So, far till now we have only seen resistor being used in input and feedback, now we are going to use a capacitor in Integrator using operational amplifier, this capacitor forms an RC Circuit with an input resistor. A large value of the resistor is required, because the gain should be limited. The circuit for integrator using operational amplifier is as shown below

**INTEGRATOR USING OPERATIONAL AMPLIFIER**

From the concept of virtual ground circuit, the equation for the voltage between input and output, can be derived in terms of current I, from input to output

The impedance of the circuit can be written as 1/RC, hence we calculate the output voltage to be

From this equation, it is clearly evident that the voltage at the output is the integral of input voltage with reverse polarity and multiplier of 1/RC.

With this ability, the integrator allows the analog computer to solve differential equations. As we all know integration is the addition, adding the area under a waveform or curve over a particular period of time.

If fixed voltage is applied at the input, the output voltage grows over a period of time, and provides what we call a ramp voltage, This is opposite in polarity to the applied input and multiplied by a factor of 1/RC.

You can even use many inputs, with various voltages.

### Applications of Integrator using Op-Amp:

- With this circuit, analog computer will be able to solve differential equations
- Feeding of square wave to the input will result in a triangular wave at the output.
- If the varying frequency sine wave is fed to the output, the integrator acts as low pass filter