c t s ,
3 . 1 . 5 i n p u t and O u t p u t I mpedance
Me a s u r e me n t s ,
3 . 1 . 6 No i s e M e a s u r e me n t s ,
3 . 1 . 7 D -C Measur ements ,
Se c t i o n 2 Dynami c Tests ,
3 . 2 . 1 I n t r o d u c t i o n ,
3 . 2 . 2 S t a b i l i t y Tes t s ,
3 . 2 . 3 Ga i n vs. F r equency Measur emen t s . 39
3 . 2 . 4 Max i mum C u r r e n t and V o l t a g e
O u t p u t s . 40
3 . 2 . 5 Phase S h i f t and Dynami c A c c u r a c y . 40
Co n c l u s i o n 41
A p p e n d i x A The I npu t Impedance of the Cross -
Coup l ed S t a g e . 43
A p p e n d i x B S t a b i l i t y C o n d i t i o n s of the Cr oss -
Co u p l e d S t a g e . 45
A p p e n d i x C D e r i v a t i o n of V . 48
A p p e n d i x D The M i l l e r E f f ec t in Tr ans i s t o r s . 50
A p p e n d i x E D e r i v a t i o n of Co mmon - Mod e G a i n
E q u a t i o n . 53
Bibl i o g r a p h y 55
V I I I
CHAPTER 1
I N T R O D U C T I O N
S E C T I ON ; 1
DESI GN SPECI F I CAT I ONS
1 . 1 . 1 G e n e r a l . The des i gn of an a l l purpose o p e r a t i o n a l
a m p l i f i e r to be used in an a l l - so l i d - s t a t e i t e r a t i v e e l e c t r o n i c
d i f f e r e n t i a l a n a l y z e r ( I D A) c o n s t i t u t e s the main o b j e c t i v e o f
t h i s research . Table 1.1 compares the r e qu i r ed and f i n a l
des i gn s p e c i f i c a t i o n s .
The research r esu l t ed in d e s i g n i n g two d i f f e r e n t
a m p l i f i e r s , w i t h one h a v i n g less g a i n but b e t t e r shor t c i r c u i t
s t a b i l i t y and less noi se than the o t h e r . Fi gures 1.1 and 1 .2
present the Mode l I and Mode l II a m p l i f i e r s .
1 . 1 . 2 D e s c r i p t i o n of the O v e r a l l D e s i g n . Each t ype of
a m p l i f i e r has two c h a n n e l s . The low f r e q u e n c y channe l is
t h o r o u g h l y d - c c o u p l e d . To compensat e f o r t r a n s i s t o r p a r a
met er v a r i a t i o n s , d i f f e r e n t i a l stages are u s e d . V o l t a g e d r i f t
cance l l a t i o n is o b t a i n e d by common mode r e j e c t i o n . Cu r r e n t
o f f s e t as a f u n c t i o n of t e mp e r a t u r e is e l i m i n a t e d by using a new
method wh i c h w i l l be p r esented in the f o l l o w i n g c h a p t e r .
I npu t i mpedance is i nc r eased by using c r o s s - f e e d b a c k . The
TABLE 1.1REQUIRED and FfN/AL' DE5/QN
SPECIFICATIONS
performanceCHARACTERISTICS
RecjufredD e s ig n e d
Model x Model JT
D -C Gam m too dtb, 124^ /OZ Jb
Input Impedance 2oo k J l(min.J
500 k(abd.-<y ... % tr»)
/o o kuo. loo pP,
Output Impedance 100 5 0 -0- 4-o -Q -
Maxi'mu i diifgrfionle^ Velt"0gf£ IIO V . 5 12V
C(oo kc;± I Z V
( q° kc)Ma*imm current 6to ifig t 20m4 . 1 30mA X 36 oi 4
Band bjic/th [Croteo'j&r] I »s Mc/s 2 0 *49 6 .
D rift ' Stability I Mill,Volfs// t°
| 3 <^mv^o l o yW Vy/_0
47o
6 2 0270K 270 <loo3W
IOK
loo 1002Z0K
27C
ICO3 3 K
-I5V
FIG . 1.1FEFDFOR/MRD -3PER/AT/0N-1L AMR (M o d e u )
All (PNP) s ZN /S 6 I , a » (N P N ji 2 N 2 2 2 2 C x e p t ihe ovfpuf W^i i 's for i vohicVi o r ? 2 W 2 2 M ,
All PNlP^s ; Z N l S 6 (Co+pJt 'tranzkiors : 2NZZH
lOO K /OO•47b
INF
/ \
too
47 < Ol MF
Mo P E L 2 FEEDFORWARD a m p .
2
s i g n i f i c a n c e o f the d e v i c e Is the e l i m i n a t i o n of
c i r c u i t . In o r der to p r o v i d e 6 d b / . a t t her o c t a ve
f r e q u e n c y , f l o a t i n g r o l l - o f f ne t wor ks are used.
the chopper
c rossover
S E C T I O N : 2
D E S I G N P R O B L E M S A N D THEI R S O L U T I O N
1 . 2 . 1 The D i f f e r e n t i a l A m p l i f i e r . T h e r e is l i t t l e d o u b t t h a t
t he bes t w a y to s t a b i l i z e t he d - c o p e r a t i n g p o i n t of a
t r a n s i s t o r is to use a s e c o n d t r a n s i s t o r h a v i n g s i m i l a r c h a r
a c t e r i s t i c s in a 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 .
The c o mmo n mode g a i n e q u a t i o n ^ in 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 is
a R 1
1 3A“ ■ - T T ^ I i T " "
In t he e q u a t i o n a b o v e R R , and R^ a r e c o l l e c t o r l o a d ,
e m i t t e r l o a d and e m i t t e r co mmo n r e s i s t o r s , r e s p e c t i v e l y . The
m a g n i t u d e of A a p p r o a c h e s to z e r o as R 0 b e c o m e s l a r g e r , c c J
S i n c e t h e r e is a p r a c t i c a l l i m i t to t he v a l u e o f R^ o w i n g to
t he f i n i t e p o w e r s u p p l i e s , t he i n c r e m e n t a l c o l l e c t o r r e s i s t a n c e
of a t r a n s i s t o r is used as R . Thi s e m i t t e r l o a d t r a n s i s t o r
s er v es as a c o n s t a n t - c u r r e n t s o u r c e .
M i d d I e b r ook , R. P . , D i f f e r e n t i a l A m p l i f i e r s , p p . 2 5 - 2 9 , W i l e y , 1 9 6 3 . A l s o see A p p e n d i x E .
'W /V
Q1 ^ r Sounce Im p e c h n c e
% Ouip^t lfTip€c/qn£6 £>f
i Input I rm p ^^O ce o - f
FIS . 1.3T h e d i f f e r e n t i a l a m p l i f i e d
<?oMotes !■ (, and ar<? twpz- td a n c e s with Q 2 d*nd q r f Consid e r e d a s in c c m f ^ o n - b a s c c o n p ^gurcL^.on / ^
2 . ($2 j ‘fc f tk e enizn'flq S^nal^2 '* C dth tnon-W '^rNc;ljf iV < ? r; in -th is e y o m p |> -= < 9 ,
s »
F I G . 1.4
S i mp l e e q u i v a l e n t c i r c u i t f or Q 1 stage of F i g . 1.3 d e f i n i n g the base c u r r e n t i ^ j .
This e q u i v a l e n t c i r c u i t is d e r i v e d w i t h the f o l l o w i n g assumpt i ons : R , R smal l compared to h . e , Rl arge compared to R g . The i n p u t i mpedance of <3 2, wh i c h appears as a common base stage is
( Z i n ) Q2 = h ib + RB 2 ^ " a ^ [ RE( eq ) ] Q1
Thus the i n p u t i mpedance for Q ] is
( Z : n ) Q) = h ie + P [ h ib + RB2( , ' a ) ] = h ie + h ie + RB2
Since ph . ^ = h . e and ( l - a ) ^ ~ .
Now we can w r i t e the l oop equ a t i o ns .
! b, ( h ie + RB1 + RB2 + h i e ) = ' s RB1R
i b i ‘ ^ '-t N ; ’ ' ' b , rbA j = ( Cu r r e n t G a i n ) = — R + h;
, _ . R , ‘ c 1RL_ BRl3-8___1 c 1 L * v R 7 ^ - ^ b (Rb + h . e)
i e
N o t e : R ^ i s the eq . l oad r e s i s t o r .
4
1 . 2 . 2 G a i n And Impedance Pr oper t i es of the D i f f e r e n t i a l
A m p l i f i e r . Re f e r r i ng to F i g . 1 . 3 the i mpedance at p o i n t (A)
appears as the i n p u t i mpedance of a s i ng l e ended s t age, where
the e q u i v a l e n t e m i t t e r res i s t or R consi s t s o f R^j in
ser ies w i t h the p a r a l l e l c o m b i n a t i o n of the o u t p u t i mpedance
o f Q ^ and the i n p u t Impedance o f Q g , both a p p e a r i n g as
common base stages; the r e s u l t i n g i mpedance is a p p r o x i m a t e d
by R , ,
R R.
w h e r e RE( Eq ) = RE1 + R Q + R. ( ' - 3)
A p o t e n t i o m e t e r is i nse r t ed be t ween the two e m i t t e r s wh i ch
permi t s b a l a n c i n g of the c o l l e c t o r c u r r e n t s . No t e t ha t Rj^ is
abou t t w i c e as l a r ge as t ha t of a s i m i l a r s i n g l e ended stage .
Stage ga i n as shown in F i g . 1.4 is
S i n c e o n l y one h a l f o f t h e i n p u t s i g n a l is used a t Q ,
t he s t a g e g a i n w i l l be f i f t y p e r c e n t less t h a n t h a t o f a
s i m i l a r s i n g l e e n d e d c o mmo n - e m i t t e r s t a g e .
I t is p a r t i c u l a r l y s i m p l e to c o n s t r u c t a m u l t i s t a g e
o p e r a t i o n a l a m p l i f i e r c a s c a d i n g c o m p l e m e n t a r y d i f f e r e n t i a l
- o E .
—■O — £<« 1 1 W ‘-,h
F I G . I. 5High in p u t i*»'pW<,ncc DC, / tm p ,_ i— - -|—i-L* iniiimimi-i- wr --n -n> i •-ir * 1 I L i
E in
b o
in
- 1 % - )
W i u i h ^ ^
2:
C
i A
•f 2 ; ; ^ 2 ift
•Alio k . - L a r
E :in-O E«
c - E.
FIG. 1.6V\ igh in p u t ‘i rn p e d a n c e in b g q n a t o r ,
r t n t a The in te rna i ga in ) $ ( ^ .
-E,
FIG. 1.7Different!a I Amotfjrit~r in_opj rob«tm!
c o n n e c t i o n ,
in z in
, For i n t e g r a t o r a p p l i c a t i o n the e q u a t i o n w i l l become
/E;n d t
NOTE: This i n t e g r a t o r , due to the low i npu t i mpedanceof the t r ans i s t o r s , may have a t i me con s t an t i n a d e q u a t e f or c o mpu t i n g a p p l i c a t i o n s . Most s u i t a b l e i n t e g r a t o r c i r c u i t is p r esented in F i g . 1 . 6 .
a m p l i f i e r s tages, thus zero i n p u t and zero o u t p u t can be
o b t a i n e d .
I f two ou t - o f - ph as e p u s h - p u l l vo l t a g e s are unequal
at any s t age , the d i f f e r e n c e appears d i f f e r e n t i a l l y at the
f o l l o w i n g stage and w i l l t end to e q u a l i z e two c o l l e c t o r
v o l t a g e s . Some t y p i c a l exampl es of the o p e r a t i o n a l a m p l i
f i e r s e mp l o y i n g d i f f e r e n t i a l stages are shown in Fi gures
1 . 5 , 1 . 6 , and 1 . 7 .
1 . 2 . 3 D r i f t S t a b i l i z a t i o n M e t h o d s . Chopper s t a b i l i z a t i o n2 Q
methods due to G o l d b e r g : and F. H. B l echer were f i r s t
a p p l i e d to vacuum tube c i r c u i t s . S i nce these c i r c u i t s
ope r a t e at h i gh v o l t a g e s , the m e c h a n i c a l chopper noi se
appears r e l a t i v e l y s m a l l . Ho we v e r , t h i s noi se is l a r ge when
me c h a n i c a l choppers are used in t r a n s i s t o r c i r c u i t s . To
c omp l y w i t h the need, new t ypes of choppers were dev e l o p ed
( i e . p h o t o e l e c t r i c , t r a n s i s t o r e t c . ) . A l t h o u g h t r a n s i s t o r
choppers are l i g h t , compac t and have low power c o ns u mp t i o n ,
some i m p o r t a n t c h a r a c t e r i s t i c s l i m i t t h e i r usage:
^ G o l d b e r g , E. A . , " S t a b i l i z a t i o n of d - c A m p l i f i e r s , " RCA Rev. I I , p. 296 , 1 950.
^ B l e c h e r , F . H . , " T r a n s i s t o r C i r c u i t s f or A n a l o g and D i g i t a l Sys t ems , " Bel l Sys. Tech . J . 35, pp. 2 9 5 - 3 3 2 , M a r c h , 1956.
