Q. Draw and explain an RC integrator, with equations

RC Integrator is a low pass RC circuit in which the output is taken across capacitor. The low pass RC circuit gives considerable gain when low frequency signal is applied. It is because of the high reactance offered by the capacitor at low frequencies. The integrator circuit gives the output proportional to the integral of the input signal.

Voltage across the capacitor  Vo = 1/C∫idt

                                                Ie, 1/RC∫Vidt

                                                Vo∝ ∫Vidt

               The gain shown by this circuit decreases considerably with increase in frequency. This gives triangular wave to square wave input, cosine wave to sine wave input and a parabolic wave to a triangular wave input.