C H A P T E R 02
Operational Amplifiers
(Op-amp) Dual-in-line
package
(DIP)
Surface mount:
small-outline
integrated circuit
(SOIC) package
Microelectronic Circuits, Sixth Edition
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The Op-amp
Requires DC power to run,
amplifies ac signal
Figure 2.1 Circuit symbol
for the op amp.
Figure 2.2 The op amp shown
connected to dc power supplies
(dual or single supply).
Microelectronic Circuits, Sixth Edition
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The Ideal Op-amp
1. Infinite input impedance
2. Zero output impedance
3. Zero common-mode gain
(i.e., infinite commonmode rejection)
4. Infinite loop-gain A (A=∞)
5. Infinite bandwidth
Microelectronic Circuits, Sixth Edition
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Differential and Common-mode signals
vId=v2-v1
vIcm=1/2(v1+v2)
Microelectronic Circuits, Sixth Edition
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Model of internal of an op-amp by circuit
Microelectronic Circuits, Sixth Edition
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The inverting closed-loop configuration.
Current at a node
(Iin=Iout)
Microelectronic Circuits, Sixth Edition
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Analyzing an inverting amplifier
Rin=R1
Rout=0
Gain 
v0
R
 2
vI
R1
Figure 2.6 Analysis of the inverting configuration. The
circled numbers indicate the order of the analysis steps.
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
Inverting Configuration, taking gain A into account
R2
v0
R1
G

R
vI
1  (1  2 ) / A
R1

Figure 2.7 Analysis of the inverting configuration taking
into account the finite open-loop gain of the op-amp.
Microelectronic Circuits, Sixth Edition
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Copyright © 2010 by Oxford University Press, Inc.
vO
R
R
R
  2 (1  4  4 )
vI
R1
R2 R3
Example 2.2. The circled numbers indicate the sequence of the
steps in the analysis.
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
Figure 2.9 A current amplifier based on the circuit of Fig. 2.8. The amplifier
delivers its output current to R4. It has a current gain of (1 + R2 /R3), a zero
input resistance, and an infinite output resistance. The load (R4), however,
must be floating (i.e., neither of its two terminals can be connected to
ground).
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
A weighted summer (using
superposition technique).
A weighted
capable of implementing
summing
of both
signs.
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Copyrightcoefficients
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Press, Inc.
Microelectronic summer
Circuits, Sixth Edition
Figure 2.13 Analysis of the non-inverting circuit. The sequence of the
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Copyright
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Oxford University Press, Inc.
Microelectronic Circuits,
Sixth
steps
inEdition
the analysis is indicated
by the
circled
numbers.
Non-Inverting Configuration
1. Effect of finite loop gain
R2
)
V0
R1

G
R
Vi
1 ( 2 )
R1
1
A
2. Input/output impedance
- Infinite input
- Zero output
1 (
R2
)
R1
% _ gain _ error  
x100
R2
A 1 ( )
R1
1 (
3. Voltage follower
Microelectronic Circuits, Sixth Edition
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Single Op-amp Difference Amplifiers
vO 2
R4
R2
R2
 vI 2
(1  ) 
vI 2
R3  R4
R1
R1
Given
( R 4 / R3)  ( R 2 / R1)
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
Instrumentation Amplifier
Figure 2.20 A popular circuit for an instrumentation amplifier. (a) Initial
approach to the circuit
Microelectronic Circuits, Sixth Edition
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Copyright © 2010 by Oxford University Press, Inc.
Instrumentation Amplifier
(buy, don’t build)
AD623ARZ
Figure 2.20 (c) Analysis of the circuit assuming ideal op amps.
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
Figure 2.22 The inverting configuration with
general impedances in the feedback and the
feed-in paths.
Microelectronic Circuits, Sixth Edition
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Copyright © 2010 by Oxford University Press, Inc.
Integrators
vC (t )  VC 
Microelectronic Circuits, Sixth Edition
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1
C


0
i1 (t ) dt
Copyright © 2010 by Oxford University Press, Inc.
Differentiator
Microelectronic Circuits, Sixth Edition
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Figure 2.39 Open-loop gain of a typical general-purpose internally
compensated op amp.
Microelectronic Circuits, Sixth Edition
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Copyright © 2010 by Oxford University Press, Inc.
Figure 2.40 Frequency response of a closed-loop amplifier with a nominal
gain of +10 V/V.
Microelectronic Circuits, Sixth Edition
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Copyright © 2010 by Oxford University Press, Inc.
Output Voltage Saturation
Figure 2.42 (a) A non-inverting amplifier with a nominal gain of 10 V/V
designed using an op amp that saturates at ±13-V output voltage and has ±20mA output current limits.
(b) When the input sine wave has a peak of 1.5 V, the output is clipped off at
±13 V.
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
Slew Rate
Microelectronic Circuits, Sixth Edition
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Figure 2.44 Effect of slew-rate limiting on output
sinusoidal waveforms.
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.
EE 221 Lab
(Check EE 221 class website)
Microelectronic Circuits, Sixth Edition
Sedra/Smith
Copyright © 2010 by Oxford University Press, Inc.