1. The v o l t a g e drop across the t r a n s i s t o r , even in
s a t u r a t i o n is never e x a c t l y z e r o . T y p i c a l
s a t u r a t i o n v o l t a g e is less than 1 m v „ , and the
s a t u r a t i o n r es i s t ance is 5 0 - 1 0 0 ohms .
2 . J u n c t i o n c a p a c i t a n c e w i l l p r oduce spi kes at the
o u t p u t w h i c h may range f rom m i l l i v o l t s to t en ths
of a v o l t .
Advances in the c hoppe r t e c h n o l o g y have p r oduced
ve r y c ompa c t e l e c t r o m e c h a n i c a l choppers w i t h o u t the
l i m i t a t i o n s o f t r a n s i s t o r c h o p p e r s .
In f a c t , many m e c h a n i c a l ch o p p e r ma n u f a c t u r e r s c l a i m
as noi se l i m i t a t i o n s t he t he r ma l or s o - c a l l e d Johnson no i se .
Ho we v e r , m e c h a n i c a l modu l a t o r s do s u f f e r c o n t a c t we a r , w h i c h
f i xes the l i f e o f a d e v i c e at 1000 to 9000 hours; f o r h i g he r
l i f e e x p e c t a n c y t he s i ze of t he m o d u l a t o r i nc r eases .
The noi se p resent i n m e c h a n i c a l choppers is not more
t han 100 pv and some s u p e r i o r d ev i ces go as low as 4 pv „ In
c o n c l u s i o n one observes t h a t m e c h a n i c a l c h o p p e r s , In t he
present s t a t e of a r t , are p r e f e r a b l e in t he use o f c o mp u t i n g
a m p l i f i e r s ; howe ve r s i z e , cost and the presence o f noi se are
s t i l l l i m i t i n g f a c t o r s .
1 . 2 . 4 The Ko e r n e r S t a b i l i z a t i o n M e t h o d . A new and
i n g e n i o u s d r i f t s t a b i l i z i n g method was dev i sed by H. Koe r ne r
7
and a p p l i e d by the au t ho r to va r i ous a m p l i f i e r c i r c u i t s w i t h
very s a t i s f a c t o r y r esu l t s . The method does not r e qu i r e
a d d i t i o n a l componen t s , n e i t h e r a c t i v e nor pass i ve , but c a l l s
for ma t ch i n g as c l ose as one p e r c e n t of the t rans i s t o r s based
on a c c u r a t e measurements of V g and (3 . ^
The Koer ne r s t a b i l i z i n g method works w i t h a d i f
f e r e n t i a l - a m p l i f i e r e m p l o y i n g a cons t an t c u r r e n t source .
Cons i de r the a m p l i f i e r shown in F i g . 1 . 8 c o ns i s t i ng of
c o mp l e me n t a r y d i f f e r e n t i a l stages des i gned for zero o u t p u t
per zero i npu t . The f i r s t stage is d i r e c t - b i a s e d t h rough the
res i s tors R g and Rgg. The a m p l i f i e r is c o mmi t t e d to ope r a t e
as an i n v e r t e r ; the res i s tors used for thi s purpose are shown in
do t t ed l i n e s .
A t e mpe r a t u r e i nc r ease w i l l cause pa r amet e r v a r i a t i o n s
wh i c h w i l l be co ns i d e r e d on l y at the i n p u t s t age . The I
and V g , 5 v a r i a t i o n s are p a r t i a l l y compensat ed by the second
t r an s i s t o r in the d i f f e r e n t i a l stage as e x p l a i n e d e a r l i e r . A t
the i n p u t stage a v a r i a t i o n of t emper a t u r e w i l l cause the f o l
l o w i n g even t s :
1. Let us assume a q u i e s c e n t c o n d i t i o n , such t ha t
1 I Q ]1B1 = *B1' where = p 0 * 5 )
4 / 5 D u r i n g the a c t ua l measurements we had I q = 8 Ma ,V C E = 15V.
8
Si nce (3 has a p o s i t i v e t e mp e r a t u r e c o e f f i c i e n t , in
h i g h e r t emper a t u r es I ^ w i l l be less than i ts
q u i e s c e n t v a l u e . C o n s e q u e n t l y , an excess c u r r e n t
o f I g j w i l l f l ow t h r ough Rp and w i l l appear as an
o f f se t at the a m p l i f i e r o u t p u t .
2 . The base v o l t a g e V ^ anc base c u r r e n t I g of Q
r emai n p r a c t i c a l I y c o n s t a n t , but due to the
n e g a t i v e t emp e r a t u r e c o e f f i c i e n t of Vggg the
v o l t a g e drop across R g i nc reases w i t h the t e m
p e r a t u r e . C o n s e q u e n t l y , the t o t a l c o l l e c t o r
c u r r e n t l C ( T o t a | ) = 2 I C ) = 21^% i n c r eases ,
caus i ng the base- c u r re n ts I g and I ^ i nc r ease
a l s o . Si nce the base c u r r e n t e q u a t i o n I ^ = 1 ^ = I
has to be s a t i s f i e d , an excess c u r r e n t must be
s u p p l i e d to the bases of Q j and Q g . The base of
Q is a l so c o n n e c t e d to Rp. Hence the excess
c u r r e n t is s u p p l i e d f rom the c o l l e c t o r o f Q ^ , wh i ch
o b v i o u s l y w i l l appear as a v o l t a g e d r i f t at the o u t
p u t .
F o r t u n a t e l y , h o we v e r , the two phenomena d esc r i bed
above have oppos i ng e f f e c t s on the a m p l i f i e r o u t p u t . Thus,
i f these r e s u l t i n g v o l t a g e changes are ma t c h e d , no c u r r e n t
w i l l f l ow across Rp and Eo u j. w i l l r emain c ons t an t w i t h
i n c r e a s i ng t e mp e r a t u r e . The s e l e c t i o n of res i s tors is a
r o u t i n e design p r o b l e m . As a h y p o t h e t i c a l e x a mp l e , assume
the t e mpe r a t u r e range of the a m p l i f i e r be i ng T1 to T2 . We
can present a set of equ a t i ons wh i c h d e f i n e one and o n l y one
va l ue of Vgg wh i c h is the key of the p r o b l e m.
Si nce the ma t c h i n g of the v o l t a g e changes , desc r i bed
?n the p r e c e d i n g pa r ag r aphs , is r e q u i r e d , we can w r i t e the
f o l l o w i n g e q u a t i o n :
[■' E ( T o t a l ) _ T2 _ V B3 ~ (v BE3) l 2 %T2
T 1 V B3 - ( V BE3 ) T1 %TtP E ( T o t a l )
wher e P is the c u r r e n t ga i n of the matched p a i r Q , Q ^ . The
parameters PT 2 , P , (V B£) j 2 ' (V B£) T1 are known; e q u a t i o n
( 1 . 6 ) de t e r mi nes V ^ ^ . R g and R ^ must , h o w e v e r , be s u f
f i c i e n t l y low to secure a l arge va l u e o f I g^ wh i c h w i l l keep
V B3 c o n s f a n t - N o f e t h a t V B3 = ' s RS1 and VTetal " V B3 = V S
v _ ( v B E 3 h ) %T2 ■ ( V BE 3 ) T 2 %TI
" (S,T2" - " ■ 71
V B3 " ^V BE3^T1 = ^V ER3^T) ( ' - S )
VTotal V CC + V EE
C22 czl 0 8
07
B30 3 OUTPUT\ / \ / \
8E3
V v
FIG. 1.0 Threfi dtrezi -bibs inYtfrtcr
10
V EE " ^V ER3^T1= R „ ( 1 . 9 )
* C 1 + 1C2 E3
A c c o r d i n g to the equa t i ons abo v e , and r e f e r r i n g to F i g . 1 . 8
the s e l e c t i o n of the component s w i l l be in the f o l l o w i n g
sequence:
1 . S e l e c t p r oper c o l l e c t o r v o l t a g e and c u r r e n t for
each s t age . These w i l l de t e r mi ne the c o l l e c t o r
res i s tors .V c c - v c
R = _ £ £ _ ^ E ( 1 .10)' c
2. Using eq u a t i o n ( 1 . 7 ) f i nd V ^ .
3 . Se l ec t ( I r i + I r «)l s > 100 — — p— — ( i . n )
4. Se l ec t res i s tors R g and R ^ •
RS 1 - - i f (K12)
and R = - 2 l = Vb3 + ( 1 . 1 3 )52
5. Se l e c t R ^ using e q u a t i o n ( 1 . 9 ) .
I f the pa r amet e r v a r i a t i o n s are known , the Koer ner
method becomes a ve r y speedy process . The Koe r ne r method
permi t s a maximum of ( 1 - 2 ) n^ / cj e g q d r i f t g r a d i e n t
11
and c l ose r ( i e . one p e r c e n t ) ma t c h i n g of the t r ans i s t o r s , w i t h
n e g l i g i b l e I cQ, m i gh t r educe th i s number by a f a c t o r o f f i v e .
The best chopper s t a b i l i z e d a m p l i f i e r a v a i l a b l e has a d r i f t
g r a d i e n t va l u e of ( . 0 1 - . 1 ) n A / j Q f thus the Koer ne r
method appears co mpa r a b l e and s i nce i t does away w i t h c h o p
pers and chopper no i se , i t is p r e f e r r e d by the a u t h o r .
A m o d i f i e d ve r s i on of t he Koer ne r s t a b i l i z a t i o n method
as d ev e l o pe d by the a u t h o r ^ has some o t h e r supe r i o r
q u a l i f i e s and w i l l be i n t r o d u c e d in the second c h a p t e r .
1 . 2 . 5 Adv an t ages And Di sadvan t ages of the Koe r ne r M e t h o d s .
The most o u t s t a n d i n g f ea t u res of t he Koer ne r methods are
l i s t e d be I ow :
1. Ve r y l ow d r i f t g r a d i e n t , c o m p a t i b l e w i t h the
choppe r s t a b i l i z e d a m p l i f i e r s .
2. Si nce the con s t an t c u r r e n t source is a l r e a d y used in
d i f f e r e n t i a l s tages, no a d d i t i o n a l components w i l l
be r e q u i r e d , thus d r i f t s t a b i l i t y is a c h i e v e d w i t h a
mi n i mum number of component s .
3. No chopper noi se is present .
^ Th i s method was suggested to the a u t ho r by M r . T. R. Brown, Pr es i den t , Bu r r - B r own Research C o r p o r a t i o n .
12
L i m i t a t i o n s of t he Koe me r methods may be s t a t ed as
fol I ows:
1. Tr ans i s t o r t ypes used must have co ns t a n t t e m
pe r a t u r e c o e f f i c i e n t s f or (3 and V ^ g o v e r the
o p e r a t i n g - t emp e r a t u r e r ange .
2. In a d d i t i o n to c I ose (I e . one p e r c e n t ) ma t c h i n g o f
the t r a n s i s t o r s , h i gh and low l i m i t va l ues of |3 and
V g £ in the w o r k i n g - t e m p e r a t u r e range must be
measured.
3. An a d j u s t me n t o f R ^ is necessary to p r o v i d e zero
I npu t and ze r o o u t p u t c o n d i t i o n .
4 . At t h i s t i m e , i t is not poss i b l e to p r e d i c t the
d i r e c t i o n and s i ze of the d r i f t due to t r a n s i s t o r
a g i n g . ^
5. The Koe r ne r method a p p l i e s o n l y to d i f f e r e n t i a l
amp I i f i ers .
6. S l i g h t t emp e r a t u r e d i f f e r e n c e s in the matched
t r a n s i s t o r s , such as due to bad c o n d u c t i o n in the
common heat s i n k , may upset the m a t c h i n g in the
or der o f mi l I i v o l fs .
7 The f i r s t model a m p l i f i e r us ing the Ko e r n e r method was mar ke t ed in Sep t ember , 1962. I f is e x p e c t e d to have the resu l t s o f the componen t a g i n g i n abou t No v e m b e r , 1963.
1 3
The m a t c h i n g and pa r ame t e r measurements r e q u i r e d f or
the Koe r ne r method i n t r o d u c e a d d i t i o n a l costs, bu t w i t h the
adv anc e o f t he t r a n s i s t o r m a n u f a c t u r i n g t e c h n i q u e s , t h i s cost
may be r e d u c e d .
CHAPTER H
OVERALL D E S I G N , FREQUENCY RESPONSE
A N D STABI L I TY
SE CTI ON: 1
S I N GL E C H A N N E L AMPLIFIER
2 . 1 . 1 I n t r o d u c t i o n and Componen t S e l e c t i o n . This s e c t i o n
presents a s i n g l e - c h a n n e l a m p l i f i e r des i gn p r o c e d u r e . I t is
c l e a r t ha t many o t h e r approaches can be used i n s t e a d ,
depend i ng to the p a r t i c u l a r i t i e s o f a s p e c i f i c des i gn p rob l em
or the d e s i g n e r s p r e f e r e n c e .
