ANOTHERVIEWOF
RobertR.Cordell
38
In recent years the use of large amounts of negative feedback in audio amplifiers has become controversial. Several
people have examined the time-responseproperties of feedb a c k a m p l i f i e r sa n d h a v e c o n c l u d e d t h a t a m p l i f i e r s w h i c h
employ large amounts of negative feedback are prone to a
form of high-frequency distortion called "transient intermod u l a t i o n d i s t o r t i o n " ( T l M ) [ 1 - 4 ] .S i m p l y p u t , t h i s d i s t o r t i o n i s
s a i d t o o c c u r w h e n a s i g n a lc h a n g e st o o q u i c k l y f o r t h e a m plifier to follow it properly.
The observation that a large amount of negative feedback
c a u s e sT I M t e n d s t o r u n c o u n t e r t o t h e c o n v e n t i o n a lw i s d o m
that increasednegative feedback generally improves a given
amplifier's performance, so long as adequate stability is preserved. Several other researchershave recently questioned
t h e s ef i n d i n g s a n d c o n c l u d e t h a t l a r g ea m o u n t s o f n e g a t i v e
f e e d b a c kd o n o t i n c r e a s et h e p o s s i b i l i t yo f T I M a n d c a n i n
f a c t i m p r o v e a m p l i f i e r p e r f o r m a n c ea s l o n g a s t h e a m p l i f i e r
has an adequate slew rate [5,6].
TIM is thus a popular subject surrounded by a certain
amount of controversy.lt has also become a frequently cited
reasonfor degraded sound. Advertisementsindicate that seve r a l m a n u f a c t u r e r sh a v e b e e n i n f l u e n c e d b y t h e d i s c u s s i o n s
as well, some proudly pointing out that they use very little
negativefeedback.
M u c h o f t h e m i s u n d e r s t a n d i n ga n d d i s a g r e e m e n t s u r r o u n d i n g t h e s u b j e c ts e e m st o s t e m f r o m i n a d e q u a t ec o n s i d eration of the trade-offs and constraints involved in the aoplication of negative feedback, especiallyas it relatesto cont e m p o r a r y ,r e a l - w o r l d a m p l i f i e r c i r c u i t s . T h i s i s p a r t i c u l a r l y
true of feedback compensation. For this reason,we will take
t h e t i m e t o r e v i e w i m p o r t a n t n e g a t i v ef e e d b a c k p r i n c i p l e s
where necessary.Given a good understanding of negative
f e e d b a c ka s i t i s a p p l i e d t o a u d i o a m p l i f i e r s s, o m e o f t h e T I M
issuesshould become easierto resolve.
, e should point out that TlM, which is
B e f o r ep r o c e e d i n g w
associatedwith negative feedback and its compensation, is
o n l y o n e f o r m o f h i g h - f r e q u e n c yi n t e r m o d u l a t i o nd i s t o r t i o n .
The term "dynamic intermodulationdistortion" (DlM) has
been used to describe the general class of intermodulation
d i s t o r t i o n sw h i c h d e p e n d o n f r e q u e n c ya s w e l l a s a m p l i t u d e .
T I M i s t h u s o n e f o r m o f D l M . S i n c et h e p r o d u c t o f f r e q u e n c y
a n d a m p l i t u d e i m p l i e s r a t e - o f - c h a n g ea, n d s i n c e t h e m a x i m u m r a t e - o f - c h a n g et h a t a n a m p l i f i e r c a n f o l l o w i s c a l l e d i t s
s l e w r a t e ,t h e t e r m " s l e w i n d u c e d d i s t o r t i o n " ( S l D ) h a s a l s o
b e e n u s e d a s a l a b e l f o r D l M . T h e s ed i s t i n c t i o n sa r e , h o w e v er, relatively weak and unimportant, referring more to the
mechanism than to the measured or audible effect. Because
it is the source of most of the controversy, we will concent r a t e o n T I M ; h o w e v e r , o u r d i s c u s s i o nw i l l c o n s i d e r o t h e r
sources of DIM as well, some of which may in practice be
moreserious.
TransientI ntermodulationDistortion
to get
First,let'stakea lookat the popularTIMarguments
some background. What follows is a sort of composite parap h r a s i n go f m a n y o f t h e a r g u m e n t sw h i c h h a v e a p p e a r e d .
F e e d b a c ka m p l i f i e r so p e r a t e o n t h e p r i n c i p l e t h a t a l a r g e
p o r t i o n o f t h e i n p u t s i g n a li s c a n c e l l e db y f e e d b a c kf r o m t h e
a m p l i f i e r o u t p u t , l e a v i n g a s m a l l s i g n a l - p l u s - e r r o rw h i c h
d r i v e s t h e a m p l i f i e r s o a s t o p r o d u c e t h e d e s i r e do u t p u t . I n
a m p l i f i e r sw i t h l a r g ea m o u n t s o f n e g a t i v ef e e d b a c k ,t h i s s i g n a l - p l u s - e r r o ri s f o r c e d t o b e v e r y s m a l l a n d t h u s , i n t h e o r y ,
l o w d i s t o r t i o n r e s u l t s .U n d e r t h e s e c o n d i t i o n s , t h e n e t g a i n
w i t h f e e d b a c k ( c l o s e d - l o o pg a i n ) d e p e n d s a l m o s t e x c l u s i v e l y
on how much of the output signal is fed back; i.e.,if onet e n t h o f i t i s f e d b a c k , t h e g a i n w i l l b e 1 0 . T h e l a r g ef e e d b a c k
f a c t o r ( r a t i o o f g a i n w i t h o u t f e e d b a c kt o g a i n w i t h f e e d b a c k )
i s o b t a i n e d b y p u t t i n g a l a r g ea m o u n t o f g a i n i n t h e f o r w a r d p a t h o r o p e n - l o o p a m p l i f i e r .T h e o p e n - l o o p a m p l i f i e r i s t h u s
v e r y s e n s i t i v ea n d w i l l o v e r l o a d i f t h e e r r o r , f o r s o m e r e a s o n ,
g e t sa t a l l a p p r e c i a b l e .
A l l a m p l i f i e r sh a v e a f i n i t e d e l a y f r o m i n p u t t o o u t p u t . l f a
f e e d b a c ka m p l i f i e r i s d r i v e n w i t h a s i g n a l h a v i n g a v e r y f a s t
r i s e t i m e ( l i k e t h e l e a d i n g e d g e o f a s q u a r ew a v e ) , t h e r e w i l l
b e a b r i e f i n t e r v a ld u r i n g w h i c h t h e o p e n - l o o p a m p l i f i e r s e e s
the full input signal, undiminished by negative feedback
w h i c h h a s n ' ty e t g o t t e n b a c k t o t h e i n p u t . O v e r l o a d w i l l t h u s
o c c u r a n d d i s t o r t i o n w i l l r e s u l t .T h e m o r e s e n s i t i v ei n p u t s o f
a m p l i f i e r sw i t h h i g h f e e d b a c k f a c t o r s a r e t h a t m u c h m o r e
proneto suchan overload.
S i n c et h i s f o r m o f d i s t o r t i o n i s b r o u g h t a b o u t b y f a s t t r a n s i e n t si n t h e i n p u t s i g n a la n d b e c a u s ea n o v e r l o a d c o n d i t i o n
causesintermodulation distortion, the phenomenon ts ref e r r e dt o a s t r a n s i e n ti n t e r m o d u l a t i o nd i s t o r t i o n ( T l M ) .
Returningto the origins of TlM, the situation is further
a g g r a v a t e db y t h e a d d i t i o n a l s l o w n e s s o f r e s p o n s e i n t r o d u c e d i n t h e o p e n - l o o p a m p l i f i e r b y n e c e s s a r yf e e d b a c k
c o m p e n s a t i o n .E a c h s t a g e i n a m u l t i - s t a g ea m p l i f i e r i n t r o d u c e s p h a s e s h i f t t h a t i n c r e a s e sw i t h f r e q u e n c y . F e e d b a c k
c o m p e n s a t i o n r o l l s o f f t h e o p e n - l o o p r e s p o n s es o t h a t t h e
feedback factor falls below unity before enough excessphase
shift accumulatesto cause instability or peaking in the
c l o s e d - l o o p r e s p o n s e .T h e f r e q u e n c y w h e r e t h e f e e d b a c k
f a c t o r f a l l s t o u n i t y i s c a l l e d t h e g a i n c r o s s o v e rf r e q u e n c y .I n
order to achieve a stable gain crossoverfrequency, the 6 dB/
octave compensation roll-off must begin at some lower frequency. Amplifiers with large feedback factors (at low freq u e n c i e s )h a v e m o r e g a i n t o " g e t r i d o f " a n d m u s t s t a r t t h e i r
compensationroll-off at a lower frequency, resultingin a
smalleropen-loop bandwidth. An amplifier with 20 dB of
feedbackneedn't start its roll-off until 100 kHz for a 1-MHz
g a i n c r o s s o v e rw
, hile one with 60 dB of feedbackmust start
a t 1 k H z . T h e l a t t e ra m p l i f i e r ,w i t h h e a v i e rf e e d b a c kc o m p e n -
AUDIO o Februarv
1980
@
E
.l
F
-20
F
t o p o l o g y w i t h r e a l i s t i cc o m b i n a t i o n so f f e e d b a c k f a c t o r a n d
o p e n - l o o p b a n d w i d t h . R e c o g n i z i n gt h a t i n a d d i t i o n t o l i m i t s
o n a m p l i . t u d ea, m p l i f i e r sa r e l i m i t e d t o p r o v i d i n g a m a x i m u m
r a t e - o f - c h a n g ea t t h e i r o u t p u t , m u c h a t t e n t i o n w l l l b e o a i d t o
a m p l i f i e r s l e w - r a t ep e r f o r m a n c ea n d i t s r e l a t i o n s h i pt o T l M .
