R-C or RC circuit integrator is kind of first order circuits. First order circuit means that it’s behavior is described with differential equation of first order. R-C circuit integrator is actually just series R-C circuit. RC circuit integrator looks like it is shown in figure bellow.
In the time instant when switch is just closed, current through circuit is maximal and equal to
This current is charging up capacitor, and capacitor voltage is proportional to charging time and current intensity, and reversely proportional to capacitance.
In the next time instant, capacitor is charged up a bit, and current drops exponentially. As the time runs, current is dropping more and more, but capacitor is charged more and more with slower pace. If input is steady state DC voltage, after time that is equal to time constant of Ï„=RC, capacitor voltage i.e. output voltage is raised to roughly 63% of VCC. Series R-C circuit is not perfect integrator, but it has better performance with higher time constant Ï„ and with higher the input signal frequency. So it is desirable to increase R, C and f as well. This can be easily checked on RC integrator online simulation. If R, C and f are relatively small, edge is curved with typical “exponential look”.
This is serious disadvantage of R-C circuit integrator comparing with op-amp integrator. As R, C and f are increased, edge takes more linear shape. Advantages are same phase of input and output voltage and fact that R-C circuit integrator has no voltage offset to be integrated.