S e l e c t i o n o f t r ans i s t o r s is d i c t a t e d by t he f r e q u e n c y
r ange , ( V CE) ma x , C8c ) max# and ( Pc ) m a x ®’ The s p e c i f i c a t i o n s
o f t he t r ans i s t o r s s e l e c t e d by the w r i t e r are l i s t e d in Tab l e
2 . 1 . The s e l e c t e d NPN t r a n s i s t o r 2 N 2222 has a (3 c u t o f f
f r e q u e n c y of over 2 0 me ga cyc l es per second and V(] g of
3 0 V ; c o n s e q u e n t l y t he des i gn p r ob l em has r educed to the
s e l e c t i o n o f o p e r a t i n g p o i n t s .
2 . 1 . 2 C h o i c e o f O p e r a t i n g Points and Stage G a i n s . A ve r y
8 No t e t ha t t h i s permi t s a f a v o r a b l e c o m b i n a t i o n be t ween noi se and HF response, s i nce HF channe l does not c o n t r i b u t e LF n o i s e . N o n - f e e d f o r w a r d a m p l i f i e r must compromi se i n p u t - stage P to ge t l ow n o i s e .
T A B L E 2.1T R A N S IS T O R C H A R A C T E R I S T I C S
TRAUSISTOR c/-C j$ £ c .b Pw 4(25'%C)
2N2222fW PN)
30 V. 60 4 o o M cs. 5 PT.
.
1.8 VV. 60 V.
2N86I
(PUP) 25 V. 35 4oMcs. S p .f 150 mW. 55 V.
1 5
genera l r u l e f or e s t i m a t i n g d i f f e r e n t i a l - a m p l i f i e r ga i n is to
assume be t ween 20 and 30 d b c ga i n per s t a g e . On th i s basis
i t was d e c i d e d to use t h r ee v o l t a g e - a m p l i f i e r stages and a
h i gh c u r r e n t o u t p u t stage . The o p e r a t i n g po i n t s are s e l e c t e d
as + 6 V for the f i r s t s t a g e , + 12V for the second stage and 0V
at the c o mp l e me n t a r y t h i r d s t age . The s e l e c t i o n o f the f i r s t
and second stages as NPN t r ans i s t o r s is not a r b i t r a r y ; the h i gh
P c u t o f f and low noi se q u a l i t y a v a i l a b l e f rom NPN dev i ces
d i c t a t e d th i s p r e f e r e n c e . Fu r t he r mo r e , to ensure l ow no i se ,
the i n p u t stage was des i gned to o p e r a t e w i t h lOOpA c u r r e n t ,
2 . 1 , 3 I npu t Stage De s i g n , Re f e r r i n g to F i g . 1 . 8 where the
o p e r a t i n g p o i n t is s e l e c t e d to be abou t V q g = 6 V ,
the c o l l e c t o r res i s tors are compu t ed as;
_ V c c - VC,
^ ' c i
V C 1 = V C2 ' * 01 = * 0 2 / RC 1 = RC 2 ( 2 . 2 )
For l ^ i = 90p A , Rq i =: 1 0 0 K
We s e l e c t R £ j = ^£2 = 470 SL- and p o t e n t i o m e t e r
R g £ = 1 00 _OL , The e m i t t e r r es i s tors R £ and R p r o v i d e
b I as s t a b i l i z a t i o n t h rough e m i t t e r d e g e n e r a t i o n , a l t h o u g h t hey
do decrease the s tage g a i n .
F I G . 2 . IDerflonstrcttfon of the comma0-(oQS€ C6O06ctiOr)
3R f
To
To&
Second and th/rdstaoes t be. same
Fig. /• 8as /o
-J Eo
F I G . Z Z
Cross feed sb alolhzed fnput st«3^e fo r athree stage Inverter. Note tlia't stalpiiemlton currents a r t sbcDf) any «> 0 ! ;^trk.e Q2 ba:e i? ptr- monenttu Grounded , j? ^ mvsi b*deleted;Ty : Total bias Current ,
- Ba e current z = Offset (error) current.
16
9Q g acts as a c o n s t a n t - c u r r e n t s i n k . F i g . 2 .1 shows
a s i m p l i f i e d c i r c u i t f or Q ^ , wh i c h appears as a common-
base c o n n e c t i o n . Thus, the e f f e c t i v e i n c r e m e n t a l i mpedance
of Q w i l l be r (5 Megohms) . Hi gh i mpedance at the e m i t t e r 3 c
c i r c u i t w i l l p r o v i d e a h igh common- mode r e j e c t i o n r a t i o . ^
In the last se c t i o n the base is b i ased d i r e c t l y .
A l t h o u g h d i r e c t - b i a s is a w i d e l y used c o n c e p t , a new method
w i l l be i n t r o d u c e d and i ts e f f e c t s w i l l be i n v e s t i g a t e d . As
shown in F i g . 2 . 2 the bias res i s tors R ^ and R ^ are c ross-
c o u p l e d to the c o l l e c t o r s of Q g and Q , r e s p e c t i v e l y . The
res i s tors R and R are very l a r g e . ^ C o n s e q u e n t l y , t hey B 1 B 2
w i l l not s i g n i f i c a n t l y a l t e r the s t andard ga i n e q u a t i o n of a
d i r e c t - b i a s e d d i f f e r e n t ! a I - a m p l i f i e r s t age . Ho we v e r , thei
i n p u t i mpedance R j n w i l l have a d i f f e r e n t a p p e a r a n c e ,
R. RR: _ j. n d. n I ITT ( 2 . 3 )
1 i n ” Bin RB + R j p O - K )
V c 2K = ~~rf thus K ^ 0
V B 1
o 'In a PNP stage Q ^ wou l d be p r o p e r l y c a l l e d a
c o n s t a n t - c u r r e n t source .
^ M i d d l e b r o o k , R. D . , O p . C i t .
^ S t a b i l i t y c o n d i t i o n s r e q u i r e bias r es i s t o r magn i t udes to be in the Megohm range; thi s w i l l be shown in the f o l l o w i n g c h a p t e r s .
17
where K is the s tage ga i n and R. ^ is the i n p u t i mpedance of12
a d i r e c t - b i a s e d d i f f e r e n t i a l - a m p l i f i e r stage 0 Equat i oni
( 2 . 3 ) i mp l i e s t ha t R. n is a l ways g r e a t e r t han R. n , i . e . ,
c r o s s - c o u p l i n g i ncreases the i n p u t i mpedance „ The s t a b i l i t y
1 3c o n d i t i o n o f the stage is ensured by t he I n e q u a l i t y
R * n R i /R < R;n + RB ( 2 . 4 )eq
Let us app l y t h i s c o n d i t i o n to our p r ob l em:
V B = OV , V C2 = +6V , I C1 = 90p A , p = 80
RB = I c 7 7 r ' " = ( 9 0 ) ( , 0 ) - 6 7 — = SMegohms
For R^ = 1 00 K , the s t a b i l i t y c o n d i t i o n is s a t i s f i e d w i t h a
marg i n f a c t o r o f 6 .
We now t urn to the ques t i on o f t e m p e r a t u r e - e f f e c t
compensa t i on w i t h the c r o s s - c o u p l e d i n p u t s t a g e . In the
case o f the c r o s s - c o u p l e d a m p l i f i e r , h i gh c o l l e c t o r c u r r e n t
w i l l l owe r the c o l l e c t o r v o l t a g e thus caus i ng the base-
c u r r e n t to d ec r ea s e . We sha l l a t t e mp t to match t h i s decrease
1 2 The d e r i v a t i o n o f the I np u t i mpedance of a c ross - co u p l e d stage is shown In A p p e n d i x A e
The i n e q u a l i t y ensur i ng the s t a b i l i t y o f t he stage is a r e s u l t o f a l o o p - g a i n a n a l y s i s . The cons t an t s a p pe a r i n g in e q u a t i o n ( 2 . 4 ) and the ana l ys i s are p resen t ed in A p p e n d i x B.
1 8
to a b a s e - c u r r e n t i nc r ease due to the cons t an t c u r r e n t s i nk in
the e m i t t e r c i r c u i t . For the sake o f s i m p l i c i t y , assume an
NPN stage and n e g l i g i b l e base-c u r re n ts to the f o l l o w i n g stage
The f i r s t step Is to f i n d the va l ue of the c o u p l i n g res i s t or R^ .
For = 0 we have
, , • v c c " i c r l•ft = ' b = ----------6 - ---------- ( 2 . 5 )
Al so s i nce 1 - is known I d ~ . C o n s e q u e n t l y ,P
- p l _ RRB . CC 1 £ _ L }
‘ b
Equat i on ( 2 . 6 ) g i ves an a c c u r a t e v a l u e f or R ^ . Howev e r ,
t h i s va l ue must sa t i s f y the s t a b i l i t y f o r mu l a ( 2 . 4 ) . A t the
h i gh t emp e r a t u r e Equa t i on ( 2 . 5 ) becomes
v c c - ( ' c + I,c ) r l _ ‘ c + ' crb p + | f ( 2 . 7 )
where
(■c + ) = ( *0^72 ancl (P + P" ) = P72
C o m b i n i n g Equat i ons ( 2 . 6 ) and ( 2 . 7 ) , we f i nd
, * _ ' c ^ c c 13 " l C R l P ■ V C C p 7 2 + ' c R kP 72 ^' c t l c P R L - l c P T 2 R L - P V C C ) ( 2 - 8)
Equa t i on ( 2 . 8 ) is e x t r e m e l y i m p o r t a n t . I t g i ves one h a l f of
the c o l l e c t o r c u r r e n t i n c r e a s e , necessary to match the (3
i nc r ease in h i gh t e mp e r a t u r e . The nex t step is to des ign a
19
14 *c u r r e n t s i nk wh i c h w i l l p r oduce 2 1q at the s e l e c t e d h i gh*
t e mp e r a t u r e . Using t he known va l ues o f V g ^ , V g £, I q and# ' ] 5
I q we c a n f i n d a s p e c i f i c v a l u e f o r V g g .
V BEV B3 = 1 * - ' C + V BE ( 2 . 9 )
The last step is to c a l c u l a t e the values of R g ^ , R g g and RE3
Si nce V r r + V FF , V RF
' T T a ' l f 'c * < » • ' • >
Rear rang i n g g i ves
" s i _ ‘ c < V C C * V EE - V » i ) ' V l i i l C .
" S2 " I J V SE . I c v j £ | 2 - " )
Also we can d e f i n e
V d c qRE3 = - j r f (2 « 12)
The des ign sequence for the i n p u t s tage Is as f o l l o w s :
1. Se l e c t o p e r a t i n g p o i n t s .
^ No t e t h a t f o r PNP stage des i gn , the s i nk is r e p l a c e d by a s o u r c e .
^ D e r i v a t i o n o f V gg is shown I n A p p e n d i x C .
20
2 . Se l e c t c o l l e c t o r res i s tors using E q . ( 2 . 1 ) .
3 0 Se l e c t c r o s s - c o u p l e d res i s tors using E q . ( 2 . 6 ) and
Eq . ( 2 . 4 ) .*
4. C a l c u l a t e 1 . using Eq . ( 2 . 8 ) .
5 0 Se l e c t us ing E q . ( 2 . 1 2 ) ._ /
6 o Se l e c t I <- 1 0S / ' B3 'Vee ” Y l + v cjc
•sS e l e c t R g g us i ng Eq. 2 . 11
S e l e c t RS1 = —^ ------ r 5 — ( 2 . 1 3 )/
8
9. R e c a l c u l a t e the o p e r a t i n g p o i n t s .
There are two ver y i m p o r t a n t p rob l ems wh i c h must be
cons i de r ed in the process p r esent ed above*
1. Somet i mes, in o r der to m i n i m i z e no i se , ve r y smal l
q u i e s c e n t cu r r en t s as l ow as 3 Op A may be us e d .
In cases l i k e t h i s , or in the case where the base
cu r r en t s o f t he f o l l o w i n g stages are not n e g l i g i b l e ,
a more e x t e n s i v e ana l ys i s is r e q u i r e d . In a case
l i k e t h i s , the c o l l e c t o r c u r r e n t I ^ is p resent ed as,
ER3 ± ( 1 . , ) ^ ( 2 . 1 4 )Cl 2 R £3 B1 Q 2
In some s p e c i f i c cases, where the base c u r r e n t
IQ3 of Q g may also not be n e g l i g i b l e , t he n , e q u a t i o n
21
(2 «, 1 4 ) w i l l be s l i g h t l y a l t e r e d :
■ c . ■ " Y " " ' " 1 , 3 > C . , » Q , ( « . > . )
I n c l u d i n g the e x t r a c t i o n o f base c u r r e n t I ^ ,
e q u a t i o n ( 2 . 1 5 ) can be expressed as a f u n c t i o n o f
t e mp e r a t u r e ,
V ( 9 ) RE3 l ( 0 ) B3, <0 ) C 1 - '2 R ™ - - ' ( e ) B M . ( 6 ) B1) Q2
( 2 . 1 6 )
I t shou l d be p o i n t e d out t ha t the l as t term of
e q u a t i o n ( 2 , 16) may al so i n c l u d e the I e f f e c t , I f
any , o f the f o l l o w i n g s t a g e .