F i n a l l y ,t e c h n i q u e sf o r m e a s u r i n ga m p l i f i e r T I M p e r f o r m a n c e
will be discussed.
U -30
Program Characteristics
l u s t a s a l l r e a l a m p l i f i e r sa r e b a n d l i m i t e d , s o a r e a l l r e a l
J
U -40
p r o g r a m s o u r c e s .N o p r o g r a m s o u r c e w i l l e v e r p r o d u c e a
G
s q u a r e w a v e w i t h r a z o r - s h a r pe d g e s . I n f a c t , n o t o n l y a r e
p r o g r a m s o u r c e sb a n d l i m i t e d i n t h e s m a l l _ s i g n asl e n s e ,b u t
t h e y a r e m o r e s e r i o u s l yl i m i t e d i n l a r g e - s i g n abf a n d w i d t h , o r
p o w e r b a n d w i d t h . A s a n e x a m p l e ,a f i n e t i p e m a c h i n e m i g h t
b e f l a t t o 2 0 k 1 z a t l o w l e v e l s ,b u t i t t y p i c a l i yc a n n o t p r o d u c e
FREQUENCY-Hz
a n y w h e r e n e a r f u l l o u t p u t a t 2 0 k H z . S u c h r e s t r i c t i o n sa r e
u s u a l l yd u e t o e q u a l i z a t i o nw h i c h p r e - e m p h a s i z e st h e h i g h
Fig. l-Post-RIAA spectral distribution for phonograph
f r e q u e n c i e ss o t h a t t h e s u b s e q u e n td e - e m p h a s i sa t t h e r e p [ _
records.
d u c i n g e n d w i l l r e d u c e h i g h - f r e q u e n c yn o i s e . H i g h f r e q u e n _
s a t i o n a n d a l o n g o p e n - l o o p t i m e c o n s t a n t ,i s t h u s s l o w e r i n
c i e s w i l l , t h e r e f o r e ,o v e r l o a d t h e m e d i u m m o r e r e a d i l y t h a n
r e s p o n d i n gt o i n p u t s i g n a l s .
l o w f r e q u e n c i e s .S u c h e q u a l i z a t i o n c h a r a c t e r i s t t cas r e c o m _
I n r e s p o n d i n gt o a f a s t i n p u t s i g n a l ( e . g . ,a s q u a r ew a v e ) , a
m o n t o a t m o s te v e r y t y p e o f p r o g r a m s o u r c e ,i n c l u d i n g p h o _
l a r g e i n t e r n a l v o l t a g e o r c u r r e n t o v e r s h o o tw i l l b e p r o d u c e d n o g r a p h , F M , a n d t a p e .
A s a r e s u l t ,t h e m a x i m u m h i [ L r _ f r e i n o r d e r t o q u i c k l y c h a r g e t h e c o m p e n s a t i n gc a p a c i t o ra n d
quency output of each program source is constrainedto
o v e r c o m e t h e e f f e c t o f t h e l o n g t i m e c o n s t a n t i t i n t r o d u c e s . r a t h e rw e l l - d e f i n e dl i m i t s .
The large overshoot is produced during the interval between
S i n c e s i g n a l sw i t h a l a r g e r a t e - o f - c h a n g eo r , , t i m e d e r i v a t h e f a s t i n p u t c h a n g e a n d t h e t i m e w h e n t h e f e e d b a c k t i v e " a r e g e n e r a l l yt h e
cause of TlM, we need a way of
c a t c h e s u p w i t h t h e i n p u t , w h e n a l a r g e d i f f e r e n c eo r e r r o r characterizing the tendency
of a given program source to
s i g n a li s a p p l i e d t o t h e o p e n - l o o p a m p l i f i e r .
p r o d u c e t h e m . S u c h a m e a s u r es h o u l d n o t b e a b s o l u t e ,l i k e
I n s o m e c a s e st h i s o v e r s h o o t m a y b e 1 0 t o 1 0 0 t i m e s a s t i m e d e r i v a t i v e ,b u t r a t h e r
s h o u l d b e r e l a t i v es o t h a t i t c a n b e
l a r g ea s t h e n o m i n a l s i g n a l l e v e l sa t t h a t p o i n t . U n f o r t u n a t e _ a p p l i e d e q u a l l y w e l l
a t d i f f e r e n t p o i n t s i n t h e s y s t e mr e g a r d _
l y , t h e s t a g e sp r i o r t o t h e c o m p e n s a t i o np o i n t c a n n o t a l w a y s l e s so f s i g n a l l e v e l .
We will thereforeuse the ratio of oeak
h a n d l e s u c h .a l a r g e s i g n a l w i t h o u t n o n l i n e a r i t yo r o u t r i g h t t i m e d e r i v a t i v et o p e a k
a m p l i t u d e e x p r e s s e di n , , v o l t s : D e r _
c l i p p i n g . l f t h e o v e r s h o o tc a u s e st h e s e s t a g e st o c l i p o r g e n - m i c r o s e c o n dp e r v o l t " ( V /
and call it the normalized
e r a t e d i s t o r t i o n , T I M r e s u l t s . W h e n t h e s e o v e r s h o o t s a r e t i m e d e r i v a t i v e .T h e i n v e r s et t s l / V ,
o f t h i s q u a n t i t y i s s i m i l a rt o , b u t
c l i p p e d ,t h e a m p l i f i e r i s i n t o t h e w e l l - k n o w n p h e n o m e n o no f
n o t q u i t e t h e s a m e a s l a r g e - s i g n a rl i s e t i m e . K n o w i n g t h e
s l e w - r a t el i m i t i n g .
n o r m a l i z e dt i m e d e r i v a t i v e ,w e c a n g o t o a n y p o i n t i n t h e
I t c a n b e s h o w n m a t h e m a t i c a l l yt h a t i f t h e i n p u t s i g n a l i s s y s t e m a n d , g i v e n
the maximum amplitude at that point,
b a n d l i m i t e d t o a f r e q u e n c y l e s s t h a n t h e o p e n - r o o p d e t e r m i n et h e c o m m e n s u r a t e
maximum time derivative.
b a n d w i d t h o f t h e a m p l i f i e r , n o o v e r s h o o tc a n o c c u r , e u e n i f
With the exceptionof a microphone, the best source of
the input signal is a bandlimited squarewave. Thus, wide
f a s t p r o g r a m s i g n a l si n t h e h o m e i s p r o b a b l v t h e o h o n o open-loop bandwidth eliminates the possibility of TIM
g r a p h . H o w e v e r , i t s p e r f o r m a n c ei s w e i l - c o n s t i a i n e db y m e _
c a u s e db y o v e r s h o o t s H
. a v i n gw i d e o p e n - l o o p b a n d w i d t h ,i n
c h a n i c a lp r o c e s s e s u c h a s t r a c k i n g .T h e p e r f o r m a n c ei s a l s o
t u r n , p l a c e s a l i m i t o n t h e f e e d b a c k f a c t o r f o r a g i v e n g a i n w e l l c h a r a c t e r i z e d I. n
Fig. 1, the dots are a scatterplot of
crossoverfrequency. For example, if we choose an open-loop
m a x i m u m o b s e r v e do u t p u t l e v e l sa t v a r i o u sf r e q u e n c i e sf r o m
bandwidth ol 2O kHz and a gain crossover frequency of 1
a survey of many records. These data were taken from the
M H z , t h e n w e a r e l i m i t e d t o a f e e d b a c kf a c t o r o f o n l y 3 4 d g .
t r a c k a b i l i t yd i a g r a mw i d e l y p u b l i s h e d b y S h u r e B r o s .
