A practical integrator. Note that the resistor in parallel with the feedback capacitor provides a path for the capacitor to discharge the DC voltage. Usually, the time constant RF CF is chosen to be long enough not to interfere with the integration.
a. If RS = 10 k2, RF = 2 M2, CF = 0.008 μF, and vS (t) = 10 V + sin(2,000πt) V, find vout(t), using phasor analysis.
b. Repeat part a if RF = 200 k2, and if RF = 20 k2.
c. Compare the time constants RF CF with the period of the waveform for parts (a) and (b). What can you say about the time constant and the ability of the circuit to integrate?