2 . 1 . 4 I n t e r m e d i a t e Stage Des i g n . The c h o i c e of the
q u i e s c e n t o p e r a t i n g po i n t s f or t he second and t h i r d stages
p r ov i des the necessary constant s to c a l c u l a t e the c o l l e c t o r
l oad and e m i t t e r res i s tors A f t e r the r es i s t o r va l ues
c l oses t to those c a l c u l a t e d have been s e l e c t e d , the p r ob l em Is
wor ked backwar ds and the new q u i e s c e n t va l ues are c a l c u l a t e d .
2 . 1 . 5 Frequency Response and S t a b i l i t y . A t t h i s p o i n t we
t urn to the p r ob l em o f shap i ng the o p e n - l o o p response of the
^ T h i s s i mp l e a p p l i c a t i o n o f bas i c c i r c u i t l aws are not r epea t ed in t h i s s e c t i o n . The necessary e qua t i ons are shown in Sec . 2 .1 . 3 «,
GAIN
IN
db
0 0
6 0
d e c o d e
\ Uncompensated
10 Kcs FREQUENCY
F I G . 2 , 3
T h e f requency response corves of the three sfcctge ampl i f i e r .
N o t e i The. b r d o k p g ,'n t o f 4h-d uncom pen-s a t e d curve includes tuJo poltis ^W, and W , y c/ue to th ird omd Second stages , respectively.
22
a m p l i f i e r to y i e l d a s t ab l e c l o s e d - l o o p o p e r a t i o n . In o r de r
to s a t i s f y the N y q u i s t c o n d i t i o n f or s t ab l e o p e r a t i o n , the
a m p l i f i e r o p e n - l o o p response must go t h rough u n i t y w i t h a
20 d b / s l ope* This ensures the a m p l i f i e r p h a s e - s h i f to c t a v e ■ r rto be no more than 90 - d e g *
The shap i ng is o b t a i n e d by using r o l l - o f f or l a g - l e a d
ne t wo r k S o ^
The response cu r ve o f t he o p e n - l o o p uncompensat ed
t h r e e - s t a g e a m p l i f i e r Is shown in F i g , 2 . 3 , The doub l e po l e
a pp e a r i ng at w ^ = 12 K c ps , is due to the f o l l o w i n g reasons:
1, The 3 db p o i n t due to t he f i r s t stage w i l l be at a
r e l a t i v e l y h i gh f r e q u e n c y ( i e . I Me) s i nce the
s i gna l source i mpedances are u s u a l l y v e r y l ow . * ^
2 , The second and t h i r d stages are d r i v e n f rom c o mmo n -
e m i t t e r stages . Si nce the c o m m o n - e m i t t e r o u t p u t
i mpedances are h i g h , t he t i me cons t an t s f ormed by
the o u t p u t i mpedance and the M i l l e r c a p a c i t a n c e ^
. . '
Huskey , H . D . and K o r n , G . A , , Comp u t e r Handb o o k , Se c t i on 2, pp . 4 9-51 , M c G r a w - H i l l , 1 962 .
^ T y p i c a l s i gna l g e n e r a t o r o u t p u t i mpedanc e is less t han I K
19 The M i l l e r e f f e c t is d e r i v e d in A p p e n d i x D ,
C l
C2
^H A A A / 1 [= ^liu
F | G, . 2 O . - O 's i ' - I ' ( - r e r d i Q t * f , r r
C2
2 C
u W V
«V f G , 2 >4 bfC\ 16 r.t Load u i s i n i J ; CYl
»f I o f 2
F j(= i, 2 z)it c i r c u U o j " I k e T' l£ gui falent circuU o f 'ike
de\/dcfifl& We ho^s fe r (l/nHton c f r&ll -offf)£i
23
o f t h e f o l l o w i n g s t a g e w i l l b e l a r g e , c a u s i n g a
l o w f r e q u e n c y 3 d b p o i n t s
H o w e v e r , t h e w o r s t s i t u a t i o n w i l l a p p e a r d u e t o t h e s i m i l a r
v a l u e s o f t i m e c o n s t a n t s . S i m u l t a n e o u s o r v e r y c l o s e b r e a k
p o i n t s w i l l i n t r o d u c e 1 2 d b / o c f a v e s l o p e . S i n c e t h e
c o r r e s p o n d i n g z e r o s o f t h e p o l e s w i l l a p p e a r c o n s i d e r a b l y
b e l o w u n i t y g a i n , t h e s l o p e a t c r o s s o v e r w i l l n o t s a t i s f y t h e
s t a b i l i t y c r i t e r i o n .
T h e t r a n s f e r f u n c t i o n o f t h e r o l l - o f f n e t w o r k , s h o w n
I n F i g . 2 . 4 a
S i m i l a r l y , a r o l l - o f f n e t w o r k f o r t h e s e c o n d s t a g e c a n a l s o
b e d e s i g n e d h a v i n g a t r a n s f e r f u n c t i o n o f
T h e w r i t e r h a s u s e d f l o a t i n g r o l l - o f f n e t w o r k s w h i c h
/ p r o v i d e f o r m o r e f l e x i b l e c o n t r o l o f p o l e - z e r o c o n f i g u r a t i o n .
Z(s)
w h e r e a n dR + R
S L
W b C ( R s R l + R R s + R R l )
/ wd
( 2 . 1 9 )
0
TT2
_1T
r -7 - x I I \ I
..... 1---------11X]
___ i . X\aZ w/. .
1| Crtnsoier ------ 1---------- fr&l~
w,
A ( s ) : A(o) r s t w j , . F o r ff3 .2.3 tie have A ft ) , _355_opis.t£ Trxio4j f ftu jbj (i+LOj) Cs+zmio)(uzirx£3o)
I = B t j C - For F y . ^ 3 , $ - 2 2 0 KC (CrosboJei^
0 f r a d ) = A rc ta n _ Arc "tan J& . - Arc ton Wt s' gW2. tV b ^
Phase Mangif) ; l e o L 8 8 : 2 y. PM ^ > 4 5 °
F i g . 2 . 5S ta b if / iy equations and th e yd
24
R e f e r r i n g to F i g . 2 . 3 , we see t h a t on e o f t he p o l e s a t w^ is
r e p l a c e d by t h e t wo z e r o s w q and w c o f t h e c o m p e n s a t i n g
n e t w o r k s . The a p p e a r a n c e o f t h e p o l e s at w^ and w^ has
c a u s e d t he p o l e due to t he t h i r d s t a g e to mo v e b e l o w u n i t y
g a i n . A g a i n r e f e r r i n g to F i g . 2 , 3 , we o b s e r v e t h a t a f t e r t h e
s e c o n d b r e a k p o i n t w ^ , we h a v e a s l o p e of 12 OCf a v e °
The p r e s e n c e o f t wo z e r o s and o n e p o l e a t t h e t h i r d b r e a k
p o i n t w i l l r e s u l t in a 6 ^ b / o c t a v e c u r v e up and b e y o n d t h e
c r o s s o v e r f r e q u e n c y .
S i n c e t h e b r e a k f r e q u e n c i e s a r e k n o w n , t h e a c t u a l
c r o s s o v e r f r e q u e n c y ca n be c a l c u l a t e d . W i t h t he c r o s s o v e r
f r e q u e n c y , one may c o m p u t e t h e ph a s e a n g l e w h i c h is to
s a t i s f y t he s t a b i l i t y c r i t e r i o n . Thi s is shown in F i g . 2 . 5 .
The s e l e c t i o n o f t h e b r e a k f r e q u e n c i e s d e p e n d s on t he
p a r t i c u l a r a p p l i c a t i o n . In ma n y c a s e s , t h e f i r s t s t a g e n e t
w o r k may h a v e e n s u r e d s t a b i l i t y , so t h a t t h e s e c o n d s t a ge
r o l l - o f f n e t w o r k b e c o me s q u i t e u n n e c e s s a r y . F i g . 2 . 3 shows
t ha t be t ween w , and w_ the s l ope is 12 d b / . ; i f thed 2 o c t a v e
l o o p is c l o s e d f o r a g a i n of b e t w e e n A ( w ^ ) and A ( w ^ ) , t he
a m p l i f i e r w i l l be m a r g i n a l l y s t a b l e . C o n s e q u e n t l y , i f h i g h e ri
g a i n is n e c e s s a r y , b r e a k p o i n t s may be a d j u s t e d a t some
e x p e n s e o f ope n l o o p g a i n and a c c u r a c y . S e l e c t i o n o f b r e a k
25
po i n t s f rom the e q u a t i o n is a s i mp l e ma t t e r w i t h Smi th char t s
or a Shu r e - Ru l e . In p r a c t i c a l a p p l i c a t i o n s , h o we v e r , a r o l l
o f f decade box is used. One f i r s t t r i es f or c l osed l oop
s t a b i l i t y w i t h maximum c a p a c i t a n c e by s e l e c t i n g a p p r o p r i a t e
r es i s t ance R , t hen a c a p a c i t a n c e co r r es p o nd i n g to the
a t t e n u a t o r and des i r ed break f r e q u e n c y is c a l c u l a t e d or
o b t a i n e d e x p e r i m e n t a l l y .
2 . 1 . 6 O u t p u t Stage Des i gn . The most common l y used ou t pu t
stage is the emi t t e r - f o l l owe r due to i t s l ow i mpedance
c h a r a c t e r i s t i c s . O u t p u t i mpedance is a p p r o x i m a t e d as,
Z Q = Rs ( l - a ) ( 2 . 2 0 )
where R g is the source i mpedance . In our a m p l i f i e r , s i nce
the source i mpedance is a c o m m o n - e m i t t e r o u t p u t s t age , the
o u t p u t i mpedance is somewhat l i m i t e d . Low f r e q u e n c y o u t
put i mpedance c o u l d be r educed by cas cad i ng t wo emi t t e r -
fol l owers ( D a r l i n g t o n c o n n e c t i o n ) . The D a r l i n g t o n c o n n e c t i o n ,
h o w e v e r , w i l l p r esent a d o u b l e - p o l e and is ve r y usefu l on l y in
r e l a t i v e l y nar row band a m p l i f i e r s , s i nce p r ope r zeros may be
i ns e r t ed to the d e v i c e . I t was d e c i d e d to use an emi t t e r -
f o l l owe r w i t h h i gh « thus ensur i ng a low o u t p u t i mpedanc e ;
a l so , a c o n s t a n t - c u r r e n t s i nk w i l l p r o v i d e h i gh d ynami c
i mpedance at the e m i t t e r , ye t w i l l p resent con s t a n t c u r r e n t .
cc
A T Y P I C A L OUTPUT S T A G E "
26
The des i gn equa t i ons are present ed be l ow ( F i g . 2 . 6 ) :
RS ™ RS 1 + RS2 ( 2 . 2 1 )
l s = V_ C C ^ E ( 2 . 2 2 )
V RS2 = I SRS2 ( 2 . 2 3)
V ER2 V R52 ~ V BE ( 2 . 2 4 )
| = l i i l ( 2 . 25 )E E2
The des i gn p r ocedur e is so s i mpl e and f l e x i b l e t h a t one may
s t a r t f rom any of the eq u a t i o ns present ed a b o v e . The on l y
i m p o r t a n t p o i n t is to s e l e c t a l a rge va l ue f or I g in o r der to
keep V Q g c o ns t a n t . As a t y p i c a l exampl e , a mi n i mum of
±2 0 MA d e v i c e w i l l be d e s i g n e d . No t e t ha t the p o s i t i v e swing
is ensured by the l ow c o l l e c t o r r e s i s t o r .
Rs = 8 . 2 K + 680 = 8 . 8 8 K
' s - STFSTK - 3 , 3 7 M A -
All (PNP)s : 2N86f , oil (WPtf)s •. 2N2222 , tke output(NPNy 5 : 2N22i9
-f* 15 o • -
3 3 0100 K
----------------R»i
- — / \ / ' ^------------220
i ►■■ - 1 j-- ■ — — W vy i N .01 / 'k y r
K005
% 4 7 K470!
220 220
470 S 4 7 0
t o o
15 K
Sing 12 channel op, amp . stabfiizcc/ with roll-oft
l o o v3 W
OUTPUT— c
6S
27
V RS2 = 2 * 3V ' V =
V ER2 = 2 . 3 - 0 . 7 = 1 . 6 V
1 . 668
= 2 3 . 5 MA
0 . 7 V
wh i c h sa t i s f i e s our r equ i r ement , ,
A t h ree stage o p e r a t i o n a l a m p l i f i e r des i gned w i t h the
p r i n c i p l e s di scussed up to t h i s p o i n t is p r esented in F i g . 2 . 7 .
<A >a
FIG- Z .8 aBasic {eeJf ciuJord Ck
A,(-s)
FIG - <2.8bF eedforward ^MPuiFfER c o MVEc t e D
A S O P E R A T I O N A L A M P L I F I E R
28
S E C T I O N : 2
F E E D F O R W A R D A M P L I F I E R
2 . 2 . 1 I n t r o d u c t i o n . U t i l i z i n g a m e d i u m ba n d w i d t h , h i gh
g a i n a m p l i f i e r and a l a r g e b a n d w i d t h , s ma l l g a i n a m p l i f i e r
2 oc o n s t i t u t e s a t wo c h a n n e l f e e d f o r w a r d s y s t e m .
R e f e r r i n g to F i g . 2 . 8 a , t h e LF c h a n n e l c o n s i s t s o f
A j ( s ) and A^ ( s ) , w h e r e a s in h i g h e r f r e q u e n c i e s t he s i g n a l I s
a m p l i f i e d o n l y by A^ ( s ) w i t h t he c l o s i n g o f t he s w i t c h ( S )
w h i c h r e p r e s e n t s t he f o r w a r d c o u p l i n g c i r c u i t . In F i g . 2 . 8 b
t he f e e d f o r w a r d sys t em is c o n n e c t e d as an o p e r a t i o n a l
a m p l i f i e r and s w i t c h ( S ) o f F i g . 2 . 8a is r e p l a c e d by a t r a n s
f e r i m p e d a n c e Z ^ ( s ) ; t he l o o p g a i n is
- Z F ( S) G (s) = Z F ( s ) A , ( s ) A 2 ( s) + Z f ( s ) Z c ( s ) A 2 ( s) ( 2 . 2 7 )
The s i g n a l s a r e a d d e d t h r o u g h a d i f f e r e n t i a l a m p l i f i e r .
In F i g . 2 . 1 3 , G a i n v s . R a d - F r e q c u r v e s f or v a r i o u s
A j ( s ) and A^ ( s ) a m p l i f i e r s a r e p r e s e n t e d . In e a c h case
t h e r e e x i s t s a f r e q u e n c y f w h e r e t wo g a i n s a r e e q u a l .
Th i s e q u a l g a i n f r e q u e n c y ( f 0 g) * $ a l m o s t t h e same f r e q u e n c y
2 ]( f Q) w h i c h is p r e s e n t e d by S c o t t D e e r i n g as t h e c h a n n e l
^ ^ D e e r i n g , S . C . , 11A W i d e Band D i r e c t C o u p l e d O p e r a t i o n a l A m p l i f i e r , " P r o c . N a t . S i m . Co n f . , J a n u a r y 1 9 , 1 9 5 6 .
2 , ibld„
-H 5 V
1003 m A
47 K lo o lo o
O V
-1 2 v
I 0 O
Amplifier k- is should in Fig. I.<?
F IG . 2 . 9
gyPEeiMCMTAL FEEDF0PN4PO AMPLIFIED
NOTE: Th/5 is the -first owplifier configc.fcJ CtS fe^c/(t>riOotrtl.
29
" 1 " ga i n be i ng equal to channe l " 2 " ga i n in e q u a t i o n ( 2 . 2 7 ) .
B e l o w ( f ) t h e g a i n o f c h a n n e l " 1 " is g r e a t e r , a b o v e ( f )
channe l " 2 " is d o m i n a n t . The same s ta tement s can be a p p l i e d
f o r ( f ) w i t h no l oss o f a c c u r a c y . S i n c e Bo d e p l o t s f o r eg 7 r
gain and phase s h i f t response curves are c l o s e l y assoc i a t e d ,
each channe l w i l l have a do mi n a n t phase s h i f t c h a r a c t e r i s t i c
be l ow or above the f r e q u e n c y (f ) . C o n s e q u e n t l y , the moste g
l o g i c a l c h o i c e in des i gn i n g the a m p l i f i e r Agts) is to have a
s i n g l e t ime c o n s t a n t , t hus, ensur i ng 6 d b / oc f a ve s l ope at
the c r ossover f r e q u e n c y . Howe ve r , the e f f e c t of the phase
r e l a t i o n s h i p s at f r e q u e n c y ( f q ^ ) on s t a b i l i t y have yet to be
c o n s i d e r e d . S t a b i l i t y is ensured by k e e p i n g the phase lag of
A j ( s ) a m p l i f i e r at less than 1 80° at the f r e q u e n c y ( f ) . A
c o n s e r v a t i v e des i gn , h o we v e r , d i c t a t e s a phase lag of not
more than 90° ; s i nce in Chap t e r 1, methods of p o l e - z e r o
o p e r a t i on s ensur i ng slopes at des i r ed f r e q u e n c i e s were i n t r o
d uced , t h i s is not much of a p r ob l em . To c o mp l e t e the
p r ob l em, the c o u p l i n g n e t wo r k Z^, (s) is des i gned to i n t r o d u c e
l i t t l e or no phase s h i f t at h i gh f r e q u e n c i e s .
2 . 2 . 2 HF Channe l Design . An e x p e r i m e n t a l f e e d f o r w a r d
a m p l i f i e r is p r esented in F i g . 2 . 9 . This d e v i c e uses the
s i ng l e channe l a m p l i f i e r des i gned in the f i r s t c h a p t e r as the
GAIN
IN cib
I oo
60 - GO ..
Ao .. 4o ..
2o -
100 IKC \OKc 100 u I Me
BOTTOMfLF) AMP.
IKC tore idOkc imc
T O P ( H F ) AMP.F I G . 2.10b
Frequency r e s p o n s e c u n t s of t "fop cmj boffon? ar>f\ ' i ft€r<> o f i k e H*f>er<fr'i-ji1al -(eecl-fof^arJ
a m p l ip e r thouon in F ig 2 , 9
131 1 5 V
loo
IM P U T?N2ZZ& 2 7 K
I6 K
I C O
^ ^ v F i g . i 5 . HTOi f f l Qe ^ t i Al A M P L in t iQ %TAa>e vo i i r t - i CCKji -TAkJr C u < K t U r L o A b A Mb
30
L F a m p l i f i e r and a d i f f e r e n t i a I - a m p l i f i e r w i t h an e m i t t e r -
f o I l owe r o u t pu t wh i c h compr i ses the H F channe l . F i g . 2 . 1 0
shows the ga i n vs. f r e q u e n c y curves . Si nce both channe l s
have e m i t t e r - f o l l o w e r ou t pu t s , we can e l i m i n a t e the low
f r e q ue n c y a m p l i f i e r o u t p u t s t age, and c o n n e c t i t d i r e c t l y to
the h i gh f r e q u en cy a m p l i f i e r . Si nce the i n p u t stage o f the
second channe l is a d i f f e r e n t i a l a m p l i f i e r , the f i r s t t r a n
s i s t o r acts as a common c o l l e c t o r s t age; c o n s e q u e n t l y , the
second t r a n s i s t o r o f the d i f f e r e n t i a l - a m p l i f i e r is d r i v e n f rom
a low i mpedance sour ce , thus a h i gh f r e q u e n c y break p o i n t
is ensured .
2 . 2 . 3 Cons t an t C u r r e n t Load C o n c e p t . The presence of the
s t ray c a p a c i t a n c e in the i np u t stage of the h i gh f r e q ue n cy
a m p l i f i e r causes rate l i m i t i n g , and a sine wave i n p u t appears
t r i a n g u l a t e d at the o u t p u t .
The rate l i m i t i n g can be e l i m i n a t e d by using a
cons t an t c u r r e n t l oad , v i z . a c o mp l e me n t a r y t r a n s i s t o r
co n n e c t e d in a common base c o n f i g u r a t i o n ( F i g . 2 . 1 1 ) . The
design cons i s t s o f the f o l l o w i n g steps:
1. Se l e c t o p e r a t i n g po i n t s for Q and Q ^ •
2 . Se l ec t a c ons t an t l oad c u r r e n t (1 ^ ) •
3. Se l ec t the maximum c o l l e c t o r s w i n g i n g v o l t a g e of
Q 2 and set i t at the e m i t t e r o f .
31
4. C a l c u l a t e R _ . asE4V - V V
R = — ^ ------- — = — 111 ( 2 . 2 8 )E4 C2 C2
5. Find base v o l t a g e of Q ^
V = V - V ( 2 . 2 9 )B4 RE4 BE4
6 . C a l c u l a t e the r es i s t or va l ues w i t h r espec t to Vd 4
< 2 - 3 0 )4 5 4
where V ^ and V ^ are abso l u t e v a l u e s .
S i m p l i f y i n g Eq . ( 2 . 3 0 ) g i ves
R4 <V CC + V EE) = R4 V B4 + R5V B4 02 ' 3 1 )
_ V B4R5 " <V CC + V EE - V B4) ( }
The va l ues of R and R ^ must be a d e q u a t e l y low to
ensure a l a rge I g ; s i nce V and as a r esu l t I ^
are the f u n c t i o n s of t e m p e r a t u r e , a l a rge va l ue of
I g w i l l keep V ^ cons t an t .
7 . Se l e c t the c o l l e c t o r c u r r e n t I ^ of Q and c a l
c u l a t e the t o t a l c o l l e c t o r cur ren t s .
8 . Se l e c t a p r oper c u r r e n t s i nk n e t wo r k to p r ov i de the
t o t a l c o l l e c t o r c u r r e n t I y ; th i s process is p r esented
in Cha p t e r 1. R q may be ad j us t ed to p r ov i d e the
p roper o p e r a t i n g p o i n t o f Q j .
Wi t h the cons t an t c u r r e n t l oad co n n e c t ed in a common -base
c o n f i g u r a t i o n , the i mpedance r , in the o r der o f o n e - t o - t w o
Megohms, w i l l appear as the c o l l e c t o r r es i s t ance o f Q g , and
the ga i n of the stage w i l l be i nc r eased to more t han 1 0 0 .
U n f o r t u n a t e l y , t h i s h i gh ga i n al so i ncreases the M i l l e r
c a p a c i t a n c e . The p a r a l l e l c o m b i n a t i o n o f the o u t p u t
i mpedance o f c ons t an t c u r r e n t l oad Q ^ and the o u t p u t
i mpedance of t r a n s i s t o r Q 2 appear as an e q u i v a l e n t source
impedance for the o u t p u t e m i t t e r - f o l l o w e r . Th e r e f o r e , the
o u t p u t i mpedance of the e m i t t e r - f o l l owe r is i n c r e a s e d .
An a m p l i f i e r d e v e l o p e d w i t h p r i n c i p l e s p r esented
above gave ver y s a t i s f a c t o r y r esu l t s . A s t a t i c noise t es t ,
h o we v e r , r e v e a l e d t ha t an e q u i v a l e n t no i se , i n the or der of
12 Op V , is p resent at the i n p u t . The source o f t he noi se and
a method of e l i m i n a t i o n of i t w i l l be p r esented in the
F"- N
oi se
fqctor
in
oit>
6 0
loo 10 KC 00 KCkro
n ^ - 2 . i 2
Transistor noi'sC V.s, {reoventy
f o l l o w i n g s u b s e c t i o n .
2 . 2 . 4 N o i s e a n d I t s E l i m i n a t i o n . N o i s e is a n y s p u r i o u s
or u n d e s i r e d s i g n a l t h a t t e n d s t o o b s c u r e t h e s i g n a l t o be
22a m p l i f i e d . T r a n s i s t o r n o i s e a p p e a r s d u e to t h r e e s o u r c e s :
1 . T h e r m a l or J o h n s o n n o i s e o f t h e b a s e r e s i s t a n c e .
2 . F l u c t u a t i o n s i n t h e d i f f u s i o n o f t h e m i n o r i t y
c a r r i e r s .2 3
3 . R e c o m b i n a t i o n f l u c t u a t i o n s i n t h e b a s e r e g i o n .
T h e t r a n s i s t o r n o i s e f a c t o r ^ F is d e f i n e d as
N O I S E P O W E R O U T P U T _______________________________F — /2 3 5 )
N O I S E P O W E R O U T P U T O F A N O I S E L E S S S Y S T E M *
T h e f r e q u e n c y d e p e n d e n c y ^ o f t h e t r a n s i s t o r n o i s e v s .
f r e q u e n c y is s h o w n i n F i g . 2 . 1 2 . In t h e n o i s e f a c t o r F p r e
s e n t e d a b o v e , o u t p u t n o i s e is a l w a y s r e f e r r e d t o t h e i n p u t ;
t h e n o i s e g e n e r a t e d in t h e f i r s t s t a g e is c r i t i c a l . In t h e
22S c h w a r t z , M . , I n f o r m a t i o n T r a n s m i s s i o n , M o d u l a t i o n ,
A n d N o i s e , M c G r a w - H i l l , 1 9 5 9 .
100
80Uncom pensated boitcm am p *Bottom amp * ooi^h q
sfmplg d o m i n a n t po le
\ \ d v e to the f i l te r .
60
o p am p.
20
K/lkf Un<ty-gam response
Wfc Me100 1KC
Response cones o f the feedforward amjo.
W o T E r I t is noi necesiQfy /& compert Sa.te ktith <\mp1i Cr$ t f ^ f i f t e r is used. Hoioevtrj necessery <xdjosttne*)+$ <hoo/d be m ade & $ s /c .b ////y c o n d /t.aya dem and.