{11!liar
T h e a b o v e e x p l a n a t i o n o fT I M s e e m sp l a u s i b l ee n o u g h , a n d
[ 7 ] W h i l e t h e u s u a l p r e s e n t a t i o ni s i n t e r m s o f g r o o v e v e l o c i _
i t h a s a p p e a r e d i n v a r i o u s f o r m s i n m a n y p l a c e s .l t i s t h e
t y , t h i s i n f o r m a t i o nh a s b e e n R I A A e q u a l i z e da n d n o r m a l i z e d
o r i g i n o f t h e p o p u l a r b e l i e f t h a t s m a l l f e e d b a c k f a c t o r sa n d
t o 2 5 c m , / Sa t 1 k H z a n d 1 V p e a k . l t s h o w s w h a t a c t u a l l vc a n
w i d e o p e n - l o o p b a n d w i d t h a r e n e c e s s a r yf o r m i n i m i z i n g b e e x p e c t e da t
t h e o u t p u t o f o n e , sp h o n o p r e a m p ( a ss h o w n ,
T l M . A l t h o u g h i t m a y a t f i r s t g l a n c e s e e m c o n v i n c i n g ,t h i i
t h e d a t a a r e n o t u s e f u l f o r p o i n t s i n t h e s y s t e mp r r o r t o R I A A
explanation is somewhat oversimplified and misleading. equalization,
such as the phono preamp input). The data
W h i l e s o m e o f t h e i s s u e sh a v e b e e n a n a l y z e di n g r e a t d e t a i l represented
by the X's are spectral data for a single cymbal
in technical papers,other more important considerations crash and were presented
by Tomlinson Holman t8l. The
have been ignored. In several respects,theproblem seems to
crash is one from a Sheffield Lab direct-to-disc recording
l i e w i t h n o t s e e i n gt h e f o r e s tf o r t h e t r e e s .A f e w m o r e r e c e n r w h i c h i s n o t e d
f o r i t s t r a c k i n gd i f f i c u l t y .
p a p e r s h a v e , h o w e v e r ,d o n e a v e r y g o o d j o b i n l e n d i n g i n _
W i t h r e f e r e n c et o F i g . ' 1 w
, e s e e t h a t t h e h i g h e s ta m p l i t u d e
s i g h t a n d p e r s p e c t i v et o s o m e o f t h e m o r e i m p o r t a n t i s s u e s o c c u r s a t 4
k H z a n d i s 1 . 3 5V p e a k , w h i l e t h e h i g h e s t t i m e
Is,6j.
d e r i v a t i v eo c c u r sa t 1 0 k H z a n d i s 0 . 0 3 5V / u S . T h i s r e s u l t si n
T h e a p p r o a c h t a k e n h e r e w i l l i n v o l v e l e s sd e t a i l a n d m o r e a n o r m a l i z e d
t i m e d e r i v a t i v eo f o n l y 0 . 0 2 6 ( V / p S ) / V . T h u s ,
scope and perspective. For example, we.ll attempt to deter_ i n a s y s t e m
s u b l e c t e dt o a w i d e v a r i e t y o f m a t e r i a l s u c h a s
mine just how fast audio program signalsreally are. The represented
b y t h e d o t s o f F i g .1 , a p o i n t i n t h e s y s t e mw h i c h
length of the unavoidabletime delay ln the amplifier and
must handle an amplitude of 1 V peak with low distortion
h o w i t i s a f f e c t e d b y f e e d b a c k c o m p e n s a t i o ni s a n o t h e r i m m u s t h a n d l e a t i m e d e r i v a t i v eo f 0 . 0 2 6V / p S w i t h e q u a l l y
p o r t a n t a r e a i n n e e d o f d i s c u s s i o nW
. e w i l l a l s o e x a m i n et h e
low distortion.
conditions.governing
o v e r l o a do f a n a m p l i f i e r , si n t e r n a ls t a g _
Before proceeding further, we should take note of the fact
e s . T h i s w i l l b e d o n e i n t h e c o n t e x t o f a p r a c t i c a la m p l i f i e r t h a t a n a d v a n c e d
t r e b l e c o n t r o l w i l l t e n d t o i n c r e a s et h e n o r _
F
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;
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m a l i z e d t i m e d e r i v a t i v eo f t h e p r o g r a m , b u t n o t a s m u c h a s
o n e m i g h t a t f i r s t t h i n k . T h e r e a s o nf o r t h i s i s f o u n d u o o n
f u r t h e r e x a m i n a t i o n o f F i g . 1 . T h e p e a k t i m e d e r i v a t i v ew i l l
i n c r e a s ei n p r o p o r t i o n t o t h e g r e a t e ra m p l i t u d e o f t h e h i g h f r e q u e n c y s i g n a l s .H o w e v e r , m o s t t r e b l e c o n t r o l a c t i o n o c curs between 2 kHz and-10 kHz, meaning that the overall
p e a k a m p l i t u d e ( o c c u r r i n ga t 4 t o 5 k H z i n F i g . 1 ) w i l l i n c r e a s es o m e w h a t a s w e l l . B a s e d o n t h e s e o b s e r v a t i o n s ,w e
c a n c o n c l u d e t h a t 6 d B o f t r e b l e b o o s t w i l l i n c r e a s et n e n o r _
m a l i z e d t i m e d e r i v a t i v eb y p e r h a p s5 0 p e r c e n t .
W h i l e t h e c y m b a l c r a s he x h i b i t ss u b s t a n t i a lu l t r a s o n i cc o n t e n t , i t s a m p l i t u d e g e n e r a l l yl i e s b e l o w t h e e n v e l o p e o f t h e
o t h e r p o i n t s . N o t i c e t h a t i t s m i d - b a n d r e c o r d i n gl e v e l i s a c t u a l l y r a t h e r l o w i n c o m p a r i s o n .T a k e n a l o n e , t h e n o r m a l i z e d
t i m e d e r i v a t i v ef o r t h e c y m b a l c r a s h m i g h t b e f a i r l y h i g h , b u t
t h e r a t i o o f i n t e r e s tm u s t b e b a s e d u p o n t h e p e a k a m p l i t u d e
for all the music.
Even if the three highest points on Fig.1 are ignored,an
o v e r a l l p o w e r b a n d w i d t h o f l e s st h a n 1 0 k H z i s o b t a i n e d ,a n d
a m a x i m u m n o r m a l i z e dt i m e d e r i v a t i v eo f a p p r o x i m a t e l y0 . 0 5
(V/ LtS) ,/V results. By comparison, a 2O-kHz sinusoid has a
n o r m a l i z e dt i m e d e r i v a t i v eo f 0 . 1 2 6( V/ t t S ) / V .
Music, of course, produces many simultaneous points
w h o s e a m p l i t u d e s a n d t i m e d e r i v a t i v e sa d d i n s o m e f a s h i o n
t o p r o d u c e a t o t a l a m p l i t u d e a n d a t o t a l t i m e d e r i v a t i v ef o r
t h e c o m p l e t e s p e c t r u m .W e c a n g a i n f u r t h e r i n s i g h t b y r e c ognizing that for mid-band frequencies between about 500
Hz and 2 kHz, post-RIAA amplitude is directly related to recorded velocity. Above 2 kHz, post-RIAA time derivative and
recorded velocity are directly related, i.e., a 50-cm/S, 10-kHz
c o m p o n e n t p r o d u c e st h e s a m e t i m e d e r i v a t i v ea t t h e o u t p u t
of the phono preamp as a 50-cm,/S,2O-kHzcomponent. This
l a t t e r r e l a t i o n s h i pi s d u e t o t h e i n t e g r a t i n ge f f e c t o f t h e 2 - k H z
RIAA high-frequencyroll-off. Knowing this, we can get a
good idea of the normalized time derivative by assuming
r e a l i s t i cv a l u e sf o r t h e m a x i m u m t o t a l m i d - b a n d v e l o c i t y a n d
t h e m a x i m u m t o t a l h i g h - f r e q u e n c yv e l o c i t y . N o t i c e t h a t a
smaller assumption for the maximum mid-band velocity
y i e l d s a l a r g e rn o r m a l i z e d t i m e d e r i v a t i v e .K e e p i n m i n d t h a t
t h e m i d - b a n d a n d h i g h - f r e q u e n c ym a x i m a n e e d n o t o c c u r
simultaneously.
A s a n e x a m p l e ,i f w e a s s u m ea m a x i m u m m i d - b a n d v e l o c i t y o f 2 5 c m , / Sa n d a l a r g e m a x i m u m h i g h - f r e q u e n c yv e l o c i t y
of 150 cmlS (probably impossible to track), we arrive at a
figure of 0.076 (V/pS) /V. Based on this figure, a 100-watt
amplifier which can deliver 4O V peak with an B-ohm load
m u s t c l e a n l y r e p r o d u c es i g n a l sw i t h 3 V / p 5 t i m e d e r i v a t i v e s .
Fig.2-{ompensated and uncompensated power amplifier
open-loop gain vs. frequency.
