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Operational Amplifiers and Active Filters
An operational amplifier (op amp) is an integrated circuit
comprised of transistors and resistors that can be used to
increase the strength (amplify) or filter an input signal.
The symbol used for an op amp in the schematic
diagram of an electronic circuit is as follows:
The equivalent electrical circuit for the op amp is given by:
R
in
and
R
out
are, respectively, the op amp
’
s
input
and
output resistances
, and
A
is the
open-loop gain
.
All voltages are referenced to the ground node.
Output signal
V
out
V
–
R
in
V
+
+
–
A(
V
+
–
V
–
)
R
out
V
out
Signal inputs
:
V
–
(inverting input)
V
+
(non-inverting input)
voltage-controlled
voltage source

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*Sign up* Now, consider what is probably the most basic
connection of the op amp, the
inverting amplifier
.
We want to obtain
V
out
in terms of
V
in
. Observing
that there are only two unknown node voltages,
V
out
and
V
–
, we can write a pair of node equations
to solve the problem:
V
–
R
in
V
+
= 0
+
–
A(
V
+
–
V
–
)
R
out
V
out
V
–
V
+
= 0
V
out
R
1
R
2
V
in
R
1
V
in
R
2
R
load
R
load

At
V
–
:
V
!
!
V

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