34f
i n p u t stage des i gn , i t was s t i p u l a t e d t ha t the q u i e s c e n t
c o l l e c t o r cu r r en t s shou l d be no more than 1 OOpA, and i n p u t
stages w i t h 3 Op A c o l l e c t o r cu r r en t s are not unusual » These
low va l ues ensure a low noise f a c t o r .
The noise o f the h igh and low f r e q u e n c y a m p l i f i e r s of
the f e e d f o r w a r d system, measured i n d e p e n d e n t l y , are ve r y
l o w . Ho we v e r , when two a m p l i f i e r s are c o n n e c t e d in f e e d
f o r war d f a s h i o n , the f i r s t a m p l i f i e r noi se is a m p l i f i e d by the
second and appears as a l arge e q u i v a l e n t noi se source at the
i n p u t .
A s i mp l e way to e l i m i n a t e t h i s noi se is to use a f i l t e r
at the o u t p u t o f the f i r s t a m p l i f i e r . The f i l t e r is f ormed by
using the o u t p u t i mpedance o f t he l ow f r e q u e n c y a m p l i f i e r
and a c a p a c i t a n c e to g r o u n d . This method has r educed the
noi se by a f a c t o r o f 12. Using a f i l t e r makes the p o l e - z e r o
m a n i p u l a t i o n s unnecessar y , s i nce the po l e due to the f i l t e r
w i l l have a d o mi nan t e f f e c t ; as a con se qu enc e , t he r o l l - o f f
ne t works are not used. The f r e q u e n c y of the f i l t e r po l e is
s e l e c t e d as low as l O c p s . , thus ensur i ng a 6 ^ ^ / o c j.ave
s l ope f rom l Ocps . to the c rossover f r e q u e n c y . Si nce the zero
o f the f i l t e r may o c c u r be l ow the u n i t y g a i n , i t p r ov i des an
a d d i t i o n a l marg i n of s t a b i l i t y . The F i g . 2 . 1 3 is the ga i n vs.
f r e q u e n c y curves o f the l ow and h i gh f r e q u e n c y a m p l i f i e r s .
35
I t shou l d be noted t ha t thi s f i n a l des i gn f u l f i l l s the
s t a b i l i t y r equ i r emen t s of the f e e d f o r w a r d a m p l i f i e r .
2 . 2 . 5 Some C o n s t r u c t i o n P r e c a u t i o n s . T r a n s f e r r i n g bread
board model i n t o a mar ke t i t em is not a s u b j e c t o f thi s paper .
Howev e r , to ensure a p r oper o p e r a t i o n , some i m p o r t a n t po i n t s
have to be p o i n t e d out as f o l l o w s :
1 . Trans i s tors must be s e l e c t e d in pai r s and matched .
2 . Heat sinks must be common for each s t a g e .
3 . For h i g h e r c u r r e n t o u t p u t stages ( i . e . 50 MA or
more) the power t r ans i s t o r s must have c o n v e c t i o n
c o o l e r s , separa t e f rom the o t h e r t r a n s i s t o r s .
I C O A lOK-O.----- v w — <1-----/WXy-
lCO.il iv / ' • / - k___AAA,__\2.
F I G - 3 . la
A Coarse h a la r C - t r y c_j
IMj l
/ V W
P"/£> - 3 * I lo
Av o t e if. *thr
A 4* i C tx t lo f Ci,^j ^
Tin C P o t . 7 ’ I - ^ ' vi
f*, i h e t-Trsf locJccnzio* p o t , ind icatedsj f ( 5 Ji n ~ H i e / a r / c u i t ' i w r e s o r c h a p t e r s I a r d £ , C tfz . See 7 , )
' f ig u re s a b c v s
CHAPTER i l l
TEST METHODS A N D RESULTS
SE CT I ON: 1
STATIC TESTS
3 . 1 . 1 I n t r o d u c t i o n . A l t h o u g h d i f f e r e n t ma nu f a c t u r e r s use
d i f f e r e n t test p r ocedu r es , the a m p l i f i e r t es t i ng methods used
at Bu r r - B r own Research C o r p o r a t i o n , p r esented in the f o l
l o w i n g subsec t i ons , appear to p e r m i t a ver y c a r e f u l
e v a l u a t i o n of a m p l i f i e r s ,
3 . 1 .2 Zero B a l a n c i n g . The o f f s e t p resent at the a m p l i f i e r
o u t p u t is due to two componen t s , v i z . v o l t a g e and c u r r e n t .
A d i f f e r e n t c a l i b r a t i o n setup is used in each case.
1 . V o l t a g e o f f s e t c a l i b r a t i o n : The a m p l i f i e r is
c a l i b r a t e d f o r zer o v o l t o f f s e t using the test setup
shown in F i g . 3 . 1 a . No t e t ha t i n p u t is
e s s e n t i a l l y g r ou n d e d . C a l i b r a t i o n must be
a c c o mp l i s h e d to an a c c u r a c y of ± 5 M V , by a d j u s t
i ng the p o t e n t i o m e t e r T^ .
2 . C u r r e n t o f f s e t b a l a n c i n g : The a m p l i f i e r is
c a l i b r a t e d f o r c u r r e n t o f f s e t by using t he test s e t
up shown in F i g . 3 . 1 b . In t h i s setup the o u t p u t
T A B L E 3.1E F FE C TS o f POWER-SUPPLY-VOLT4CE
C H A N C ES
B U o B M ib ) E ^ i iu / k )
15 15 _2
12 15 + 150
1 8 15 - 1 5 0
18 18 - 3 3
12 12 + 2 5
15 12 - l 3 0
IZkle 3 . 1.a
G> f Vo Its,) B o i t s ) E mii/iVolto)
15 15 - 2
12 15 - 2 5 0
18 15 - 6 0
18 16 + 2 2 0
15 IS + 6 4
12 12 - 2 2 0
AN/ALY5/5 :C i r c u i t 1' t t o n a e c t e d a s in
Rj* 2 .b and I K-O. resisto r i s r e m o v e d .
A L = 5 0 x: id " 3 V / y AB^ / V
A l f =. 50 n A Z .A 6t / v
A & = 26O A I0~ ! 4 . .^ 7 y ir tZu /. A 6 " 6 ^
A C g _ £ 8 o x i o f - 4 ^ „ 7 n A /^ g ' * 6X1X lo 6 * V
Cor»mo/i Supplif dhafac: ^ (03 A 8t j‘ " 6
o .s .c - q .6 7 x 10 w ,
= 9 . 6 7 x i o ^A 8V
Kioto circuit is connected c-5 fn Rg.z?.aFor 6L _AE, .
100x40%
-3
For 6 *. AEcIOOx4o%
Common C b a n c j i ^Same direcFioiJ
. 6 0 x IQ'S_ 3o/ f ^ 100x20 % Zo
“Table 3 .1 .b
Table 3.2 d r i f t Melas u f t E M t w r s
WOT&: AmplT-er j s rcn/lfctaj (^r Tesi yt . Ter \etf # 2 ref lace J$- <a icc< r^s/Vcr.
O U T P U TUN .Mill vtoLTAGE.iV/ilh.) l^ rrn o .
vIn c^CTest * 1 Test #3
c 2 2 6
2 0 4 5 5
D r i f t C u r r m f :
‘Te.sf a- |
D r i f t Vblfac^: 'J 4 T ' R p
est f<2.
37
o f f s e t is d u e t o t h e c u r r e n t c o m p o n e n t . O n e c a n
r e d u c e t h i s o f f s e t by c h a n g i n g t h e c r o s s f e e d
r e s i s t o r s R a n d R ; a p r a c t i c a l c a l i b r a t i o n d I B2
l e v e l i s a b o u t ( 1 - 2 ) M V .
A f t e r b o t h c a l i b r a t i o n s a r e o b t a i n e d t o t h e r e q u i r e d a c c u r a c y ,
c o m p l e t e d - c m e a s u r e m e n t s m u s t be m a d e a n d w i t h t h e k n o w n
q u i e s c e n t v a l u e s , t h e c u r r e n t s i n k n e t w o r k m u s t be r e c a l
c u l a t e d U s i n g t h e e q u a t i o n s g i v e n i n S e c . 2 . 1 . 3 .
I f t h e a m p l i f i e r is g o i n g t o be m o l d e d , t h e t e s t s mu s t
be r e p e a t e d b e f o r e a n d a f t e . r m o l d i n g .
3 . 1 . 3 P o w e r S u p p l y V a r i a t i o n E f f e c t s . T a b l e 3 . 1 p r e s e n t s
t h e o f f s e t c u r r e n t a n d o f f s e t v o l t a g e v a l u e s p r o d u c e d b y t h e
p o w e r s u p p l y v a r i a t i o n s .
3 . 1 . 4 T e m p e r a t u r e V a r i a t i o n E f f e c t s . T h e i n c r e a s e a n d
d e c r e a s e i n t e m p e r a t u r e w i l l c a u s e o f f s e t s a t t h e o u t p u t o f
t h e a m p l i f i e r ( T a b l e 3 . 2 ) .
T h e s e t u p w i t h 1 M e g o h m f e e d b a c k m e a s u r e s t h e
c u r r e n t o f f s e t , b n d t h e o n e w i t h 1 0 0 K _j"L. f e e d b a c k d e t e r
m i n e s t h e v o l t a g e c o m p o n e n t o f t h e o f f s e t .
3 . 1 . 5 i n p u t a n d O u t p u t I m p e d a n c e M e a s u r e m e n t s . The
i n p u t i m p e d a n c e i s m e a s u r e d s e p a r a t e l y f o r t h e t o p a n d b o t t o m
a m p l i f i e r s ( F i g . 3 . 2 a ) . Th e c a p a c i t o r a t t h e f e e d b a c k p a t h
lo o kA A /V
D e c . Box
Z:m -
I M e go h m D C
i O K J L ( 5 ) i ^ c p s .
db-Met<?Cr
O
™T~F I (o . 3 • 2 Q
Input Impedance meosunem£/it s e tu p ,
I OCX^ v w
I
S I C ' ^ ^ N
13 se / So x cj.fa«. M f*
? o u t : 2 5 - f i
n s • 3.2 la
Outpui I f f t p e d a n c c f t .easurerr ien j S e tu p
- • £>2. Mill/volt's
Vi VM
F IS . 3 . 3fVOlS’b M E A U S U £ £ M E S J T
SETUP
TABLE 3.3D 4 _ V O L T A G E S
X^5TA6E5
Volta^es^.STAGE I stage i r STAGE M STAGE JjE
Coutput)
V c , + 4 eqvo\t$ t i 0 .9 Vo its 095 Volts —
X a ^ Volts «b 10.9 Veits « |4.7 V lts -e“w”‘
vE -5,1 \4fe +4.^5 Volts *!■ i 1.3 Veits ~~A25 V,
S p e c ia l V o lta g e s :
Vgg* s 6 52 Volts.
Veits. ) F<y. ^ c ^ t s«t.
C - 4 .8 Volts J
38
e n s u r e s DC s t a b i l i t y 0 A l t h o u g h I t Is no t s h o wn in t h e c i r c u i t *
t h e o u t p u t f i l t e r Is d i s c o n n e c t e d 0 S i g n a l f r e q u e n c y I n use Is
s e l e c t e d in t h e f l a t r e g i o n o f t h e o p e n l o op f r e q u e n c y
r e s p o n s e « T h e d e c a d e b o x is a d j u s t e d f o r a s p e c i f i e d out put ™
v o l t a g e d r o p ; f o r e x a m p l e . I f 1 db d r o p is m e a s u r e d , t h e
i n p u t I m p e d a n c e is f e n t i m e s t h e v a l u e se t a t t h e d e c a d e b o x „
For t h e o u t p u t I m p e d a n c e , a s i m i l a r p r o c e d u r e is a p p l i e d w i t h
t h e d e c a d e b o x c o n n e c t e d t o t h e o u t p u t ( F i g „ 3 . 2 b ) .
3 P I 06 N o i s e M e a s u r e m e n t s o N o i s e m e a s u r e m e n t is ma d e i n
t h e f e e d f o r w a r d a m p l i f i e r w i t h t e s t s e t u p p r e s e n t e d I n F i g .
3 o3 . A l t h o u g h v a r i o u s n o i s e m e a s u r e m e n t me t h o d s a r e
a v a i l a b l e , t h e o n e p r e s e n t e d g i v e s a d e q u a t e i n f o r m a t i o n .
3 . 1 . 7 D—C M e a s u r e m e n t s o Th e d =c m e a s u r e m e n t s a r e
M lu s t .ra te d , in T a b l e 3 . 3 . Of has t o be p o i n t e d o u t t h a t t h e s e
d - c m e a s u r e m e n t s a r e m a d e I n t h e b r e a d b o a r d m o d e l o f t h e
s i n g l e c h a n n e l a m p l i f i e r ; n e v e r t h e l e s s , t h e t op a m p l i f i e r o f
t h e f e e d f o r w a r d sys t em has s i m i l a r o p e r a t i n g p o i n t s . The t o p
a m p l i f i e r o p e r a t i n g p o i n t s a r e s h o wn i n F i g . 2 . 4 .