This figure may seem very small to some people, but the
term "cleanly" is the key here.We are certainlynot talking
about the ultimate slew-rate capability of the amplifier,
which generally occurs under nonlinear operating condit i o n s . . C l e a r l yt h e a m p l i f i e r m u s t h a v e s o m e o p e r a t i n g m a r g i n
i n o r d e r t o s a t i s f yt h e " c l e a n l y " r e q u i r e m e n t .A s w e s h a l l i e e
l a t e r ,i n s o m e c a s e st h i s r e q u i r e d s l e w i n g m a r g i n c a n b e s u b s t a nt i a l .
A l t h o u g h i t i s v e r y u n l i k e l y t h a t a n y m a t e r i a lw i l l a p p r o a c h
the 0.076 (V/ lrS) /Y, figure, we can be even more conservative if we wish and simply say that a full-amplitude20-kHz
sinusoid, 0.125 (V/ lr S) ,/V, must be handled with adequate
s l e w i n g m a r g i n . R e q u i r i n gt h a t a s q u a r ew a v e b a n d l i m i t e d t o
2O kHz,0.25 (V/ p S) /V, be handled cleanly would add yet
a n o t h e rf a c t o r o f t w o i n c o n s e r v a t i s m .
B a s e d o n t h e s e o b s e r v a t i o n s ,w e m a y c o n c l u d e t h a t r e a l
a u d i o s i g n a l sa r e n o t n e a r l y a s f a s t a s s o m e w o u l d l i k e t o
b e l i e v e .H o w e v e r , t h i s i s n o t c a u s e f o r c o m p l a c e n c yw i t h r e s p e c t t o T l M . l t m e r e l y g i v e s u s a m o r e r e a l i s t i cp e r s p e c t i v e
f o r d e a l i n gw i t h t h e p r o b l e m .
Low-Pass Filtering
I t h a s o f t e n b e e n s u g g e s t e dt h a t a l o w - p a s sf i l t e r ( L p F ) b e
p l a c e d a h e a d o f t h e p o w e r a m p l i f i e r t o a s s u r et h a t t h e p r o g r a m b a n d w i d t h d o e s n o t e x c e e dt h e o p e n - l o o p b a n d w i d t h
o f t h e a m p l i f i e ri n o r d e r t o m i n i m i z eT I M [ 1 - 3 1 A
. l t h o u g hw e
w i l l s e e l a t e r t h a t s u c h a p r e c a u t i o n h a s n o b e a r i n go n T t U
s u s c e p t i b i l i t y i,t i s w o r t h n o t i n g t h a t t h e L P Fw i l l p l a c e a l i m i t
o n t h e p o w e r b a n d w i d t h , a n d t h u s t h e t i m e d e r i v a t i v e ,o f
s i g n a l sa p p l i e d t o t h e p o w e r a m p l i f i e r . I n t h i s l a t t e r r e s p e c t ,
t h e L P Fc o u l d p r e v e n t T I M i f s u c h a l i m i t a t i o n w e r e n e c e s s a r y .H o w e v e r ,o u r e a r l i e rd i s c u s s i o n ss h o w e d t h a t t h e p o w e r
b a n d w i d t h o f r e a l a u d i o s i g n a l si s c o n s i d e r a b l yl e s s t h a n 2 0
k H z . A s s u m i n gt h a t a n L P Fc u t o f f o f l e s st h a n 4 O k 1 z i s u n a c ceptable due to frequency-response rror (-1 d8 at 20 kHz
a s s u m i n gf i r s t - o r d e rc u t o f f ) , i t i s q u i t e s a f e t o s a y t h a t s u c h a
filter will have no effect on TIM produced by program signals.
Ticks, pops, and mistracking may, however, produce cons i d e r a b l yl a r g e rn o r m a l i z e dt i m e d e r i v a t i v e st h a n p r o g r a m ,a t
l e a s t i n t h e c a s e w h e r e w i d e b a n d m o v i n g - c o i l c a r t r i d g e sa r e
employed. Values as high as 0.1 to O.2 (V/ltsl /V may be
e n c o u n t e r e d .H o w e v e r ,e v e n a s t e p i n p u t w i l l o n l y b e l i m i t e d
t o 0 . 2 5 ( V / 1 t S ) / Y b y a 4 O - k H z L P F .T h e f i l t e r w i l l t h u s h a v e
o n l y a l i m i t e d e f f e c t o n t h e s m a l l e rn o r m a l i z e dt i m e d e r i v a t i v e o f t h e t i c k s ,p o p s , a n d m i s t r a c k i n g O
. ne alsohasto wond e r h o w i m p o r t a n t T I M - f r e e r e p r o d u c t i o no f t h e s e a n n o y i n g
s i g n a l sr e a l l yi s . l t i s p r o b a b l y s u f f i c i e n tt h a t s l e w - r a t el i m i t i n g
n o t b e e n c o u n t e r e di n t h e s y s t e mu n d e r t h e s ec o n d i t i o n s .
T h e o n l y s e n s i b l er e a s o nf o r a n L P Fs e e m st o b e i m p r o v e d
i m m u n i t y t o r . f . i n t e r f e r e n c ei,f t h i s i s r e q u i r e d .
Feedback
Compensation
A s m e n t i o n e d e a r l i e r ,f e e d b a c k o p e r a t e so n t h e p r i n c i p l e
of feedinga portion of the output back to the input for comp a r i s o n w i t h t h e i n p u t s i g n a l .T h e l o o p s o f o r m e d m a y b e
unstable if the phase of the signal is incorrect.Feedback
c o m p e n s a t i o ni s e m p l o y e d t o a s s u r es t a b i l i t y b y c o n t r o l l i n g
t h e n e t g a i n a n d p h a s e s h i f t a s i g n a l s e e sa s i t g o e s a r o u n d
the completeloop.
S i n c e t h e r o l e p l a y e d b y f e e d b a c k c o m p e n s a t i o ni s c r u c i a l
t o t h e T I M d i s t o r t i o n m e c h a n i s m ,a n d s i n c e i n m a n y T I M
d i s c u s s i o n si t i s n o t a d e q u a t e l yc o n s i d e r e d ,i t i s a p p r o p r i a t e
a t t h i s p o i n t t o t a k e a l o o k a t f e e d b a c kc o m p e n s a t i o n .
B e c a u s ea l l r e a l a m p l i f i e r sh a v e f i n i t e b a n d w i d t h , t h e g a i n
a n d t h u s t h e f e e d b a c kf a c t o r m u s t b e g i n t o r o l l o f f a t s o m e
f r e q u e n c y .I n a m u l t i - s t a g ea m p l i f i e r ,e a c h s t a g eu s u a l l yc o n tributes one or more "poles" (6 dB/octave roll-offs) and acc o m p a n y i n g p h a s e s h i f t . l f a t s o m e h i g h f r e q u e n c yw e h a v e
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too much phase shift while we still have gain around the
l o o p , w e w i l l h a v e p o s i t i v ef e e d b a c k a n d t h u s a n o s c i l l a t o r .
For this reason, the frequency at which the feedback factor
has decreased to unity (i.e., the gain crossoverfrequency) is
v e r y i m p o r t a n t i n d e t e r m i n i n g a m p l i f i e r s t a b i l i t y .T o p r e v e n t
o s c i l l a t i o n ,t h e p h a s e s h i f t a c c u m u l a t e d b e y o n d t h e f i x e d
18O-degreeloop inversion must be less than 180 degrees at
t h i s f r e q u e n c y .I n g e n e r a l ,g o o d e n g i n e e r i n gp r a c t i c er e q u i r e s
t h a t l e s s t h a n a b o u t 1 3 5 d e g r e e sb e a c c u m u l a t e d ,l e a v i n g a
p h a s e m a r g i n o f a t l e a s t 4 5 d e g r e e s .I n o r d e r t o o b t a i n t h e
r e q u i r e ds t a b i l i t y ,f e e d b a c kc o m p e n s a t i o ni s e m p l o y e d t o d e liberately roll off the gain so that the feedback factor goes
b e l o w u n i t y b e f o r e t o o m u c h p h a s es h i f t a c c u m u l a t e s .
T h e o p e n - l o o p g a i n a s a f u n c t i o n o f f r e q u e n c yf o r a t y p i c a l
p o w e r a m p l i f i e r b e f o r e a n d a f t e r f e e d b a c k c o m p e n s a t i o ni s
s h o w n i n F i g . 2 . T h e c l o s e d - l o o pg a i n i s s h o w n a s a d o t t e d
l i n e a t 2 6 d B , a n d t h e f e e d b a c kf a c t o r i s s i m p l y t h e d i s t a n c e
b e t w e e n t h e s o l i d a n d d o t t e d c u r v e s .l t i s i m o o r t a n t t o r e m e m b e r t h a t e a c h r o l l - o f f c o n t r i b u t e s p h a s e s h i f t ( p h a s el a g
o r d e l a y ) w h i c h i n c r e a s e sw i t h f r e q u e n c y ,b u t w h i c h c a n n e v er exceed 90 degrees.At its 3-dB point, or "corner frequency," each roll-off generates45 degrees. The gain and phase
c h a r a c t e r i s t i c fso r a s i n g l e p o l e a r e s h o w n i n F i g . 3 . N o t i c e
that a single pole placed at a low frequency can create a
g r e a t d e a l o f h i g h - f r e q u e n c yl o s s w i t h o u t e v e r i n t r o d u c i n g
6u1
44
lrJ
E.
