RC-Differentiator

OBJECTIVE:

To study the characteristic of a capacitor as a differentiator.

THOERY:

A resistor-capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The four most common RC filters are the high-pass filter, low-pass filter, band-pass filter, and band-stop filter. These circuits can also be used as a differentiator or an integrator.

RC circuit as a Differentiator

Figure 1.shows the circuit for a capacitor as a differentiator. Consider an AC source with voltage vin(t), input to an RC series circuit. The output across the resistor is to be measured at low frequency i.e.



The capacitor has time to charge up until its voltage is almost equal to the source's voltage. Considering the expression for I (current), when



so





Now,





which is a differentiator across the resistor.

Figure1: RC circuit for capacitor as a differentiator experiment

Differential Waveforms:

If we apply a constantly changing signal such as a Square-wave, Triangular or Sine-wave type signal to the input of a differentiator amplifier circuit the resultant output signal will be changed and whose final shape is dependent upon the RC time constant of the Resistor/Capacitor combination.

Figure2: (a)	Figure2: (b)

Figure2: (a) The input and output of a differentiator circuit (b) The Differentiated output waveforms are shown with red color and the input waveforms are shown with blue color (superimposed i/p and o/p)