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lecture22-150128
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Lecture 22 – Compensation of Op Amps (6/24/14) Page 22-1
CMOS Analog Circuit Design © P.E. Allen - 2016
LECTURE 22 – INTRODUCTION TO OP AMPS
LECTURE OUTLINE
Outline
• Op Amps
• Categorization of Op Amps
• Compensation of Op Amps
• Miller Compensation
• Other Forms of Compensation
• Op Amp Slew Rate
• Summary
CMOS Analog Circuit Design, 3
rd
Edition Reference
Pages 261-286
Lecture 22 – Compensation of Op Amps (6/24/14) Page 22-2
CMOS Analog Circuit Design © P.E. Allen - 2016
OP AMPS
What is an Op Amp?
The op amp (operational amplifier) is a high gain, dc coupled amplifier designed to
be used with negative feedback to precisely define a closed loop transfer function.
The basic requirements for an op amp:
• Sufficiently large gain (the accuracy of the signal processing determines this)
• Differential inputs
• Frequency characteristics that permit stable operation when negative feedback is
applied
Other requirements:
• High input impedance
• Low output impedance
• High speed/frequency
Lecture 22 – Compensation of Op Amps (6/24/14) Page 22-3
CMOS Analog Circuit Design © P.E. Allen - 2016
Why Op Amps?
The op amp is designed to be used with single-loop, negative feedback to accomplish
precision signal processing as illustrated below.
The voltage gain,
V
out
(s)
V
in
(s)
, can be shown to be equal to,
V
out
(s)
V
in
(s)
=
A
v
(s)
1+A
v
(s)F(s)
If the product of A
v
(s)F(s) is much greater than 1, then the voltage gain becomes,
V
out
(s)
V
in
(s)
≈
1
F(s)
The precision of the voltage gain is defined by F(s).
060625-01
+
-
S
F(s)
A(s)
Op Amp
Feedback Network
V
in
(s)
V
out
(s)
A
v
(s)
V
out
(s)
V
in
(s)
+
-
F(s)
V
f
(s)
V
f
(s)
Single-Loop Negative Feedback Network
Op Amp Implementation of a Single-Loop
Negative Feedback Network
Lecture 22 – Compensation of Op Amps (6/24/14) Page 22-4
CMOS Analog Circuit Design © P.E. Allen - 2016
OP AMP CHARACTERIZATION
Linear and Static Characterization of the CMOS Op Amp
A model for a nonideal op amp that includes some of the linear, static nonidealities:
where
R
id
= differential input resistance
C
id
= differential input capacitance
R
icm
= common mode input resistance
R
icm
= common mode input capacitance
V
OS
= input-offset voltage
CMRR = common-mode rejection ratio (when v
1
=v
2
an output results)
e
2
n
= voltage-noise spectral density (mean-square volts/Hertz)
Lecture 22 – Compensation of Op Amps (6/24/14) Page 22-5
CMOS Analog Circuit Design © P.E. Allen - 2016
Linear and Dynamic Characteristics of the Op Amp
Differential and common-mode frequency response:
V
out
(s) = A
v
(s)[V
1
(s) - V
2
(s)] ± A
c
(s)
V
1
(s)+V
2
(s)
2
Differential-frequency response:
A
v
(s) =
A
v0
s
p
1
- 1
s
p
2
- 1
s
p
3
- 1 ···
=
A
v0
p
1
p
2
p
3
···
(s -p
1
)(s -p
2
)(s -p
3
)···
where p
1
, p
2
, p
3
,··· are the poles of the differential-frequency response (ignoring zeros).
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