GAIN
€ -zo
U
o
1
a
-45
(o"
-40
B
I
-90
lo
too
tok
th
FREOUENCY-Hz
toot
tM
Fig. 3---Gain and phase characteristics for a 1-kHz pole.
m o r e t h a n 9 0 d e g r e e so f p h a s es h i f t . T h i s i s t h e b a s i sf o r w h a t
i s c a l l e dl a gc o m p e n s a t i o n .
A d e s i g n w i t h m a n y p o l e s s i t u a t e db e l o w t h e g a i n c r o s s o v e r f r e q u e n c yw i l l t e n d t o b e u n s t a b l e ,w h i l e o n e w i t h o n l y a
s i n g l e p o l e b e l o w t h i s f r e q u e n c yw i l l t e n d t o b e s t a b l e ,e v e n
i f t h a t p o l e i s a t a v e r y l o w f r e q u e n c y .T h e u n c o m p e n s a t e d
amplifier in Fig.2 crossesover at 2.4 MHz and has three poles
below that frequency, while the compensated version crosses
over at 1 MHz and hasonly one pole below the gain crossov e r f r e q u e n c y .A s i s t h e c a s e i n F i g . 2 , t h e c o m p e n s a t i o nn e t w o r k u s u a l l y d e c r e a s e ss u b s t a n t i a l l yt h e f r e q u e n c y o f o n e
e x i s t i n gp o l e a n d m a y a l s o s i g n i f i c a n t l yi n c r e a s et h e f r e q u e n c y o f a n o t h e r o n e . T h i s e f f e c t i s c a l l e d p o l e s p l i t t i n g ,a n d i t s
d o u b l e b e n e f i t f u r t h e r c o n t r i b u t e st o s t a b i l i t y .
T o s u m m a r i z e ,t h e o b j e c t i v e o f f e e d b a c kc o m p e n s a t i o ni s
q uite simple: Establisha gain crossover frequency low
e n o u g h t o a c h i e v e a n a c c e p t a b l ep h a s e m a r g i n . I n a p o w e r
a m p l i f i e r ,m u c h o f t h e p h a s es h i f t a t h i g h f r e q u e n c i e si s c o n t r i b u t e d b y t h e o u t p u t t r a n s i s t o r sw
, hich typically have ft's
(current gain-bandwidth products) of about 1 to 4 MHz.
Output stages will tend to contribute rapidly increasing
p h a s es h i f t a b o v e t h i s f r e q u e n c y .A s a r e s u l t ,r e a s o n a b l eg a i n
crossover frequencies for power amplifiers are generally in
the range of 0.5 to 2 MHz.
A TypicalPowerAmplifier
T o f u r t h e r p u t t h i n g s i n t o p e r s p e c t i v e ,w e ' l l n o w t a k e a
b r i e f l o o k a t t h e o p e r a t i o no f a p r a c t i c a lp o w e r a m p l i fi e r .T h i s
s i m p l e a m p l i f i e r w i l l p r o v i d e a s e t t i n g f o r t h e e x a m p l e si l l u s t r a t i n g T I M c o n s i d e r a t i o n si n t h e l a t e r s e c t i o n s .A s i m p l i f i e d
v e r s i o no f a p o p u l a r a m p l i f i e rt o p o l o g y i s s h o w n i n F i g . 4 .
T r a n s i s t o r sQ 1 a n d Q 2 f o r m a d i f f e r e n t i a la m p l i f i e r w h i c h i s
t h e f i r s t s t a g eo f t h e o p e n - l o o p a m p l i f i e r .H e r e t h e f e e d b a c k
s i g n a la p p l i e d t o t h e b a s eo f Q 2 i s s u b t r a c t e df r o m t h e i n p u t
signalapplied to the baseof Q1. Notice that the feedback
s i g n a l i s d i v i d e d d o w n b y R 4 a n d R 3 ,w h i c h s e t t h e c l o s e d l o o p g a i n a t a b o u t 2 0 . C a p a c i t o rC 2 a l l o w s f u l l f e e d b a c k a t
d . c . t o a s s u r ea s m a l l o u t p u t o f f s e t v o l t a g e .
The voltage difference between the basesof Q.l and Q2 is
t r a n s l a t e dt o a c u r r e n t s i g n a l w h i c h i n t u r n d r i v e s t h e b a s e
c i r c u i t o f t h e p r e d r i v e r ,Q 3 . T h e r e s u l t i n gv o l t a g es i g n a la t t h e
c o l l e c t o ro f Q 3 i s d e l i v e r e dt o t h e o u t p u t w i t h a p p r o x i m a t e l y
unity gain by the complementary Darlington emitter-foll o w e r o u t p u t s t a g e .T h e p r i m a r y p u r p o s eo f t h e o u t p u t s t a g e
i s t o p r o v i d e c u r r e n t g a i n a n d t h u s p r e s e n ta r e l a t i v e l yh i g h i m p e d a n c e l o a d t o t h e c o l l e c t o rc i r c u i t o f Q 3 . T h e c o l l e c t o r
current for Q3 is provided by a current source so that the
o n l y r e a l l o a d a t Q 3 ' s c o l l e c t o r i s t h a t p r e s e n t e db y t h e o u t p u t s t a g e .T h i s a r r a n g e m e n tp r o v i d e s v e r y h i g h g a i n i n t h e
p r e d r i v e r s t a g e ,e s p e c i a l l yi f t h e c u r r e n t g a i n i n t h e o u t p u t
s t a g ei s h i g h .
T h e u n c o m p e n s a t e dl o o p g a i n o f t h i s a m p l i f i e r i s s h o w n i n
t h e t o p c u r v e o f F i g . 2 ( a s s u m i n gt r a n s i s t o rb e t a so f 5 0 ) . F e e d b a c k c o m p e n s a t i o no f t h i s a m p l i f i e r i s p r o v i d e d b y a s i n g l e
c a p a c i t o rC 3 c o n n e c t e df r o m c o l l e c t o rt o t h e b a s eo f Q 3 . T h i s
type of compensationis often referred to as Miller-effect
compensation.
A t l o w f r e q u e n c i e s ,C 3 i s a n o p e n c i r c u i t a n d t h e g a i n i s
q u i t e h i g h . A t h i g h e r f r e q u e n c i e s ,C 3 ' s r e a c t a n c ed e c r e a s e s ,
a n d i t b e g i n s t o f o r m a t i g h t n e g a t i v ef e e d b a c k l o o p a r o u n d
Q 3 . A t h i g h f r e q u e n c i e s a, l m o s t a l l o f t h e s i g n a lc u r r e n t f r o m
q1 flows through C3, rather than R2 and-the base of Q3.
U n d e r t h e s e c o n d i t i o n s ,w e c a n a l m o s t t h i n k o f Q 3 a s a n
o p e r a t i o n a la m p l i f i e r a n d i t s b a s e n o d e a s a v i r t u a l g r o u n d .
A t m i d - t o h i g h f r e q u e n c i e s ,t h e v o l t a g e a t t h e c o l l e c t o r o f
Q 3 i s t h e n a p p r o x i m a t e l yt h e s i g n a l c u r r e n t f r o m Q 1 t i m e s
t h e r e a c t a n c eo f C 3 . F u r t h e r m o r e t, h e o p e n - l o o p g a i n o f t h e
a m p l i f i e r w i l l s i m p l y b e t h e t r a n s c o n d u c t a n c e( g m ) o f t h e
d i f f e r e n t i a la m p l i f i e r ( h e r e a b o u t 1 0 m A p e r v o l t ) t i m e s t h e
r e a c t a n c eo f C 3 . S i n c e t h i s r e a c t a n c ei s d e c r e a s i n gw i t h f r e q u e n c y a t 6 d B , / o c t a v e ,s o w i l l t h e o p e n - l o o p g a i n o f t h e
a m p l i f i e r .W h e n t h i s g a i n d e c r e a s e st o 2 0 w e a r e a t t h e g a i n
c r o s s o v e rf r e q u e n c y ( f " ) , s i n c e t h e f e e d b a c k p a t h e s t a b l i s h e s
a c l o s e d - l o o pg a i n ( C . ) o f 2 0 . T h e c h o i c e o f 8 4 p F f o r C 3
y i e l d s a r e a c t a n c eo f a b o u t 2 0 0 0o h m s a t 1 M H z , t h u s s e t t i n g
t h e g a i n c r o s s o v e ra t t h a t f r e q u e n c y a n d y i e l d i n g t h e l o w e r
c u r v e f o r o p e n - l o o p g a i n i n F i g .2 . E x p r e s s e idn g e n e r a lt e r m s ,
C3:
(1)
N o t i c e t h a t l o w - f r e q u e n c yc o n s i d e r a t i o n ss, u c h a s f e e d b a c k
f a c t o r ,d o n o t i n f l u e n c et h e c h o i c e o f C 3 .
