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Copyright 2004 by Oxford University Press, Inc.
Operational Amplifiers
ELZ 206 - Elektronik I
Dr. Mehmet Siraç Özerdem
Department of Electrical and Electronics Engineering
Dicle University
Microelectronic Circuits – Fourth Edition
Adel S. Sedra, Kenneth C. Smith, 1998 Oxford University Press
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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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
The op amp shown connected to dc power supplies.
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Equivalent circuit of the ideal op amp.
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
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
The inverting closed-loop configuration.
Analysis of inverting configuration
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Analysis of inverting configuration
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Analysis of inverting configuration
Dr. Mehmet Siraç Özerdem
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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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
op amp : ideal
a) (vo / vI) = ?
b) (vo / vI) = 100 and Ri = 1Mohms.
Find the other values of components.
E
E
E
E
E
EE
E
E
E
E
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.ExampleMicroelectronic Circuits - Fifth Edition Sedra/Smith
Example-Solution
a)
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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.
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
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 ?)
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Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.ExampleMicroelectronic Circuits - Fifth Edition Sedra/Smith
Example-Solution 2
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
Other Application of the Inverting Configuration
2. The inverting integrator
Copyright 2004 by Oxford University Press, Inc.Example
2. The inverting integrator
Frequency response
of the integrator
Z1=R Z2=1/sC
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Copyright 2004 by Oxford University Press, Inc.
The Miller or inverting integrator
Comparision
Example
A low-pass STC circuit
Problem
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
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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Copyright 2004 by Oxford University Press, Inc.
Example
E E
Microelectronic Circuits - Fifth Edition Sedra/Smith
Example
a) vo(t) = ?
b) If the integrator capacitor is shunted
by RF=1MΩ resistance, vo(t) = ?
Example
R=10kΩ
C=10nF
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.Example
Example-Solution
Input pulse
Output linear ramp of
ideal integrator with
time constant of 0.1 ms.
(a)
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Copyright 2004 by Oxford University Press, Inc.Example
Example-Solution
(b)
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Other Application of the Inverting Configuration
3. The Op-amp differentiator
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Copyright 2004 by Oxford University Press, Inc.
3. The Op-amp differentiator
Frequency response of
a differentiator with a
time-constant CR.
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Other Application of the Inverting Configuration
4. The Weighted Summer
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Copyright 2004 by Oxford University Press, Inc.Microelectronic Circuits - Fifth Edition Sedra/Smith
The Noninverting Configuration
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Analysis of the noninverting circuit.
The Noninverting Configuration
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The unity-gain buffer or follower amplifier.
The Voltage Follower
Its equivalent circuit model.
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Example
vo(v1, v2) = ?
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A Difference Amplifier (Example)
vo(vI1, vI2) = ?
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Application of superposition to the analysis of the circuit
A Difference Amplifier (Example - Solution)
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Input resistance of the difference amplifier for the case
R3 = R1 and R4 = R2.
A Difference Amplifier (Example - Solution)
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
Representing the input signals to a differential amplifier in
terms of their differential and common-mode components.
Example
E
E
A Difference Amplifier (Example - Solution)
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An Instrumentation Amplifier (Example)
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vo(vI1, vI2) = ?
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
A Difference Amplifier (Example - Solution)
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