RC-Integrator

OBJECTIVE:

To study the characteristic of a capacitor as an Integrator or RC integrator.

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.

Figure 1.shows the circuit for a capacitor as an integrator. Consider an AC source with voltage vin(t), input to an RC series circuit. Consider the output across the capacitor at high frequency i.e.

-----------------------(1)

This means that the capacitor has insufficient time to charge up and so its voltage is very small. Thus the input voltage approximately equals the voltage across the resistor.
Consider the expression for I given above:



And from eq. 1



So



Now,



So



This is an integrator across the capacitor.


Figure1: RC circuit for capacitor as an integrator experiment


Fig 2. Input and output of an integrator circuit.