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Reviewing of concepts related to:

RC Low Pass Filter RC High Pass Filter Bode Plots for Low Pass Filter Bode Plots for High Pass Filter

Lecture Goals

EE 332

DEVICES AND CIRCUITS II

Lecture 21

FREQUENCY RESPONSE (1)

REVIEWFORPASSIVECIRCUITS/RCLOWPASSFILTER

vivo

R

C

1

1

1

1 2

1

2

1

Evaluate the transfer function at s j :

since:

)

c

H(jj RC

H(jf)j fRC

fRC

H(jf)f

REVIEWFORPASSIVECIRCUITS/RCLOW PASSFILTER

0

0

1

1

11

( ) ( )

( )

i

sCv s v s

RsC

v s

1 1( )

( )i

sCH sv s sRC

R

=+

Impedanceofacapacitoris

= = = ++

1CZ sC=

Byvoltagedivision:

Transferfunction

vivo

R

C

1c

jf

= = + = +

=

=+

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REVIEWFORPASSIVECIRCUITS/RCLOWPASSFILTER

vivo

R

C

1

0

1

1

c

c

c

For f f :

For f f :

For f f :

o

i

o c

i

o

i

v

v

v f

jv f

v

v j

>

= = +

BODEPLOTS/RCLOWPASSFILTER

1

0

1

1

c

c

c

For f f :

For f f :

For f f :

o

i

o c

i

o

i

v

v

v fj

v f

v

v j

>

= = +

AsymptoticBodePlotofRClowpassfilter:

0dBFc

1020log

o

i

v

v

Slope=20dB/decade

f,log

REVIEWFORPASSIVECIRCUITS

/RCHIGHPASSFILTER

vi voR

C 1CZ sC=

Impedanceofacapacitoris

Byvoltagedivision:

Transferfunction

0

0

1iR

V (s) V (s)

RsC

V (s)

1 1i

R s

= =+

= = =

H(s)

V (s)R s

sC RC

+ +

REVIEWOFBODEPLOTS:(AMPLITUDEONLY)

Everyzeroresultsinanincreaseof20dB/decadeintheslopeofthefrequencyresponse

Everypoleresultsinandecreaseof20dB/decadeintheslopeofthe

frequency

response

Thecutofffrequenciesarethefrequenciesatwhichthemagnitudeofthetransferfunctionis3dBlowerthanH(s)midband(maximum)value

Theunitygainfrequencyisthoseatwhichthemagnitudeofthetransferfunctionis1

TheBodePlotisarepresentationoftheamplitudeofthetransferfunction

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1 2

1

2

EQ

c

EQ

R R R

then

fR C

= +

=

Byinspecting,

1

1 2

1

1 2

1

1

( )1

11

( )1 ( ) 1

1

2

o

i

z

c

z

Rv sCH sv

R RsC

fj

fsR CH s

fs R R C jf

fR C

+= =

+ +

++ = =+ + +

=

R1

R2

C

vi

vo

ANOTHERMORECOMPLEXCIRCUIT

EXAMPLE

Thecircuitdepictsasource

followerusedinahighquality

audioamplifier. HereRi

establishesa

gate

bias

voltage

equaltoVDD forM1,andI1definesthedrainbiascurrent.

Find:Cimin andCLmax

Given:

VDD

Ri

Ci

M1

VO

Vi

I1 CL

1(200 ) ; 100m i

g R k =

1

( )1

z

c

fj

fH s

fj

f

+=+

1

1 2

0( ) 1o

i

o

i

vf DC

v

v Rf

v R R

=

= +

0dBfc

1020logo

i

v

v

f,log

fz

1

1 2

R

R R

ANOTHERMORECOMPLEXCIRCUIT

EXAMPLE

VDD

Ri

Ci

M1

VO

Vi

I1 CL

ANSWERANSWER Ciishighpass,

min

min

120

2

1

2 3.14 100 2079.6

low

i i

i

i

f HzR C

Ck Hz

C nF

=

= C nF=

92