Integrator Amplifier


Working principle

An integrator produces an output voltage, which is proportional to the integral of the input voltage:

Formula derivation

Because of virtual ground and infinite impedance of the op-amp’s input terminals, all of the input current flows through R and C:

An application for this circuit could be integrating water flow and measuring the total quantity of water that has passed by the flowmeter.


Set the AC voltage source’s amplitude and frequency to 0 and the DC voltage source’s value to 1 V. Observe the output. If a fixed voltage is applied to the input of an integrator, the output voltage will be a ramp with a constant slope of the negative input voltage multiplied by a factor of 1/RC.