The feedback configuration shown in Figure 1 is the most common op-amp
circuit for obtaining what is known as an inverting
amplifier.
R
F
R
out
R
out
−G
R
F
1
R
out
+1
R
in
+1
R
L
1R+1
R
in
+1
R
F
−1
R
F
v
out
=1R
v
in
R
F
R
out
R
out
G
R
F
1
R
out
1
R
in
1
R
L
1
R
1
R
in
1
R
F
1
R
F
v
out
1
R
v
in
(1)
provides the exact input-output relationship. In choosing
element values with respect to op-amp characteristics, we can
simplify the expression dramatically.
- Make the load resistance
R
L
R
L
much larger than
R
out
R
out
.
This situation drops the term
1
R
L
1
R
L
from the second factor of Equation 1.
-
Make the resistor
R
R
smaller than
R
in
R
in
, which means that the
1
R
in
1
R
in
term in the third factor is negligible.
With these two design criteria, the expression (
Equation 1) becomes
R
F
+
R
out
R
out
−G
R
F
1R+1
R
F
−1
R
F
v
out
=1R
v
out
R
F
R
out
R
out
G
R
F
1
R
1
R
F
1
R
F
v
out
1
R
v
out
(2)
.
Because the gain is large and the resistance
R
out
R
out
is small, the first term becomes
-1G
1
G
, leaving us with
-1G1R+1
R
F
−1
R
F
v
out
=1R
v
in
1
G
1
R
1
R
F
1
R
F
v
out
1
R
v
in
(3)
- If we select the values of
R
F
R
F
and
R
R
so that
R
F
≪GR
≪
R
F
G
R
, this factor will no longer depend on the op-amp's inherent
gain, and it will equal
-1
R
F
1
R
F
.
Under these conditions, we obtain the classic input-output
relationship for the op-amp-based inverting amplifier.
v
out
=-
R
F
R
v
in
v
out
R
F
R
v
in
(4)
Consequently, the gain provided by our circuit is entirely
determined by our choice of the feedback resistor
R
F
R
F
and the input resistor
R R. It can even be less than one, but
cannot exceed the op-amp's inherent gain and should not produce
such large outputs that distortion results (remember the power
supply!). Interestingly, note that this relationship does not
depend on the load resistance. This effect occurs because we use
load resistances large compared to the op-amp's output
resistance. Thus observation means that, if careful, we can
place op-amp circuits in cascade,
without
incurring the effect of succeeding circuits changing
the behavior (transfer function) of previous ones; see
this analog
signal processing problem.
