In use, re sisto rs and capacitors are connected as input and feedback elem ents in such a way as
to perform various mathematical operations. For use as a multiplier, r e sis to rs are used as
input and feedback elem ents, as shown in Figure 2.
Rf
AMPLIFIER AS MULTIPLIER AND INVERTER
In this Figure, e i represents the input voltage, eg the grid voltage, e0 the output voltage, Ri
the input re sisto r and Rf the feedback re sisto r.
The gain of an am plifier is given by
On solving for eg, the expression
e
= — .
is obtained.
9
A
From this it can be seen that e g approaches z ero as A approaches infinity. In practice, A is
made large with respect to eQ by using high gain am plifiers so that eg becom es very small, and
fo r practical purposes eg can be considered to be at ground potential.
Since the input to the am plifier is the grid of a tube, the current through the am plifier from the
input can be considered to be zero, with the result that the current if through the re sisto r Rf is,
fo r all p ractical purposes, equal to the current if through the resisto r Rf, with the result that
* l ~
* o
.
e
-jp --—jj—
since
I
—
(The sym bol = means
'
*
"approxim ately equal to")
2s Rf
which becom es
e o — —
# s
* i
♦For a m ore rigorous approach, see Korn and Korn, ELECTRONIC ANALOG COMPUTERS
(M cG raw-H ill Book Company, In c ., New York, 1956), Second Edition, Page 12.
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