Integrator

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An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.

The integration function is often part of engineering and scientific calculations. Mechanical integrators are used in such applications as metering of water flow or electric power. Electronic analog integrators were the basis of analog computers.

Integrator in signal processing

See also Integrator at op amp applications

Electronic devices have been constructed to perform integration (usually with respect to time) of signals. This operation 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 voltage integrator is an electronic device performing a time integration of an electric voltage, thus measuring a total electric flux.

A current integrator is an electronic device performing a time integration of an electric current, thus measuring a total electric charge. Charge amplifier is an example of current integrator. 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.

Integrator in computer simulation

In some computational physics computer simulations, such as numerical weather prediction, molecular dynamics, flight simulators, reservoir simulation, noise barrier design, architectural acoustics, and electronic circuit simulation, an integrator is a numerical method for integrating trajectories from forces (and thereby accelerations) that are only calculated at discrete time steps.

There are a variety of explicit and implicit methods used in computer simulations. The most basic and least accurate kind of numerical integration is Euler integration. Verlet integration improves the accuracy of the integration to within fourth-order Taylor series terms, and the Runge–Kutta method which is gaining popularity further improves this accuracy to within fifth-order Taylor series terms.

Mechanical integrators

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.

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References

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    Further reading

    • Keng C. Wu (2003). Transistor Circuits for Spacecraft Power System. Springer. pp. 85–87. ISBN 1-4020-7261-9.  Unknown parameter |isnb13= ignored (help)
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