PropagationDelay
S o m e a u t h o r s h a v e r e a s o n e dt h a t a n a m p l i f i e r o r e s e n t e d
w i t h a v e r y f a s t t r a n s i e n tw i l l b e w i t h o u t n e g a t i v ef e e d b a c k
f o r a s h o r t p e r i o d o f t i m e u n t i l t h e f e e d b a c k s i g n a l ,h a v i n g
s u f f e r e di n e v i t a b l ed e l a y , a r r i v e st o c a n c e l m o s t o f t h e i n p u t
s i g n a l [ 1 , 3 ] .D u r i n g t h i s d e l a y t i m e , i t i s r e a s o n e d s, o m e s t a g e s i n t h e o p e n - l o o pa m p l i f i e rm a y c l i p d u e t o t h e u n u s u a l l y
l a r g ei n p u t s i g n a l .
Thereis little question that such a problem will occur if a
square wave with a 1 nS rise time is applied to an audio
a m p l i f i e r .H o w e v e r ,t o a s s e s st h e p r a c t i c a ll i k e l i h o o d o f s u c h
AUDIO o Februarv
1980
rf i
Fig.'l Simplified schematic of a popular power amplifier
design.
46
a p r o b l e m ,w e m u s t c o n s i d e rt h e t i m e i t t a k e sa r e a l p r o g r a m
s i g n a lt o r i s e ,w h a t t h e d e l a y t i m e r e a l l yi s ( i t i s n o t t h e o p e n loop rise time as some have implied), and the overload
m e c h a n i s mo f o p e n - l o o p a m p l i f i e rg a i n s t a g e s .
The open-loop amplifier can be modeled as a block of
gain, a dominant first-ordercompensation roll-off, and a
p u r e d e l a y a s s h o w n i n F i g .5 . E f f e c t so f t h e o t h e r n o n d o m i nant poles are lumped in with the delay with little lossof
a c c u r a c y .l t i s w e l l - k n o w n t h a t , f o l l o w i n g a s t e p c h a n g e a t
t h e i n p u t o f a f i r s t - o r d e rR C l o w - p a s sf i l t e r ,t h e o u t p u t b e g i n s
t o c h a n g e i m m e d i a t e l y ,n o m a t t e r h o w l o n g t h e R C t i m e
c o n s t a n t ;o n l y t h e r a t e o f c h a n g e w i l l d e p e n d o n t h e t i m e
c o n s t a n t .T h u s ,a f t e r a s u d d e n c h a n g e a t t h e a m p l i f i e r i n p u t ,
the output will begin to change after the above-mentioned
p u r e d e l a y . T h i s i s t h e p r o p a g a t i o nd e l a y t i m e o f t h e a m p l i fier and is the delay time during which we must be conc e r n e d a b o u t o v e r l o a d i n gt h e a m p l i f i e r i n o r d e r t o d e a l w i t h
the issueraisedabove.
The propagation delay time can be estimated by consider-,
ing the phase margin of the feedback loop. lf an amplifier
h a s a p h a s e m a r g i n o f 4 5 d e g r e e sa t a 1 - M H z g a i n c r o s s o v e r ,
t h e n t h e t o t a l f o r w a r d p a t h d e l a y ( a s s u m n i n ga f l a t f e e d b a c k
path) must be 135 degrees,of which about 90 degrees is f rom
t h e c o m p e n s a t i o np o l e a n d 4 5 d e g r e e si s f r o m t h e p r o p a g a t i o n d e l a y .T h i s w o r k s o u t t o 1 2 5 n S . M o s t p o w e r a m p l i f i e r s
w i l l h a v ec o n s i d e r a b l yl e s sp r o p a g a t i o nd e l a y t h a n t h i s .
It should be pointed out that it is incorrect to say that the
amplifier is without feedback during this interval. The
c l o s e d - l o o pa m p l i f i e r i s a l i n e a r s y s t e m s o l o n g a s t h e g a i n ,
r o l l - o f f ,a n d d e l a y e l e m e n t so f t h e m o d e l a r e l i n e a r .l t i s a l s o
Fig.5-A simple model of the open-loop amplifier showing
time response lo a step input. In practice, gain and delay aie
distributed throughout the amplif ier.
OUT
DELAY
I J. ENOEAGATION
a continuoussystemin spite of the delay,and feedbackis
present100 percentof the time as long as no stagesare
clipped. The feedback is, however,continuously"out of
date" by a time equalto the delay.Fortunately,
the feedback
equationsreadilytakethis into accountin both the frequenc y a n dt i m ed o m a i n s .
Cana full-amplitude
i n p u t s i g n a l s, u c h a s a b a n d l i m i t e d
s q u a r ew a v e ,r i s ef a r e n o u g hi n 1 2 5n St o c a u s ea n y a m p l i f i e r
stagesto becomenonlinearor to overload?The integrating
actionof the compensationwill preventstagesbeyond the
compensationfrom overloading,typicallyleavingonly the
input stagebeforeit to worry about (seeFig.4).
Consideras a worstcasea 2-V peaksquarewave bandlimi t e d t o 2 0 k H z .l t w i l l r i s ea b o u t6 3 m V i n 1 2 5n S ,a n d t h i s i s
e n o u g ht o d r i v es o m ei n p u t s t a g e si n t o n o n l i n e a r i t yT.h i s i s
particularly
true of the differentialpair without emitterresistors (local feedbackoften called emitter degeneration),as
shown in the design of Fig. 4. With a 63-mV error signal
g la i n i s l e s st h a n h a l f i t s n o m i n a l
d r i v i n gi t , i t s s m a l l - s i g n a
value.This nonlinearitywould result in ,,soft,'TIM under
theseconditions.However,most high-qualityamplifierdesignshaveenough local feedbackof one sort or anotherat
t h e i n p u t s t a g et o a l l o w g o o d l i n e a r i t yi n h a n d l i n gs u c ha n
error signal.As we will see momentarily,such feedbackis
u s u a l l ya l s oa n i m p o r t a n ti n g r e d i e nitn a c h i e v i n gh i g h s l e w
rate.
Feedback
factorand open-loopbandwidthare clearlynot
relevanthere,sincedesignswith different valuesfor these
parameters
could easily have the same input stagedesign
and propagationdelay. The important criterion here is to
h a v ea n i n p u t s t a g et h a t c a n h a n d l el a r g e, i n p u t s i g n a l sa, t
leastundertransientconditions.
Slew Rate
Realpoweramplifiersare not only limited in termsof output amplitude;they are alsolimitedwith respectto the rateof-change
or timederivativo
e f t h e o u t p u t .W h e n a n a m p l i f i e r i s a s k e dt o d e l i v e rm o r et h a n i t s m a x i m u ma m p l i t u d ei,t
clipsand producesa constantamplitudeindependentof the
i n p u ts i g n a lS. i m i l a r l yi f, a n a m p l i f i e irs c a l l e du p o n t o d e l i v e r
a greatertime derivativethan its slew rate,the amplifierwill
go into slew-ratelimiting and produce an output rate-ofc h a n g ei n d e p e n d e not f t h e i n p u t s i g n a lA
. swith amplitudei n d u c e dd i s t o r t i o ns, l e w - i n d u c eddi s t o r t i o n( S l D ) ,o r ( T l M ) ,
hasa gradualonset.lt is non-zerobelow the slew-ratelimit
and risesasthe slew-ratelimit is approached.
Havingdiscussedamplifierbehaviorduring the propagat i o n d e l a yi n t e r v aflo l l o w i n ga s u d d e ni n p u tc h a n g ew
, e must
n o w d e t e r m i n ei f t h e a m p l i f i e rc a n k e e p u p w i t h t h e t i m e
d e r i v a t i vcea l l e df o r b y t h e i n p u t s i g n aw
l i t h o u t b e i n gd r i v e n
into nonlinearityby internalerror signals(i.e.,overshoots).
This is basicallya questionof marginagainstslew-ratelimiting, sinceslewingis the resultwhen the internalovershoots
are so big they are clipped.Recallthat theseovershootsare
g e n e r a l l yt h e r e s u l t o f t h e c i r c u i t a t t e m p t i n gt o q u i c k l y
particularly
chargecapacitances,
the compensating
capacitor.
