DC and Small Signal Components

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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DC and Small Signal Components