Integrator

It accumulates the input quantity over a defined time to produce a representative output.

Mechanical integrators are the oldest type[1] and are still used for metering water flow or electrical power.

[3] Such a simple circuit works because the capacitor's current–voltage relation when written in integral form mathematically states that a capacitor's final voltage equals its initial voltage plus the time integral of its current divided by its capacitance:

More sophisticated current integrator circuits build on this relation, such as the charge amplifier.

Figure 1) is a voltage integrator that works over all frequencies (limited by the op amp's gain–bandwidth product) and provides gain.

Thus, an ideal integrator needs to be modified with additional components to reduce the effect of an error voltage in practice.

Main description at: Op amp integrator § Practical circuit The gain of an integrator at low frequency can be limited to avoid the saturation problem, by shunting the feedback capacitor with a feedback resistor.

This practical integrator acts as a low-pass filter with constant gain in its low frequency pass band.

Mechanisms such as the ball-and-disk integrator were used both for computation in differential analysers and as components of instruments such as naval gun directors, flow totalizers and others.