Download - Lecture21(20-3-11)
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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=
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