frequency response elz 303 - elektronik ii · microelectronic circuits - fifth edition sedra/smith...
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Frequency Response
ELZ 303 - Elektronik II
Dr. Mehmet Siraç Özerdem
Elektrik Elektronik Müh. Bölümü
Dicle Üniversitesi
Microelectronic Circuits – Fourth Edition
Adel S. Sedra, Kenneth C. Smith, 1998 Oxford University Press
Copyright 2004 by Oxford University Press, Inc.
s-Domain Analysis
Microelectronic Circuits - Fifth Edition Sedra/Smith
Impedance 1/sC
Impedance sL
Voltage transfer function T(s)=Vo(s)/Vi(s)
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
First Order Function
General form
Low pass - STC network
High pass - STC network
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example (Bode Plot)
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example (Bode Plot)
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
The Amplifier Transfer Function
dc amplifier ac amplifier or
Capacitively coupled amp
BW = wH – wL Since wL « wH BW ≈ wH
Gain-Bandwidth product
GB = AmwH
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
The Gain Function A(s)
General form
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
If a dominant low frequency pole does not exist, an
approximate formula can be derived for wL
Example
at w=wL
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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.
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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 )
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Common source FET amp.
R=100kohm
Rin=420kohm
Cgs=Cgd=1pF
gm=4mA/V
RL=3.33kohm
a) Midband voltage gain
b) fH=?
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Next we outline the use of short-circuit time constant to
determine the lower 3_dB frequency, wL.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Low Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Analysis of the Common-Source Amplifier
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Analysis of the Common-Source AmplifierDr. MS Özerdem
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
R=100kohm
RG1=1.4Mohm
RG2=0.6Mohm
RD=5kohm
RS=3.5kohm
RL=10kohm
ro=∞
Vp=-2V
IDSS=8mA
Am=?
CC1, CC2, CS=?
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Low Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Analysis of the Common-Emitter Amplifier
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Analysis of the Common-Emitter Amplifier
Equivalent circuit
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Analysis of the Common-Emitter Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
The determination of wL
1. Find RC1 seen by CC1
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Analysis of the Common-Emitter Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
2. Find RE” seen by CE
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Analysis of the Common-Emitter Amplifier
Microelectronic Circuits - Fifth Edition Sedra/Smith
3. Find RC2 seen by CC2
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Microelectronic Circuits - Fifth Edition Sedra/Smith
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
RL=4kohm
ro=100kohm
rX=50ohm
VCC=12V
Find the midband gain Am=?
IE=1mA → βo=100
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Example (Solution)
Set the capacitors short circuit
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Microelectronic Circuits - Fifth Edition Sedra/Smith
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
RL=4kohm
ro=100kohm
rX=50ohm
VCC=12V
Find
RC1=? RC2=? RE’=? fL=?
IE=1mA → βo=100
CC1=CC2=1µF CE=10µF
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
High Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Dr. MS Özerdem
16
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
High Frequency Response of
the Common-Source and Common-Emitter Amplifiers
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Let’s use Miller’s Theorem
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
First order low pass filter
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
ro=∞
Vp=-2V
IDSS=8mA
wH = ?
Cgs= Cgd = 1pF
CC1 ,CC2 ,and Cs will
be short circuit for
estimate wH
R=100kohm
RG1=1.4Mohm
RG2=0.6Mohm
RD=5kohm
RS=3.5kohm
RL=10kohm
VDD=20V
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example (solution)Ri
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Verification
Node G
Node D
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Verification Dr. MS Özerdem
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
Microelectronic Circuits - Fifth Edition Sedra/Smith
R=4kohm
R1=8kohm
R2=4kohm
RC=6kohm
RE=3.3kohm
RL=4kohm
ro=100kohm
rX=50ohm
VCC=12V
AM= -22.5 V/V
a) Use Miller theorem and determine
dominant high fr pole.
b) Obtain transfer function and verify
that the dominant pole is colse to value
obtained in a)
IE=1mA → βo=100
Cπ=13.9 pF Cμ=2 pF
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/SmithMicroelectronic Circuits - Fifth Edition Sedra/Smith
Example (solution)Dr. MS Özerdem
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Analysis of the Common-Base Amplifier
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Analysis of the Common-Base AmplifierDr. MS Özerdem