An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output.
Integration is an important part of many engineering and scientific applications. Mechanical integrators are the oldest type and are still used for metering water flow or electrical power. Electronic analogue integrators are the basis of analog computers and charge amplifiers. Integration can also be performed by algorithms in digital computers.
An electronic integrator is a form of first-order low-pass filter, which can be performed in the continuous-time (analog) domain or approximated (simulated) in the discrete-time (digital) domain. An integrator will have a low pass filtering effect but when given an offset it will accumulate a value building it until it reaches a limit of the system or overflows.
A current integrator is an electronic device performing a time integration of an electric current, thus measuring a total electric charge. A capacitor's current–voltage relation makes it a very simple current integrator:
More sophisticated current integrator circuits build on this relation, such as the charge amplifier. A current integrator is also used to measure the electric charge on a Faraday cup in a residual gas analyzer to measure partial pressures of gasses in a vacuum. Another application of current integration is in ion beam deposition, where the measured charge directly corresponds to the number of ions deposited on a substrate, assuming the charge state of the ions is known. The two current-carrying electrical leads must to be connected to the ion source and the substrate, closing the electric circuit which in part is given by the ion beam.
A voltage integrator is an electronic device performing a time integration of an electric voltage, thus measuring the total volt-second product. A simple resistor–capacitor circuit acts as an integrator at high frequencies above its cutoff frequency.
See also Integrator at op amp applications and op amp integrator
An ideal op amp integrator (e.g. 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. This modified integrator is referred as practical integrator.
Main description at:
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. It only performs integration in high frequencies, not in low frequencies, so bandwidth for integrating is limited.
See main article: Numerical integration.
See main article: Differential analyser.
Mechanical integrators were key elements in the mechanical differential analyser, used to solve practical physical problems. Mechanical integration mechanisms were also used in control systems such as regulating flows or temperature in industrial processes. 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. A planimeter is a mechanical device used for calculating the definite integral of a curve given in graphical form, or more generally finding the area of a closed curve. An integraph is used to plot the indefinite integral of a function given in graphical form.