Suppose, for example, a ratio of 3.7 is desired. If
ji
is made equal to 0.37 and R f/R f = 10
(Rf = 1 megohm and Rf = 100 Kfi), then e Q = -3.7 ej. Generally this method is to be p referred
over that shown in Figure 3.
In actual p ractice, the ratio R f/R f is generally greater than unity, since the am plifiers tend to
becom e unstable for values less than unity. Also the ratio R f/R f is 100 or less, as values
greater than 100 introduce inaccuracies in the solution of the problem .
If, instead of the one input resistor shown in Figure 2, two or more r e sisto rs are used as shown
in Figure 5, the operational am plifier becom es an adder.
e°
— VW W —
e , o - J W M r -
e , * - J
WvW-
- M / W -
e0
i
Figure 5
AMPLIFIER AS ADDER
Again making use of eg
=
0, the sum of the currents in the input re sisto rs equals the current
through the feedback resistor.
T h U S
i , + '
2
+ i
3
= ' f
But, since
i = _ | r
it follow s that
— L .
e 2
.
e 3
—
D
+ R* + R3
L1
" 2
" 3
- 'f
Multiplication of both sides of the equation by Rf gives the result
S t + . . * L = -
1
R ,
2
R
2
+ °
3
R
3
which can be written
e 0 —
( K , e , + K 2 e 2 +
k
e , )
R f
K2=R-
where
= R j _
[1
2
R2
The operational am plifier can thus be used to add and at the same time multiply any of its in
puts by constants. Any number of inputs can be used as long as the output voltage does not
exceed the nominal range of the am plifier.
R f
K
3
= R
3
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