Inverting integrator amplifier realized with op-amp is given in figure bellow.
Simulate op-amp inverting integrator amplifier.
Op-amp voltage integrator is the circuit that integrates input voltage over time. Input impedance is equal to R1, and feedback is capacitive (capacitor C).
Output voltage can be calculated as function of input voltage by equaling currents. V– is on the virtual ground, so input current is
The same current flows into capacitor C, in the electrode opposite from circuit output, so output voltage, after time of integration T, is:
In here, VIN(t) is input voltage as function of time, T is the time of integration, and VOUT(0) is output voltage in starting moment of integration.
Op-amp voltage integrator is close to ideal integrator, since it can integrate both smooth and pulse inputs close to step function. It is also quite immune to surrounding noise. It is opposite to op-amp voltage differentiator that produces differentiated output for smooth input, but canâ€™t differentiate input pulses.