A circuit that performs the mathematical function of integrating an input voltage with respect to time. At any given time, the voltage present at the input determines how quickly and in what direction the output voltage ramps up and down. As an example, consider an integrator powered up with a zero voltage present at the input. As long as the input is zero, the output does not change. When a positive voltage appears at the input, the output voltage begans increasing. The rate at which the output ramps up depends on how high the input voltage is. If a negative voltage is then applied at the input, the output will began deccreasing, at a rate depending on the negative voltage at the input. If at any point the input voltage goes back to zero, the output voltage stops and holds at whatever voltage it is at.
The output voltage of any real integrator cannot rise or fall indefinitely; it is limited by the circuit's supply voltages and other circuit considerations. If a constant voltage persists at the input, the output will eventuallly stop changing when it reaches the circuit's limits; this is analagous to clipping in an amplifier. Some integrator circuits have a manual reset button, or reset trigger input, that forces the output voltage back to zero.
The core circuit of a conventional sawtooth core VCO is an integrator. The output voltage rises at a rate proportional to the frequency control voltage input, until it reaches the reset voltage, at which time a comparator circuit forces it back to the starting voltage. The higher the input voltage, the quicker the rise rate, which controls the cycle time and hence the frequency. Integrators seldom appear as stand-alone circuits in synths, aside from some of the more esoteric modular synthesizer lines. An exception was the Korg MS-50 expander, which included an integrator as a patchable circuit element.
The opposite of an integrator is a differentiator.