Safe CapocitiVe Loadircj: 25oopf 3 > d b h f e a k / n j : S O Q ^ - f
F i g - 3 A a . S T A B I L I T Y TESTsb<?ri rJ\rc\ jW C c n d . ' )
I k _n_
‘5 o fc Ccap a a h w LoacL'ncj •, bdOOpf. 3>db : ( 5 0 0 p f.
F 1G . 3 A L STABILITY t e s t( A/Th urn'^j fe e d b a c k )
l o o K-C.AA/V---------
F/ G. 3 . 5O PEN LOOP R E S P O N S E
TEST SETUP
5 0 - a
F I G . 2 .4,MoximU/Tt VcltQQZ a n d cu T ren t o v i p o t
rr<sctivre w e n t t s s f
4 Q2Sokc. h o \ / c l h )
39
S E C T I O N : 2
D Y N A M I C T E S T S
3 . 2 . 1 I n t r o d u c t i o n . T h e d y n a m i c t es t s p r o v i d e i n f o r m a t i o n
on s t a b i l i t y a n d f r e q u e n c y r e s p o n s e o f t h e a m p l i f i e r . I f
r o l l - o f f n e t w o r k s a r e p r e s e n t , t h e p o l e - z e r o c o n f i g u r a t i o n
m a y be r e a d j u s t e d t o e n s u r e s t a b l e o p e r a t i o n w i t h v a r i o u s
c a p a c i t i v e l o a d s .
3 . 2 . 2 S t a b i l i t y T e s t s : A m p l i f i e r is c o n n e c t e d as i n F i g .
3 . 4 a . T h e c a p a c i t i v e l o a d is i n c r e a s e d a n d 3 db p e a k i n g
a n d o s c i l l a t i n g v a l u e s a r e o b s e r v e d . F i g . 3 . 4 b s h o ws a s e t
up t o o b t a i n n o m i n a l 1 db a n d 3 db p e a k i n g v a l u e s .
S q u a r e w a v e r e s p o n s e is a l s o a m e a s u r e o f s t a b i l i t y ;
i f r o l l - o f f n e t w o r k s a r e p r e s e n t , w e c a n r e d u c e t h e r i n g i n g
a n d / o r o v e r s h o o t .
3 . 2 . 3 G a i n v s . F r e q u e n c y M e a s u r e m e n t s . F i g . 3 . 5 s hows a
2s e t u p t o o b t a i n o p e n l o o p r e s p o n s e o f t h e b o t t o m a m p l i f i e r .
T h e t o p a n d b o t t o m a m p l i f i e r o p e n l o o p a n d t h e f o r w a r d
a m p l i f i e r u n i t y g a i n r e s p o n s e c u r v e s a r e p r e s e n t e d i n F i g .
2 . 1 1 . F o r t h e t o t a l o p e n l o o p , t w o g a i n s mu s t be a d d e d .
T h i s s e t u p wa s d e v i s e d by M r . T . R . B r o w n , P r e s i d e n t B u r r - B r o w n R e s e a r c h C o r p o r a t i o n .
IO K w v ^w v > —#
Und'eriesIOOKV \ A / V
l Y . 1Vertical
SIGNAL! 21C; 2 5 ruroCarbon pot,
I AII resistors I 9^ ,
C a l i b r a t e the scope and the power s u p p l i e s , s e t Amp. I for zer o o u t p u t .Compensat e Amp. 2 for the test f r e q u e n c i e s , and ad j us t i t for zer o o u t p u t .Set the h o r i z o n t a l s e n s i t i v i t y at 2 V / ^ m . , set the v e r t i c a l s e n s i t i v i t y at 1 0 M V / ^ m .
4 . ) A p p l y a 20 V . p - p sine wave i n p u t .5 . ) O b t a i n mi n i mum v e r t i c a l d e v i a t i o n by a d j u s t i n g the
p o t e n t i omete r .6 . ) Cond u c t tests at ( lOcps , IK C , 1 0KC) . For each
f r e q u e n c y decade observe the v e r t i c a l and h o r i z o n t a l b a l a n c e . Er ror of the a m p l i f i e r under test is the
. v e r t i c a l d e v i a t i o n d i v i d e d by the " G a i n " of the er ro r a m p l i f i e r .Dynami c Resul ts:
ACCURACY : 2% at 10 KC .PHASE SHIFT: 0.1 Degrees at 10 KC.D i s t o r t i o n : 1% at 1 MC .
FIG . 3 . 7
Dynami c A c c u r a c y Me a s . Setup
NOTE: The Dynami c A c c u r a c y is d e f i n e d as thel i n e a r i t y of the a m p l i f i e r as a f u n c t i o n of f r e q u e n c y .
40
In F i g . 2 . 1 1 t h e g a i n a t u n i t y f e e d b a c k is 3 db d o w n
a t 9 M C z w h e r e a s , t h e t o p a m p l i f i e r o p e n l o o p r e s p o n s e is
3 db b e l o w u n i t y g a i n a t I S M C . T h i s r e s u l t j u s t i f i e s t h e
r e a s o n i n g o f t h e p r e c e d i n g p a r a g r a p h .
3 . 2 . 4 M a x i m u m C u r r e n t a n d V o l t a g e O u t p u t s . Th e a m p l i f i e r
i s c o n n e c t e d i n u n i t y g a i n w i t h a 50 ohm l o a d as s h o w n i n
F i g . 3 . 6 .
3 . 2 . 5 Phase S h i f t a n d D y n a m i c A c c u r a c y . Th e p h a s e s h i f t
is m e a s u r e d by s t a n d a r d m e t h o d s .
The d y n a m i c a c c u r a c y o f t h e a m p l i f i e r is m e a s u r e d
w i t h t h e t e s t s e t u p p r e s e n t e d i n F i g . 3 . 7 .
41
C O N C L U S I O N
1 o C o n c l u d i n g Remarks . This t hesi s is the r esu l t o f the
d e v e l o p me n t of two types of f e e d f o r w a r d a m p l i f i e r s . I f is
the a u t h o r ' s b e l i e f t ha t the c o m p l e t i o n of the des i gn is
m a i n l y due to the l a t e model test i ns t r ument s a v a i l a b l e in
Bu r r - B r own Research C o r p o r a t i o n . The design has u t i l i z e d
the c a p a b i l i t i e s of t he t r ans i s t o r s w h i c h are used in the
a m p l i f i e r to the f u l l e x t e n t . I f seems t ha t t he f r e q u e n c y
response is l i m i t e d due to C ^ o f the t r a n s i s t o r . I f an
advance in the t r a n s i s t o r t e c h n o l o g y p r ov i des n e g l i g i b l e
C ob/ t o g e t h e r w i t h a h i gh (3 c u t o f f f r e q u e n c y , o p e r a t i o n a l
a m p l i f i e r response can be ex t e n d ed to the 500MC r eg i on .
The c h a r a c t e r i s t i c s o f the t r ans i s t o r s used in the
a m p l i f i e r were pr esent ed in Tab l e 2 . 1 .
2 . Suggest i ons f or Future Work . Va r i ous and v e r y i n t e r e s t
ing methods to i mpr ove the HF channe l are suggested to the
a u t h o r ; f or e x a mp l e , t he Mi 11 e r - e f f e c t c a p a c i t a n c e o f Q ^
may be e l i m i n a t e d by i n s e r t i n g an NPN t r a n s i s t o r be t ween 2 7
Q l 0 and Q ^ • A l s o , i f Q ^ were d r i v e n by an a d d i t i o n a l
2 7 This p o w e r f u l method was suggested to the au t ho r by Dr . G . A . Korn of The U n i v e r s i t y o f A r i z o n a . No t e t ha t the r e s u l t i n g c i r c u i t is a cascode t ype c o n n e c t i o n .
42
e m i t t e r - f o l lower, , t he a m p l i f i e r o u t p u t i mpedance wou l d be
l o w e r .
The response t i me to w i t h i n 0.1 p e r c e n t of the 6 Kc
i n pu t pul se was measured to be about 2 m i l l i s e c o n d s , wh i ch
2 8is r a t h e r l o n g . Cas cad i ng an e m i t t e r - f o I l o we r to the
t r a n s i s t o r Q in F i g . 1.1 has r educed the response t i me to 1 0
2 9w i t h i n 0 .01 pe r c e n t of t he i n p u t pul se to less than 6 p.sec.
A n o t h e r i dea is to decrease the common -mode ga i n by
3 0a com mon -mode n e g a t i v e f e e d b a c k . This o l d method isO I
now be i ng used in t r a n s i s t o r d i f f e r e n t i a I - a m p l i f i e r s .
F i n a l l y one may s ta te t h a t the approach to the design
prob l em may s t a r t f rom a c o m p l e t e l y d i f f e r e n t p o i n t o f v i e w ;
in p a r t i c u l a r , s i n g l e ended stages or class B a m p l i f i c a t i o n
may ve r y w e l l p r o v i d e l arge f r e q u e n c y response w i t h f ewer
component s .
2 8 This phenomena was shown to the a u t ho r by M r . T. Br u b ak e r . M r . Br ubaker was using the a m p l i f i e r i n a s a mp l e - ho l d a p p l i c a t i o n .
2 9This method was t augh t to the a u t ho r by M r . H .K o e r n e r .
^ O f f n e r , F. F . , " P u s h - P u l l Re s i s t a n c e - C o u p l e d A m p . " , Rev. Sc i . I n s t . , V o l . 8 , pp . 2 0 - 2 1 , J anuar y 1937.
^ Mi dd I e b r o o k , R. D. op . c i t .
SI 01 ^6 + ^S2 ^
r</
FIG. A .IEquivalent cfrci^rt o f a crots-
coupled s t a g e .
Thv
Thv
K E f _ H i , •)»n
R «e.
^fn + H B
1 =f i n
R i n t R f
F I G . A . Z
TM ^ VE NlM vi VaIerl t o f ^ / G . z4.|rfs^eet to KE/ , uJifh E f source a p p e a r f f t j Q5 a l o a d .
43
A P P E N D I X A
THE I N P U T I M P E D A N C E OF THE
C R O S S - C O U P L E D S T A G E
R e f e r r i n g to F i g . A . 1 t h e b r a n c h I m p e d a n c e R j n is
t h e I n p u t I m p e d a n c e o f a s t a n d a r d ( I . e . n o n - c r o s s - c o u p l e d )
di f f e r e n t i a i - a m p I i f l e r as shown I n Eq . ( 2 . 3 ) . S i n c e t h e
base o f 0 2 I n p u t Is g r o u n d e d , R is no t s h o w n . K Is t h eb2
g a i n a t t h e c o l l e c t o r o f 0 2 f o r an i n p u t s i g n a l a t t h e base
of O l . R Is t he s o u r c e I m p e d a n c e , w h i c h is u s u a l l y so
s m a l l t h a t i t w i l l be n e g l e c t e d . W e w r i t e t h e T h e v e n I n
e q u i v a l e n t v o l t a g e and r e s i s t a n c e s w i t h r e s p e c t t o K E j
s o u r c e ( F i g . A . 2 )
ET h v = EB1 * T r i K E 1 ( A ' l )In B1
R , R n i
" T h v " R - ...... . < A „ 2 ,
w h e r e R, = -%■ ^ f l )i n 1 - a
T h e T h e v e n I n c i r c u i t sho wn I n F i g . A . 2 d e f i n e s t h e I n p u t
I m p e d a n c e o f t h e c r o s s - c o u p l e d a m p l i f i e r ,
Eq . ( A . 4 ) I m p l i e s t h a t Rj Is a l w a y s l a r g e r t h a n R ^ , I , e e ,
cross c o u p l i n g I n c r e a s e s t h e i n p u t I m p e d a n c e . H o w e v e r ,
as t h e r e g e n e r a t i o n t h r o u g h R e x c e e d s a c r i t i c a l v a l u e ,
R|n b e c o m e s n e g a t i v e . T h e s t a b i l i t y c o n d i t i o n s a r e shown
I n A p p e n d i x B.
/ N /
f 0 , \
q :in
E |
F I G . B . l
Cross-coupled Pfffe-renifal Am p .
N0TE.: Cgorft) Qt op ^ . ( B A )
IS (n ^asurdd a t p o i n t A ,
^ - 4- Rg .
R5 (i not eir<tu)n , if inc/vJsc/ m K
F I G , 6 . 2
S s r/o Model o f F / G . B . L
45
ii n
APPENDI X B
STABI L I TY C O N D I T I O N S OF THE
CROSS- COUPLED STAGE
We note t ha t the c r o s s - c o u p l e d d i f f e r e n t i a l -
a m p l i f i e r resembles a m u l t i v i b r a t o r . In o t he r words ,
p o s i t i v e f e ed b ack is p r esen t . Si nce the s w i t c h i n g p h e n o
mena takes p l a c e when the l o o p - g a i n exceeds u n i t y , to
ensure the s t a b i l i t y of the c r o s s - c o u p l e d a m p l i f i e r l oop
ga i n must be kep t be l ow u n i t y .
