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Ideal Op Amp Circuits
The operational ampli
f
er, or op amp as it is commonly called, is a fundamental active element of analog
circuit design. It is most commonly used in ampli
f
er and analog signal processing circuits in the frequency
band from
0
to
100kHz
. Highfrequency op amps are used in applications that require a bandwidth into the
MHz range. The
f
rst op amps were vacuumtube circuits which were developed for use in analog computers.
Modern op amps are fabricated as integrated circuits that bare little resemblance to the early circuits. This
chapter covers some of the basic applications of the op amp. It is treated as an ideal circuit element without
regard to its internal circuitry. Some of the limitations imposed by nonideal characteristics are covered in
the following chapter.
The notation used here is as follows: Total quantities are indicated by lowercase letters with upper
case subscripts, e.g.
v
I
,
i
O
,
r
IN
. Smallsignal quantities are indicated by lowercase letters with lowercase
subscripts, e.g.
v
i
,
i
o
,
r
out
. Transfer function variables and phasors are indicated by upper case letters and
lowercase subscripts, e.g.
V
i
,
I
o
,
Z
in
.
1.1 The Ideal Op Amp
The
ideal op amp
is a three terminal circuit element that is modeled as a voltagecontrolled voltage source.
That is, its output voltage is a gain multiplied by its input voltage. The circuit symbol for the ideal op amp
is given in Fig. 1.1(a). The input voltage is the di
f
erence voltage between the two input terminals. The
output voltage is measured with respect to the circuit ground node. The model equation for the output
voltage is
v
O
=
A
(
v
+
−
v
−
)
(1.1)
where
A
is the voltage gain,
v
+
is the voltage at the noninverting input, and
v
−
is the voltage at the
inverting input. The controlled source model of the ideal op amp is shown in Fig. 1.1(b).
Figure 1.1: (a) Opamp symbol. (b) Controlledsource model.
The terminal characteristics of the ideal op amp satisfy four conditions. These are as follows:
1. The current in each input lead is zero.
2. The output voltage is independent of the output current.
i
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IDEAL OP AMP CIRCUITS
3. The voltage gain
A
is independent of frequency.
4. The voltage gain
A
is very large, approaching in
f
nity in the limit.
The
f
rst condition implies that the resistance seen looking into both input terminals is in
f
nite. The
second implies that the voltage gain is independent of the output current. This is equivalent to the condition
that the output resistance is zero. The third implies that the bandwidth is in
f
nite. The fourth implies that
the di
f
erence voltage between the two input terminals must approach zero if the output voltage is
f
nite.
For it to act as an ampli
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This note was uploaded on 06/13/2009 for the course EE EE 110 taught by Professor Gupta during the Spring '09 term at UCLA.
 Spring '09
 Gupta
 Frequency, Signal Processing

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