A t t h i s p o i n t i t i s i m p o r t a n t o e m p h a s i z et h a t i t i s t h e
magnitudeof theseovershootswhich is important,not percentage;many papersin the literaturehaveerredin emphas i z i n gt h e l a t t e r[ 1 , 2 ] . l t s h o u l db e c l e a rt h a t g o o d m a r g i n
againstslew-ratelimitingguarantees
that the overshootswill
n o t b e l a r g ee n o u g ht o c a u s en o n l i n e a r i tayn d t h u sT l M .
How doesfeedbackfactoraffectslew rate?By itself,not at
all. Forexample,amplifierswith high feedbackfactorsusually havethe extraopen-loopgain afterthe point of compensation.The most common exampleis the use of a current
sourcecollectorloadon the predriverstage,as in Fig.4. Suppose for the moment that the predriverstagehas a shunt
capacitorat its input (base)for compensation(unlike Fig. ).
1980
AUDIO o February
.)
'.t
-t
--l
: l
t o u s i n g a h i g h - q u a l i t yc u r r e n t s o u r c e l o a d f o r t h e p r e d r i v e r ,
t r i p l e D a r l i n g t o n sa r e u t i l i z e d i n t h e o u t p u t s t a g e f o r e x t r a
c u r r e n t g a i n a n d h e n c e a l i g h t e r l o a d o n t h e p r e d r i v e rc o l l e c t o r n o d e . A d d i t i o n o f t h e p a i r o f d o t t e d p r e d r i v e rl o a d r e s i s ( o r s , R 1 5 a n d R 1 6 ,w i l l c o n v e r t i t t o a l o w - f e e d b a c kd e s i g n
w i t h a 2 0 - k H z o p e n - l o o p b a n d w i d t h . T h e r e q u i r e dc o m p e n s a t i n gc a p a c i t a n c er e m a i n su n c h a n g e d .
LOWFEEDBACK
INPUTG)
_,-T h e o p e n - l o o p g a i n f o r t h e h i g h - a n d l o w - f e e d b a c kv e r WIDEOPEN-LOOP
BANDWIDTH
s i o n so f F i g . 7 i s s h o w n i n F i g .B . T h e g a i n c r o s s o v e frr e q u e n c y
--rFEEDBACK f o r b o t h d e s i g n s i s t h e s a m e , a n d t h e o n l y d i f f e r e n c e i s i n MODERATE
MODERATE
OPEN_LOOP c r e a s e dl o o p g a i n a t f r e q u e n c i e sb e l o w 2 0 k H z f o r t h e h i g h BANDWIDTH
ERRoR
@[
f e e d b a c kd e s i g n .T h e s l e w r a t e f o r b o t h d e s i g n si s t h e s a m e
LARGEFEEDBACK
f o r a s t e p i n p u t s t a r t i n ga t z e r o v o l t s . T h i s f u r t h e r i l l u s t r a t e s
SMALLOPEN-LOOP
t h e f a c t t h a t f e e d b a c kf a c t o r a n d o p e n - l o o p b a n d w i d t h h a v e
BANDWIDTH
no effect on slew rate.
tig. LA model of the feedback amplifier showing the error
What does affect slew rate is the design of the input stage.
time response to a bandlimited step input for various
F o r a g i v e n s i z e c o m p e n s a t i n gc a p a c i t o r ,a n i n p u t s t a g ew i t h
combinations of feedback factor and open-loop bandwidth.
a h i g h e r o u t p u t c u r r e n t c a p a b i l i t yw i l l p r o v i d e a n i n c r e a s e d
Closed-loop bandwidth is held constant, and feedback is
s l e w r a t e . H o w e v e r , m e r e l y i n c r e a s i n gt h e t a i l c u r r e n t o f a
varied by changing only A2. Input level is assumedto be zero
s i m p l e d i f f e r e n t i a l p a i r s t a g e ,a s i n F i g . 4 , w i l l n o t w o r k b e prior to the step.
c a u s et h a t w i l l i n c r e a s et h e s t a g eg a i n ( t r a n s c o n d u c t a n c eb) y
t h e s a m e f a c t o r .T h i s w o u l d t h e n n e c e s s i t a t e
a proportionatelf we double the gain after the compensation by some
l y l a r g e rc o m p e n s a t i n gc a p a c i t o rt o r e s t o r et h e g a i n - c r o s s o v e r
m e a n s ,w e m u s t d o u b l e t h e v a l u e o f t h e c o m p e n s a t i n gc a frequency, and the slew rate would be back to where it was
p a c i t o rt o r e s t o r et h e g a i n c r o s s o v e rf r e q u e n c yt o i t s o r i g i n a l b e f o r e .O n e p o p u l a r s o l u t i o n i s t o u s e e m i t t e r d e g e n e r a t i o n .
value. However,the added gain means that we now need
F o r e x a m p l e ,w e c a n k e e p t h e t a i l c u r r e n t t h e s a m e ,u s e e m o n l y h a l f t h e t i m e d e r i v a t i v eo n t h e c a p a c i t o rt o a c h i e v et h e
i t t e r d e g e n e r a t i o nt o r e d u c e t h e g a i n , a n d t h e n u s e a s m a l l e r
s a m eo u t p u t t i m e d e r i v a t i v e s, o t h e m a g n i t u d eo f t h e c u r r e n t c o m p e n s a t i n g c a p a c i t o r . T h i s a p p r o a c h i s u s e d i n F i g . 7 ,
o v e r s h o o tc h a r g i n gt h e l a r g e rc o m p e n s a t i n gc a p a c i t o ri s u n where R2 and R3 reduce the gain by a factor of 10. This
c h a n g e d . T h e p e r c e n t a g eo v e r s h o o t i s a p p r o x i m a t e l yd o u p e r m i t sa d r a m a t i c i n c r e a s ei n s l e w r a t e . L o c a le m i t t e r d e g e n bfed, however, becauseof the smaller final value as a result e r a t i o n i s a l s o d e s i r a b l e b e c a u s e i t i n c r e a s e st h e o v e r a l l
o f t h e d o u b l e d d . c . g a i n . T h i s i s i l l u s t r a t e di n F i g . 6 . E v e n l i n e a r i t y o f t h e s t a g e a n d p e r m i t s l i n e a r o p e r a t i o n u p t o a
t h o u g h t h e o p e n - l o o p r o l l - o f f s t a r t so n e o c t a v e l o w e r , t h e
l a r g e rp e r c e n t a g eo f t h e u l t i m a t e s l e w i n gc a p a b i l i t y .
input stagedoesn't have to work any harder to achieve a
I t i s i m p o r t a n t t o r e a l i z et h a t t h e e x t r a g a i n i n m o s t a m p l i g i v e ns l e w r a t e .
fiers with high feedback factors is not achievedby adding
T h e s i t u a t i o n i s t h e s a m e f o r a m p l i f i e r su s i n g M i l l e r - e f f e c t m o r e v o l t a g e - g a i ns t a g e s w
, h i c h w o u l d t e n d t o i n c r e a s en o n c o m p e n s a t i o na s i n F i g . 4 . H e r e , e v e n t h e c a p a c i t o rv a l u e i s l i n e a r i t ya n d p r o p a g a t i o nd e l a y . A s c a n b e s e e n l r o m F i g . 7 ,
unchanged as the feedback factor is raised or lowered by
t h e o n l y e l e m e n t s w h i c h n e e d t o b e a d d e d t o a c h i e v ev e r y
v a r y i n gt h e l o a d i m p e d a n c eo f t h e p r e d r i v e r ( Q 3 ) . T h i s i s s o
h i g h g a i n a r e e m i t t e r - f o l l o w e r sT
. h e s e s t a g e sa r e p r a c t i c a l l y
b e c a u s e t h e f e e d b a c k a c t i o n o f C 3 c o n t r o l s t h e h i g h - f r e - d e l a y l e s sa n d a c t u a l l y t e n d t o i m p r o v e l i n e a r i t y b y i s o l a t i n g
q u e n c y g a i n r a t h e rt h a n t h e l o a d r e s i s t a n c eA. m p l i f i e r sw h i c h
d r i v i n g s t a g e sf r o m t h e i n p u t n o n l i n e a r i t i e so f t h e n e x t s t a g e .
a r e d e l i b e r a t e l yd e s i g n e dw i t h l o w f e e d b a c kf a c t o r st y p i c a l l y N o n l i n e a r i t i e sr e s u l t i n gf r o m t r a n s i s t o rb e t a d e p e n d e n c eo n
a c h i e v e t h i s b y p l a c i n g a p h y s i c a l l o a d r e s i s t a n c ef r o m t h e
c o l l e c t o r v o l t a g e ( E a r l ye f f e c t ) a n d c u r r e n t a n d j u n c t i o n c a c o l l e c t o ro f t h e p r e d r i v e rt o g r o u n d [ 9 ] .
p a c i t a n c ed e p e n d e n c eo n v o l t a g ea r e r e d u c e d i n t h i s w a y .
l f w e a s s u m et h a t a l l o f t h e s i g n a l c u r r e n t f r o m t h e i n p u t
I t w a s m e n t i o n e d e a r l i e r t h a t a 1 O O - w a tat m o l i f i e r w o u l d
s t a g ec a n f l o w i n t o C 3 , t h e n t h e s l e w r a t e f o r t h e a m p l i f i e r i n h a v e t o c l e a n l y h a n d l e t i m e d e r i v a t i v e su p t o a b o u t 3 V / p S
F i g .4 i s a b o u t ( 0 . 5m A / 8 4 p F ) : 6 V/ p S . l n p r a c t i c e ,i t w i l l b e f o r w o r s t - c a s ep r o g r a m m a t e r i a l . H o w m u c h m a r g i n a g a i n s t
s o m e w h a t l e s sb e c a u s eo f s o m e c u r r e n t f l o w i n t o R 2 a n d Q 3 .
s l e w - r a t el i m i t i n g i s r e q u i r e d f o r c l e a n , l o w - T l M o p e r a t i o n ?
