Frequency Response
ELZ 303 - Elektronik II
Microelectronic Circuits – Fourth Edition
Adel S. Sedra, Kenneth C. Smith, 1998 Oxford University Press
Dr. Mehmet Siraç Özerdem
Elektrik Elektronik Müh. Bölümü
Dicle Üniversitesi
Dr. MS Özerdem
s-Domain Analysis
Impedance 1/sC
Impedance sL
Voltage transfer function T(s)=Vo(s)/Vi(s)
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
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T(s), in general
a and b are real numbers
m≤n
m: numerator
n: denominator (order of network)
Microelectronic Circuits - Fifth
Edition Sedra/Smith
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
First Order Function
General form
Low pass - STC network
High pass - STC network
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Example (Bode Plot)
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
Example (Bode Plot)
Microelectronic Circuits - Fifth Edition Sedra/Smith
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The Amplifier Transfer Function
ac amplifier or
dc amplifier
Capacitively coupled amp
BW = wH – wL
Since wL « wH
BW ≈ wH
Gain-Bandwidth product
GB = AmwH
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
The Gain Function A(s)
General form
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The Low Frequency Response
In many cases the zeros are at such low fr. as to be of
little importance in the determining wL
Usually one of the poles – say, wP1- has much higher fr
than other poles. It follows that w close to midband.
TF of a first order high pass network
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
If a dominant low frequency pole does not exist, an
approximate formula can be derived for wL
Example
at w=wL
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
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Example
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
The High Frequency Response
In many cases the zeros are at such high fr. as to be of
little significance in determining wH
Usually one of the poles – say, wP1- has much lower fr
than other poles. It follows that w close to midband.
TF of a first order low pass network
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
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If a dominant high frequency pole does not exist, the
upper 3_dB fr wH can be determined from a plot of
An approximate formula for wH.
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Example
The dominant pole is wH ≈ 104 rad/s
The better estimate
The exact value of wH can be determined from the
given transfer function as 9537 rad/s
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
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Using Short-Circuit and Open-Circuit Time Constants
for the Approximate Determination of wL and wH
In many cases, it is not a simple matter to determine the poles
and zeros. In such cases, approximate values of wL and wH can
be determined using the following method.
b1 can be obtained by considersing the other capacitors to zero
(open circuit )
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Example
Common source FET amp.
R=100kohm
Rin=420kohm
Cgs=Cgd=1pF
a) Midband voltage gain
gm=4mA/V
RL=3.33kohm
b) fH=?
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Copyright 2004 by Oxford University Press, Inc.
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Example
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Next we outline the use of short-circuit time constant to
determine the lower 3_dB frequency, wL.
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Low Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Analysis of the Common-Source Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
Analysis of the Common-Source Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Example
R=100kohm
RS=3.5kohm
IDSS=8mA
RG1=1.4Mohm
RL=10kohm
Am=?
RG2=0.6Mohm
ro=∞
CC1, CC2, CS=?
RD=5kohm
Vp=-2V
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Low Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Analysis of the Common-Emitter Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Analysis of the Common-Emitter Amplifier
Equivalent circuit
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
Analysis of the Common-Emitter Amplifier
The determination of wL
1. Find RC1 seen by CC1
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Analysis of the Common-Emitter Amplifier
2. Find RE” seen by CE
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Dr. MS Özerdem
Analysis of the Common-Emitter Amplifier
3. Find RC2 seen by CC2
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13
IE=1mA → βo=100
Example
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
Find the midband gain Am=?
RL=4kohm
ro=100kohm
rX=50ohm
VCC=12V
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Example (Solution)
Set the capacitors short circuit
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IE=1mA → βo=100
Example
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
CC1=CC2=1µF
CE=10µF
Find
RC1=? RC2=?
RL=4kohm
ro=100kohm
rX=50ohm
RE’=?
fL=?
VCC=12V
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
High Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
15
High Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Let’s use Miller’s Theorem
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Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
First order low pass filter
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Example
R=100kohm
RG1=1.4Mohm
RG2=0.6Mohm
RD=5kohm
RS=3.5kohm
RL=10kohm
VDD=20V
Cgs= Cgd = 1pF
ro=∞
CC1 ,CC2 ,and Cs will
be short circuit for
estimate wH
Vp=-2V
IDSS=8mA
w =?
Microelectronic Circuits - Fifth Edition Sedra/Smith
H
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Dr. MS Özerdem
Example (solution)
Ri
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Verification
Node G
Node D
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
Verification
Microelectronic Circuits - Fifth Edition Sedra/Smith
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IE=1mA → βo=100
Example
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
Cπ=13.9 pF
Cμ=2 pF
a) Use Miller theorem and determine
dominant high fr pole.
RL=4kohm
ro=100kohm
rX=50ohm
b) Obtain transfer function and verify
VCC=12V
that the dominant pole is colse to value
AM= -22.5 V/V
obtained in a) Microelectronic Circuits - FifthCopyright
Edition Sedra/Smith
2004 by Oxford University Press, Inc.
Dr. MS Özerdem
Example (solution)
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Analysis of the Common-Base Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
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Dr. MS Özerdem
Analysis of the Common-Base Amplifier
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Analysis of the Common-Base Amplifier
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Copyright 2004 by Oxford University Press, Inc.
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