The Integrator and how you can use it

The op-amp integrator is a handy circuit that can be used to produce a linear voltage ramp or measure a capacitance value.

In the circuit of Fig. 1, if we put in a pulse of known time and peak value we can compute some things. First the input current is given by

Iin = Vp / R

If we also know the width of our input pulse, say Tc seconds, then we can compute the value of the capacitance by measuring Vo (if Tc is short enough to avoid pushing the op-amp output to its maximum output.) C is determined from the equation:

C = - (Vp / R) * Tc / (-Vo)

An Ocilloscope could be used to observe the input pulse height and time and the output pulse voltage output to determine the value of C.

In some unusual instances we may wish to measure an unknown resistor value such as a very high value. R can be determined from the equation

R = -(Vp / C) * Tc / (-Vo)

Notice that the output ramp is inverted so we have to use the negative signs to have R and/ or C be positive real values. The time to integrate, Tintg in Fig. 1, is determined by the energy contained in the input pulse and the time constant of the circuit RC.