Re f e r r i ng to F i g . B . l the e q u i v a l e n t i mpedance R.
is the p a r a l l e l c o m b i n a t i o n of i n p u t i mpedance R. ^ and
source i mpedance R ^ . The i mpedance R^j is the e q u i v a l e n t
o u t p u t i mpedance o f the c o n s t a n t - c u r r e n t - s i nk and is
r e t u r ned to ground . Si nce the base o f Q 2 is g r ou n d ed , the
d e v i c e opera t es as a common- base a m p l i f i e r .
F i g . B.2 Is the servo model o f F i g . B . l where the
l oop ga i n is A (3 = A A 2 (3 ; these f ac t o r s are d e f i n e d be l ow
1. Tr ans i s t o r Q 1 opera tes as a c o mmo n - c o l I e c t o r
a m p l i f i e r ha v i n g a v o l t a g e ga i n o f ,
A ' = 1 + ( r e + r b - a r b ) / R L ^ ^
46
2 . T r a n s i s t o r Q 2 o p e r a t e s as a c o m m o n - b a s e a m p l i f i e r
h a v i n g a v o l t a g e g a i n o f ,
A2 r e + Req + r b ( l ' a ) ( B * 2 )
w
( Ro u t ) Q l = RS ( ' - ” ) + R E1 ( B ' 4 )
S i n c e e q u i v a l e n t T p a r a m e t e r s (r, , r ) a r e s ma l lb e
c o m p a r e d t o c i r c u i t r e s i s t a n c e s a n d a is c l o s e t o
u n i t y , E q , (B . 2 ) c a n be a p p r o x i m a t e d as
r l
2 = ( B . 5 )
3 o T h e f e e d b a c k f a c t o r |3 Is e x p r e s s e d as
(B „ 6 )Rln + RB
Thu s , we c a n c o m b i n e t he l o o p g a i n by I ts f a c t o r s
LG = A A - p ' - ( 1 ) ( ~ ) -------------) (B . 7 )Req R, n + K
47
For s t a b i l i t y , l oop g a i n must be less t h a n o n e , t hus I t
f o l l o w s t h a t ,
R ' RI n L ^
\ R + R ( B . 8 )Re q ' I n B
Vcc
F I G . C. lpiicsr ZTAZE e Mi t t ES. TRXWSisrof?
8l45 SETTINGS .
48
APPENDI X C
D E R I V A T I ON OF VB 3
* -*■The measured and c a l c u l a t e d va l ues V ^ , V g g , I ^ , I ^
d e f i n e a s p e c i f i c va l ue for the base v o l t a g e of the f i r s t
stage e m i t t e r t r a n s i s t o r . The f o l l o w i n g equa t i ons ho l d in the
c u r r e n t c i r c u i t ( F i g . C . 1 ) ,
V RE3 = V B3 " V BE ( c • 1)
V , E 3 * V R E3 ‘ V B , - | V , E ‘ V K ^
where the as t e r i sked va l ues are the i ncreases in the
co r r es po n d i ng v o l t a g e s . S u b s t i t u t i n g (C . 1 ) i n t o (C . 2) g i ves
V RE3 = V BE ( c - 3 )
We can al so w r i t e
VRE3
2 RE3
( C . 4 )
(V + V )
' c + ' c =
The f a c t o r of 2 is due to the o t he r c o l l e c t o r c u r r e n t .
S u b s t i t u t i n g ( C . 4 ) i n t o ( C . 5 ) g i ves
VRE3
2 RE3( C . 6 )
A I so w r i t i n g the pe r c e n t i nc r ease of I ^ , we w i l l have
'c v mV
RE3
S u b s t i t u t i n g (C . 3) i n t o (C . 7) g i ves*
Vv BE
RE3 I » C
Eq . (C . 8 ) is a ver y i m p o r t a n t r esu l t , s t a t i n g t ha t f or a
g i ven V ^ change , g i v e n I ^ and c a l c u l a t e d 1 . change ,
ex i s t s o n l y one va l ue for V . A l so we can f i n d VK 13 B 3
V = v + V B3 RE3 BE
S u b s t i t u t i n g (C . 8 ) i n t o ( C . 9 ) resul t s
( C . 7 )
( C . 8 )
there
a s
( C . 9 )
FIG . D . I
A n d ysis:
>I| Z ( r — € q
-A .e :
X = §i z £ l » ( I + A )’ z , 2 /A » I j A = I4 A
r , - . i i . - e '2 ;
i . « 6 , 2 . « 2
c l4
VO
FI G. 0 . 2 Shunt capacitance in cx
Tro.niis.t6r Am p(if,'e.r,
N o 'T E : For simplicity J and f)[e (^re e.xcludc2from the Input c irc u it. The Fyure a.Love is a. K'^h-fre^uenc^ fhode/.
50
A P P E N D I X D
THE M I L L E R E F F EC T I N T R A N S I S T O R S
F i g . D o 1 p r e s e n t s a s i m p l i f i e d v e r s i o n o f t h e M i l l e r
I m p e d a n c e . Ac r oss P N j u n c t i o n s o f t r a n s i s t o r s a c a p a c i t a n c e
e x i s t s . Th i s Is d e f i n e d as,
1
C =
2(1
P n B
2f a r a d / 2 ( D . l )m
w h e r e
n^ = The d e n s i t y o f n e g a t i v e c a r r i e r s w h i c h h a v e c r oss ed
t h e j u n c t i o n I n t o t h e P r e g i o n ,
q = C h a r g e o f t h e c a r r i e r s .
p = T h e d e n s i t y o f p o s i t i v e c a r r i e r s w h i c h h a v e c r oss edn
t h e j u n c t i o n I n t o t h e N r e g i o n .
V g = The v o l t a g e acr oss t he j u n c t i o n .
€ = D i e l e c t r i c c o n s t a n t o f t h e m e d i u m .
B a s e - e m l t t e r a n d b a s e - c o l l e c t o r c a p a c i t a n c e s , h o w
e v e r , a r e p r e v e n t e d f r om b e i n g p u r e s h u nt c a p a c i t a n c e s du e
to t h e e f f e c t i v e base r e s i s t a n c e , r ^ . S i n c e t h e base
Al I e y , C . L . a n d A t w o o d , K . W . , EI e c t r o n l c E n g i n e e r i n g , p p . 6 7 - 7 0 , W i l e y , 1 9 6 3 .
51
r es i s t ance is d i s t r i b u t e d t h r o u g h o u t the t h i n wa f e r of base
m a t e r i a l , and a d i f f e r e n t r es i s t ance wou l d ex i s t be t ween
each p o i n t on e i t h e r j u n c t i o n and the base e l e c t r o d e .
F i g . D . 2 shows the h i gh f r eq u e nc y e q u i v a l e n t c i r c u i t o f a
c o m m o n - e m i t t e r s t age . At l ow and m i dd l e f r eq u en c i e s the
e f f e c t s o f s t ray c a p a c i t a n c e s and I nduc t anc es are n e g l i g i b l e ,
but at h i gh f r eq u e nc i e s t h e i r e f f e c t s must be t aken I nto
a c c o u n t . R e f e r r i n g to F i g . D . 2
' i = b + ' s = sCn V i + sC) 2 ( V i - V (D'2)V G = AV. ( D . 3)
S, + C,2(1 - A) v. (D . 4)i
Si nce a m p l i f i e r is i n v e r t i n g .
C i n = C l l + C , 2 (1 + A) ( D - 5)
Equat i on D . 5 r evea l s t ha t the second term w i l l be the
d omi na n t f a c t o r due to the h i gh ga i n A . I f the l oad
i mpedance is not p u r e l y r e s i s t i v e the e f f e c t o f C ^ i nc l udes
3 3 i b i d .
3 4 i b i d .
P/6. E. ISIMPLE PfFFEREkJriA. /IMP.
oVb e ^ O
R ;« ; ^ 8 - ' ^
* iA e ,6 =
RlA
4I
«?,A♦ - A A Z V
— O"
F i g - E..Z
B
'/8 *
£"'«I6
i?,* R , )K|g "h R
‘ ( f )^1814
^ ib R
NB
Eouifajzni Circuit of FlG / £.1 frcrr pO'OT A 'f'o pcif's'/ B t/itW E-2_-*Q <tnd C, ci pplleo/
A
R IA
L RlB
R |6- W \ A —
l
e 'RIB5E
PiA’t
FIG. t . 3EtjuiVtilffrH ( ircuiI cf F16 -E. / r<?f' pci<i+ 3 To pc'irif AjW i i k £ { z 0 a n d E , a p p h f a . _ _
IN jctF' 4 -h o .r ^ , n ce r e ; s k J I^ CF?2Br - '
"n.btrt k3 |'& ihe C c l i e c f c r t r - s t f a r m 'd t< “ ic - . e - i „
E *ju -t" HU HZ
52
a p o s i t i v e or n e g a t i v e c o n d u c t a n c e term d ep end i ng on the
35phase ang l e of the l o a d . N o t e t ha t the ou t pu t i mpedance
o f the d e v i c e w i l l be p a r a l l e l w i t h the l o a d , and w i l l not
e n t e r to the d e r i v a t i o n of Eq. D . 5 .
3 5 i b i d .
53
APPENDI X E
THE C O M M O N - M O D E G A I N E Q U A T I O N
OF THE DI FFERENTIAL AMPLIFIER
The common -mode ga i n e q u a t i o n of the s i ng l e stage
d i f f e r e n t i a l a m p l i f i e r , shown in F i g . E . 1, is d e r i v e d by
a p p l y i n g the s u p e r p o s i t i o n t heorem .
Re f e r r i ng to F i g . E . 2 and w i t h n e g l e c t i n g b a s e - t o -
e m i t t e r v o l t a g e drops, the c u r r e n t t h rough R isI B
R!BR3
RIB + R3 i( t t t ) <e - ' )
RIB R +Vi__ 16R | A + R |B + R 3
Al soI = a : ( E . 2 )R2B RIB
' R2B
E
= a —
R R IB 3
. IB 3
Re f e r r i ng to F i g . E.3 and w i t h n e g l e c t i n g the b a s e - t o -
54
e m i t t e r v o l t a g e drops the c u r r e n t t h rough R is2 B
R 2 B = a
0 ,E. R._ + R I A R3( E . 4 )
16 RI A + R 3
Now w i t h Ej and E^ both a p p l i e d and assuming
R|B = R | A = R| ' R2B = R2 A = R2 ' EI = E2 we o b t a i n f he resu l t
R2= a E
E, ' E2
r R - (R + R ) 1 3 I 3
Rl + 2R, R3
( E . 5 )
R EV = i R = a ------- -------- ( E . 6 )
2 R2 2 R + 2R
V cR2 2
Common -mode gain = A ^ = = --------------- ( E . 7)CC E R + 2 R
I 3
55
BI BL I OGRAPHY
A l l e y , L „ A . and A t w o o d , K „ W . , E l e c t r o n i c E n g i n e e r i n g , W i l e y , 1963. ------------------------------------------
Bene t eau , P. J . , B l aser , L. and Lane, R. O . , T r ans i s t o r O p . A m p . , IRE Co n v . R e c . , Mar ch 29, 1962.
B l e c h e r , F. H . , " T r a n s i s t o r C i r c u i t s f or An a l o g and D i g i t a l Systems, " Bel l Sys. Tech . J . 35, pp . 2 91 =332 . , March 1 956.
D e e r i n g , S. C . , " A Wi de Band D i r e c t Cou p l e d O p e r a t i o n a l A m p l i f i e r , " Proc . N a t . Si m. C o n f . , J a n . 1 9, 1956.
G i l l e , J . C , , P e l e g r i n , M. J . and D e c a u l n e , P . , Feedback C o n t r o l Systems, M c G r a w - H i l l , 1 959.
G o l d b e r g , E . A . , " S t a b i l i z a t i o n of d - c A m p l i f i e r s , " RCA Rev. I I , p. 296 , 1950.
H i l b i b e r , D . F . , " A New D- C Tr ans i s t o r D i f f e r e n t i a l A m p . , " TP - 1 6 , F a i r c h i l d P u b . , 1961.
H u s k e y , H . D . and Ko r n , G . A . , Comput e r Handbook , M c G r a w - H i l l , 1 962 . :
Ko r n , G . A . and Ko r n , T. M . , E l e c t r o n i c An a l og Co mp u t e r s , M c G r a w - H i l l , Four th E d . , Ch . 5, To be p r i n t e d in 1 964.
Mi dd I e b r o o k , R. D . , D i f f e r e n t i a l A m p l i f i e r s , W i l e y , 1 963 .
P e t t i t , J . M, and M c W h o r t e r , M . M . , E l e c t r o n i c A m p l i f i e r C i r c u i t s , M c G r a w - H i l l , 1961.
P o l o n n i k o v , D . E . , " W i d e Band De c i s i on A m p . , " A u t o m a t i c a T e l e m e k h a n i c a , V o l . 2 , N o . 12, pp. 1 6 1 3 - 1 6 2 2 , D e c . , 1960.
S c h w a r t z , M . , I n f o r m a t i o n Tr ansmi ss i on , M o d u l a t i o n , And N o i s e , M c G r a w - H i l l , 1 959.
St ewar t , John L . , C i r c u i t Theory and Des i gn , Ch . 10 ,W i l e y , 1958. --------------------------------------------------