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8/13/2019 DC and Small Signal Components
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DC and Small-Signal
ComponentsAlthough ( )Iv t can be anygeneral functon of t!e" #e #ll fnd
that often" n real$tc and u$eful electronc crcut$" th$ n%ut
can be deco!%o$ed nto two $e%arate co!%onent$&the DC
component I' " and the small-signal component ( )v t . I..
( ) ( )I Iv t ' v t = +
*et+$ loo, at each of the$e co!%onent$ ndvduall-
he DC component I' $ eactl- #hat -ou #ould e%ect&
the co!%onent of $gnal ( )Iv t ote th$ value $ nota
functon of t!e (other#$e t #ould not be ) and
therefore $ e%re$$ed a$ a constant ( e.g." 12 3.I' '= ).
athe!atcall-" th$ value $ the time-averagedvalue of( )Iv t
0
1( )
/
I I' v t dt /=
#here /$ the time durationof $gnal ( )Iv t .
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A$ the notaton ndcate$" the small-signalcomponent( )v t isa functon of t!e oreover" #e can $ee that th$
$gnal $ an AC signal" that $" t$ t!eaveraged value $
zero I..
0
1( ) 0
/
v t dt / =
h$ $gnal ( )v t $ referred to a$ the $!all$gnal
co!%onent becau$e t magnitude$ generall- smallfor all
t!e t.
Q: 7o# $!all $ small88
A: hat depends 9o!et!e$ t #ll be ver- $!all (e.g."
!llvolt$)" other t!e$ not$!all at all&!ore on th$ later
he total$gnal ( )Iv t $ the sumof the and $!all
$gnal co!%onent$. herefore" t $ neithera nor an A$gnal
:a- attenton to the notation#e have u$ed here. ;e #ll u$e
th$ notaton for the re!ander of the cour$e
DC valuesare denoted a$ upper-casevarable$ (e.g." 'I"
I1" or '
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AC signals(.e." =ero t!e average) are denoted #th
lower-case subscripts(e.g." ( )" ( )" ( )o cv t v t t ).
9gnal$ that are not AC (.e." the- have a non=ero
co!%onent) are denoted #th upper-case subscripts(e.g."(t)" ( )" ( )"I < 2 I v v t t ' ).
ote #e $hould neveru$e varable$ of the for! " "e b' I ' . o
you$ee #h-
A1: >r$t" the co!%onent $ t-%call- ?u$t
a bias. It $ a nownvalue" $elected anddeter!ned b- the de$gn engneer. It
carre$ or relate$ nonfor!aton&the onl-
rea$on t e$t$ $ to !a,e the electronc devce$ #or, the
#a- #e #ant the! too (e.g. to ba$ a @ to the active
!ode)
A!: onver$el-" the $!all $gnal co!%onent $ t-%call-unnown It $ the $gnal that #e are atte!%tng to
processn $o!e !anner (e.g." a!%lf-" flter" ntegrate).
he $gnal t$elf re%re$ent$ in"ormation$uch a$ audo"
vdeo" or data.
Q: Bou $a- that #e #ll often fndn%ut $gnal$ #th twoco!%onent$&a
2 and $!all6$gnal co!%onent. #hy
$ that8 ;hat $ the $gnfcance or
%h-$cal rea$on for each co!%onent8
Q: Bou $a- that #e #ll often fnd
n%ut $gnal$ #th twoco!%onent$&a
2 and $!all6$gnal co!%onent. #hy
$ that8 ;hat $ the $gnfcance or
%h-$cal rea$on for each co!%onent8
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9o!et!e$" ho#ever" th$ $!all" A" un,no#n $gnal
re%re$ent$ not nfor!aton" but no$e o$e $ a random"
un,no#n $gnal that n fact !a$,$ and corruptsnfor!aton.
or ea!%le" the emitter voltageof a @ crcut !ght havethe for!
3 5 0 01 co) $( . .(
v tt = +
It $ ho%efull- evdent that
( )e
(
v
'
t
=
=
3.5
v(
t0.0
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Agan" the DC biaster!$ n all voltage and current$ are
necessary" but of littlentere$t to u$ #hen evaluatng a!%lfer
%erfor!ance
A: ;e are ntere$ted n the three valuesthat character=e an
a!%lfer&Avo" C" and Co.
o#ever" #e are ntere$ted n deter!nng the small-signal
o%encrcut voltage" the small-signaln%ut re$$tance and the
small-signalout%ut re$$tance. I..
hu$ the small-signal" o%en crcut voltage gan of an a!%lfer
$ defned a$
( )
( )o
vo
v tA
v t=
Q: A!%lferper"ormance8 ;hat
$%ecfcall- do -ou
!ean b- a!%lfer
%erfor!ance8
Q: A!%lferper"ormance8 ;hat
$%ecfcall- do -ou
!ean b- a!%lfer
%erfor!ance8
( ) ( )I I
v t ' v t = +
( ) ( )I I
t I t = +
( ) ( )o<
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*,e#$e" the small-signaln%ut re$$tance $ defned a$
( )
( )
v tC
t=
and the small-signalout%ut re$$tance $
( )
( )oc
o
$c
v tC
t=
#here voc$ the small-signalo%encrcut out%ut voltage" and $c
$ the small-signal$hortcrcut out%ut current.
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