OPERATIONAL AMPLIFIER AS INTEGRATOR
e i _ ■_ dQ
Rj
d t
Since dQ = e f d e Q
this becom es
Solving this equation for deQ gives the result
de0 = —
ei<**
Rj cf
Integration of both sides gives
Where eiC is the constant of integration
(initial condition) and is the voltage
a cro ss the capacitor Cf at time t = o.
Thus the operational am plifier can integrate.
Figure 9
AMPLIFIER AS DIFFERENTIATOR
It is possible to show, by a sim ilar analysis, that the operational am plifier can be used to
differentiate. The am plifier is used very seldom fo r this purpose, however, since noise in the
input tends to be magnified by differentiation, whereas it tends to cancel out in integration.
Such circu its also tend to be unstable.
In p ractice, the value of the feedback re sisto r Rf, when used, is generally 1 megohm and the
value of the feedback capacitor
C f,
when used, is generally 1 pfd. The value of the input r e
s istor usually va ries from 0.1 megohm to 1.0 megohm, although in certain problem s the values
may be different from these values.
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