Integrator

The circuit configuration shown on Picture 1 is called integrator. We can assume that the input voltage signal is an arbitrary function of time. Also, the current that flows through the capacitor is the same current that flows through the input of this circuit In = Vi/R1. If we use the capacitor law, and express the output voltage using this relation, we will have the relations which are shown on Picture 2.

Picture 1: Integrator

Picture 2: Capacitor law and output voltage of the integrator


So, according to the relations shown on Picture 2, the output voltage of this circuit is the integrated input signal. As an example, on Picture 3 are shown the wave forms of the input and output signals of this circuit. The input signal is sinusoidal with amplitude of 100 mV at frequency of 500 Hz and the output has also sinusoidal form but it's actually a integral of the input function. The blue line plot on the Picture 3 is the input signal wave form and the green line plot is the output signal wave form.

Picture 3: Input and Output voltage wave forms of the integrator