### Low Pass Filter/Integrator Circuit Using Op amp 741

Here we are opening the door to a very wide range of useful and exciting application of the opamp. Here we are discussing an opamp RC circuit named as opamp integrator circuit. This circuit simply performs the integration of the input waveform.

The integrator output voltage Vo can be expressed as
where K is the constant of integration.

Opamp integrators are commonly used in analog computers and wave shaping networks. Integrator is also known as first order low pass filter. It permits low frequencies to pass to output.

## Components Required

1. Resistors (10kΩ, 15kΩ)
2. Capacitor (0.01µF x 2)
3. Op amp 741 x 1

## Working of Integrator Circuit

• The gain and linearity of the waveform are two important advantages of opamp integrators over ordinary RC integrators.
• Linearity of the waveform is achieved by the constant current through the capacitor.
• Due to the property of virtual ground, current through the input resistor (R1) is constant owing the constant potential drop across it.
• Current through the input resistor and capacitor is the same due to the high input impedance of Op-Amp.
• At low frequencies of the input voltage, capacitor behaves as an open circuit.
• Op-Amp may saturate at low frequency even for a very low input voltage. This is because the open loop gain is very high.
• Here we uses a very high value feed back resistor Rf to preventing the opamp from saturation.
• When Rf is connected, gain will be reduced considerably at low frequencies.
• At higher frequencies circuit behaves as an ordinary integrator.
• Simply the fact is that at low frequencies, Rf is effective and C is effective at high frequencies in the feedback path.
• If we are feeding a square wave form to the input of Integrator, the output will be Triangular wave.

## Design

Take input frequency = 1KHz
We know the relation, f = 1/(2πRC)
For Convenience let C = 0.01µF. Then R = 15KΩ
Select high value for Rf such that Rf = 10R Ie; Rf = 150KΩ