A n i m p r o v e d a m p l i fi e r i s s h o w n i n F i g . 7 a n d i s a n e x a m p l e T h i s d e p e n d s v e r y m u c h o n t h e p a r t i c u l a ra m p l i f i e r d e s i g n .A
o f a n a m p l i f i e r w i t h a v e r y h i g h f e e d b a c kf a c t o r . I n a d d i t i o n g o o d d e s i g nw i t h p l e n t y o f l o c a l f e e d b a c ka n d a l i n e a ro p e n l o o p r e s p o n s em a y r e q u i r e a m a r g i n o f l e s s t h a n - 1 . 5 t o 1 ,
w h i l e a r e a l l y p o o r d e s i g n w i t h g r o s so p e n - l o o p n o n l i n e a r i t y
Fig. 7-Simplified schematic of an improved power amplifier.
c o u l d r e q u i r e a s m u c h a s 1 0 t o - 1 . H o w e v e r ,e v e n t h e o f t e n criticized 741 operational amplifier, when operated under
r e a s o n a b l ec o n d i t i o n s ,r e q u i r e sl e s st h a n a m a r g i n o f 5 t o 1 .
A m a r g i n o f 4 t o 1 s h o u l d b e m o r e t h a n a d e q u a t ef o r p o w e r a m p l i f i e r so f r e a s o n a b l ed e s i g n t o g u a r a n t e et h a t T I M p r o d u c e d b y i n t e r n a l o v e r s h o o t sw i l l b e c o m p l e t e l y i n a u d i b l e .
B a s e do n t h i s a n d t h e p r e v i o u s l yd i s c u s s e dp r o g r a m c h a r a c t e r i s t i c s t, h e 1 0 0 - w a t ta m p l i f i e r s h o u l d p r o v i d e a s l e w r a t e o f
at least 12 V/ 1tS. This also gives us a 50 percent margin
a g a i n s ts l e w i n g i n t h e p r e s e n c eo f a 0 . 2 ( V / p l S ) / V f u l l - a m p l i tude pop or tick.
Notice that we've paid very little attention to what happ e n s w h e n o u t r i g h t s l e w - r a t e l i m i t i n g o c c u r s ; r a t h e r ,w e ' v e
outlined the conditions required to stay in a rather linear
r e g i o n o f o p e r a t i o n w h e r e , a t m o s t , t h e n o n l i n e a r i t i e sa r e
s o f t . T h i s i s m a i n l y b e c a u s eT I M w i l l b e c o m e a u d i b l e b e f o r e
s l e w - r a t el i m i t i n g o c c u r s . H o w e v e r , i t i s w o r t h n o t i n g t h a t
r
tu
48
A U D I O e F e b r u a r v1 9 8 0
s i g n i f i c a n t l yl o n g e r t h a n t h e t i m e i t t a k e s t h e o u t p u t t o s l e w
t o t h e n e w s i g n a lv a l u e .
At this point, it should be clearthat slew rate is the most
important single parameter governing TIM performance,
while feedback factor and open-loop bandwidth have no
b e a r i n go n T l M . I n P a r t l l , w e ' l l c o n t i n u e b y l o o k i n g a t o t h e r
c a u s e so f h i g h - f r e q u e n c yo r d y n a m i c i n t e r m o d u l a t i o nd i s t o r t i o n ( D l M ) , w h y a l a r g e f e e d b a c k f a c t o r i s g o o d i n s t e a do f
b a d , a n d t e c h n i q u e sa v a i l a b l ef o r m e a s u r i n gT I M i n t h e l a b . 7 f l
LOWFEEDBACK
@
!,
I
z
GAIN
CROSSOVER
FREQUENCY
a
e40
References
1 . O t a l a , M . , " T r a n s i e n t D i s t o r t i o n i n T r a n s i s t o r i z e dA u d i o p o w e r A m p l i f i e r s , , ,
IEEE fransactions on Audio and Erectro-.coustics, Vol. AU-18, pp. 234-239,
S e p t . ,1 9 7 0 .
2. Otala, M., and E. leinonen, "The Theory of TransientIntermodulation Distortion," IEEE fnnsactions
on Acoustics. Speech end Signal processing, Vol.
A S S P - 2 5N
, o. 1, pp. 2-8, Fet:.,1977.
loo
tk
took
tok
FREQUENCY-Hz
tM
Fig.L-Open-loop gain comparison of amplifiers with high
and low feedback factors and equal gain crossover
frequency. The maior difference is the greater feedback in
the audio band for the former case.
r e c o v e r yf r o m a s l e w i n g c o n d i t i o n f o r m o s t c o n t e m p o r a r y
a m p l i f i e r t o p o l o g i e si s n o t a f f e c t e d b y t h e o p e n - l o o p t i m e
c o n s t a n t .T h i s w a s n o t n e c e s s a r i l tyh e c a s ei n s o m e v e r y e a r l y
t r a n s i s t o ra m p l i f i e r d e s i g n s i n w h i c h a t r a n s i s t o rc o u l d s a t u r a t e d u r i n g s l e w i n g a n d c h a r g e t h e c o m p e n s a t i n gc a p a c i t o r
t o a n a b n o r m a l v o l t a g e .R e c o v e r yi n m o d e r n a m p l i fi e r s i s n o t
3 . L e a c h ,W . M . , " T r a n s i e n t l M D i s t o r t i o n i n P o w e r A m p l i f i e r s , ' , A u d i o , p p . 3 4 4'1,Feb., 1975.
4. Creiner, R.A., "Amp Designand Overload," Audio,pp.5O-62,Nov.,1977.
5 . I u n g , W . C . , M . L . S t e p h e n s ,a n d C . C . T o d d , , , S l e w i n g I n d u c e d D i s t o r t i o n
a n d l t s E f f e c to n A u d i o A m p l i f i e r P e r f o r m a n c + W i t h C o r r e l a t e d M e a s u r e m e n t
L i s t e n i n g R e s u l t s , "A E S P r e p r i n t N o . 1 2 5 2 p r e s e n t e d a t t h e 5 7 t h A t S C o n v e n t i o n , L o s A n g e l e s , M a y , 1 9 7 7.
6 . C a r d e , P . , " T r a n s i e n t D i s t o r t i o n i n F e e d b a c kA m p l i f i e r s , " l o u r . o f t h e A u d i o
Engineering Sociely, Y ol. )6, No. 5, pp. 31 4-321, M ay, 1978.
7. Kogen, j., B. iacobs, and F. Karlov, "Trackability-1973," Audio, pp.-t6-22,
Aug.,-197L
8 . H o l m a n , T . , " L ) y n a m i c R a n g e R e q u i r e m e n t so f p h o n o g r a p h i c p r e a m p l i fi e r s , , ,
Audio, pp. 72-79, luly, 1977.
9 . L e a c h , W . M . , " B u i l d a L o w T I M A m p l i f i e r , " A u d i o , p p . 3 O - 4 6 ,F e b . ,1 9 7 6 .
1O. Leinonen, E., M. Otala, and l. Curl, "A Method for Measuring Transient
f ntermodufation Distortion (IlMl," tour. of the Audio Engineering Society,
'l7O-177,
Vol. 25, pp.
April,1977
11. Cordell, R. R.,"4 Fully In-Band Multitone Test for TransientIntermodulat i o n D i s t o r t i o n , " A I S P r e p r i n t N o . 1 5 1 9p r e s e n t e d a t t h e f f t h A E SC o n v e n t i o n ,
New York. Nov.. 1979.
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OSAWA& CO. (USA) lnc., 521Fifth Avenue, New York, New York lOOlT
Distributed in Canadaby Intersound Elecffonics, Montreal, Quebec
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The Measure of Quality
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