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An input of plus one volt results in an output of minus ten volts.
This operational
amplifier has a gain of ten.
The multiplying constant can be made smaller than one
by using a 10K feedback resistor with a lOOK input resistor.
e
o
10K
lOOK
e.
~n
-0. le .
~n
An input of minus ten volts produces an output of plus one volt.
~.
Surrnnation
When multiple input resistors are used with a feedback resistor R
f
, the basic re-
lationship is extended to:
The circuit can be used to algebraically sum an indefinite number of inputs; further-
more, each input may be multiplied by an arbitrary constant.
~.
Integration with Respect to Time
When the feedback element Zf is a capacitor rather than a resistor, the operational
amplifier becomes an integrator. If Zf is a capacitor having an operational imped-
ance l/pC and Z.
is a resistor, the Easic operational amplifier relationship,
~n
Equation 2-1, becomes:
E.
~n
e
- -
o
pRC
1
t
- RC
So
e.
dt
~n
An indefinite number of inputs may be applied to produce the time-integral of the
sum of the input voltages.
f.
Other Mathematical Operations
As previously indicated, the operational amplifier has uses other than those de-
scribed above.
Complicated transfer functions can be simulated by using series
and parallel RC networks for the feedback and input impedance.
The circuit per-
formance is still governed by the basic relationship of Equation 2-1.
For the
general case where three-terminal networks are used, the short-circuit transfer
impedance of Zf and Z.
must be used.
The input and feedback elements need not be
linear; therefore,
al~gst
any non-linear characteristics can be approximated.
The
amplifier can also be used in conjunction with diodes and resistors to simulate the
non-linear operations of limiting, dead-zone generation, X2, Log X, etc.
21
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