INTERGRATOR
The operational amplifier integrator is an electronic integration circuit. Based around the
operational amplifier (op-amp), it performs the mathematical operation of integration with respect
to time; that is, its output voltage is proportional to the input voltage integrated over time.
As before, the negative feedback of the op-amp ensures that the inverting input will be held
at 0 volts (the virtual ground). If the input voltage is exactly 0 volts, there will be no current through
the resistor, therefore no charging of the capacitor, and therefore the output voltage will not change.
We cannot guarantee what voltage will be at the output with respect to ground in this condition, but
we can say that the output voltage will be constant.
However, if we apply a constant, positive voltage to the input, the op-amp output will fall
negative at a linear rate, in an attempt to produce the changing voltage across the capacitor
necessary to maintain the current established by the voltage difference across the resistor.
Conversely, a constant, negative voltage at the input results in a linear, rising (positive) voltage at
the output. The output voltage rate-of-change will be proportional to the value of the input voltage.
The formula for determining voltage output for the integrator is as follows:
