Operational Amplifiers
ELZ 206 - Elektronik I
Microelectronic Circuits – Fourth Edition
Adel S. Sedra, Kenneth C. Smith, 1998 Oxford University Press
Dr. Mehmet Siraç Özerdem
Department of Electrical and Electronics Engineering
Dicle University
Copyright
2004 by Oxford University Press, Inc.
One of the reasons for the popularity of the Op-amp is
its versatility.
Circuit symbol for the op amp.
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
The op amp shown connected to dc power supplies.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
The ideal op-amp
The gain is ideally infinite
(Open loop configuration)
We will use other
components to apply
feedback to close the
around the op-amp
Equivalent circuit of the ideal op amp.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
Analysis of inverting configuration
The inverting closed-loop configuration.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
Analysis of inverting configuration
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
Analysis of inverting configuration
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
Analysis of the inverting configuration taking into
account the finite open-loop gain of the op amp.
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
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Example
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op amp : ideal
a) (vo / vI) = ?
b) (vo / vI) = 100 and Ri = 1Mohms.
Find the other values of components.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
Example-Solution
a)
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Example
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Dr. Mehmet Siraç Özerdem
Other Application of the Inverting Configuration
1. The inverting configuration with general impedances Z1
and Z2
2. The inverting integrator
3. The Op-amp differentiator
4. The weighted summer
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
Other Application of the Inverting Configuration
1. The inverting configuration with general impedances
Z1 and Z2
The inverting configuration with general impedances in
the feedback and the feed-in paths.
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
2
Example
a) (Vo(s) / Vi(s) )= ?
Transfer function
b) Show that the transfer function is
that of a low-pass STC circuit.
c) K=? (DC gain) and
3-dB frequency (wo) = ?
d) K=40 dB fo=1kHz Ri=1kΩ
Design the circuit (R1, R2, C2 ?)
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright
2004 by Oxford University Press, Inc.
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Example-Solution
Microelectronic Circuits - Fifth Edition
Sedra/Smith
Copyright 2004 by Oxford University Press, Inc.
Example
7
Other Application of the Inverting Configuration
2. The inverting integrator
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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2004 by Oxford University Press, Inc.
2. The inverting integrator
Z1=R
Z2=1/sC
Frequency response
of the integrator
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Example
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Dr. Mehmet Siraç Özerdem
Comparision
A low-pass STC circuit
The Miller or inverting integrator
Press, Inc.
Example2004 by Oxford University
Problem
Copyright
To solve the problem
The Miller integrator with a large resistance RF connected in
parallel with C in order to provide negative feedback and
hence finite gain at dc.
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
ExampleExample
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R=10kΩ
C=10nF
a) vo(t) = ?
b) If the integrator capacitor is shunted
by RF=1MΩ resistance, vo(t) = ?
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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Example
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Example-Solution
(a)
Input pulse
Output linear ramp of
ideal integrator with
time constant of 0.1 ms.
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Example
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Dr. Mehmet Siraç Özerdem
Example-Solution
(b)
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Example
Other Application of the Inverting Configuration
3. The Op-amp differentiator
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Dr. Mehmet Siraç Özerdem
3. The Op-amp differentiator
Frequency response of
a differentiator with a
time-constant CR.
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2004 by Oxford University Press, Inc.
Other Application of the Inverting Configuration
4. The Weighted Summer
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
The Noninverting Configuration
Microelectronic Circuits - Fifth Edition
Sedra/Smith
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2004 by Oxford University Press, Inc.
The Noninverting Configuration
Analysis of the noninverting circuit.
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
The Voltage Follower
The unity-gain buffer or follower amplifier.
Its equivalent circuit model.
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2004 by Oxford University Press, Inc.
Example
vo(v1, v2) = ?
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
A Difference Amplifier (Example)
vo(vI1, vI2) = ?
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2004 by Oxford University Press, Inc.
A Difference Amplifier (Example - Solution)
Application of superposition to the analysis of the circuit
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
A Difference Amplifier (Example - Solution)
Input resistance of the difference amplifier for the case
R3 = R1 and R4 = R2.
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2004 by Oxford University Press, Inc.
A Difference Amplifier (Example - Solution)
Example
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Representing the input signals to a differential amplifier in
terms of their differential and common-mode components.
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2004 by Oxford University Press, Inc.
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Dr. Mehmet Siraç Özerdem
An Instrumentation Amplifier (Example)
vo(vI1, vI2) = ?
E
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2004 by Oxford University Press, Inc.
A Difference Amplifier (Example - Solution)
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2004 by Oxford University Press, Inc.
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