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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.
2
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
3
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
4
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.
5
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)
6
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.
7
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 ?)
2
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.ExampleMicroelectronic Circuits - Fifth Edition Sedra/Smith
Example-Solution 2
8
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
9
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.
10
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)
11
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
12
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
13
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
14
Copyright 2004 by Oxford University Press, Inc.
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) = ?
15
Copyright 2004 by Oxford University Press, Inc.
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)
16
Copyright 2004 by Oxford University Press, Inc.
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)
17
Copyright 2004 by Oxford University Press, Inc.
An Instrumentation Amplifier (Example)
E
vo(vI1, vI2) = ?
Dr. Mehmet Siraç Özerdem
Copyright 2004 by Oxford University Press, Inc.
A Difference Amplifier (Example - Solution)