An integrator in measurement and control applications is an element whose output signal is the time

integral In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...

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 Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

and

scientific Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

applications. Mechanical integrators are the oldest application, and are still used in such as metering of water flow or electric power. Electronic analogue integrators are the basis of

analog computer An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In c ...

s and charge amplifiers. Integration is also performed by digital computing algorithms.

In signal processing circuits

:''See also Integrator at op amp applications'' An

electronic Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic co ...

integrator is a form of first-order

low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...

, 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 the total volt-second product. A ''current integrator'' is an electronic device performing a time integration of an

electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...

, thus measuring a total

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...

. A

charge amplifier A charge amplifier is an electronic current integrator that produces a voltage output proportional to the integrated value of the input current, or the total charge injected. The amplifier offsets the input current using a feedback reference capa ...

is an example of current integrator. A current integrator is also used to measure the electric charge on a

Faraday cup A Faraday cup is a metal (conductive) cup designed to catch charged particles in vacuum. The resulting current can be measured and used to determine the number of ions or electrons hitting the cup. The Faraday cup was named after Michael Faraday w ...

in a

residual gas analyzer A residual gas analyzer (RGA) is a small and usually rugged mass spectrometer, typically designed for process control and contamination monitoring in vacuum systems. When constructed as a quadrupole mass analyzer, there exist two implementations ...

to measure partial pressures of gasses in a vacuum. Another application of current integration is in

ion beam deposition Ion beam deposition (IBD) is a process of applying materials to a target through the application of an ion beam. Ion beam deposition setup with mass separator An ion beam deposition apparatus typically consists of an ion source, ion optics, and ...

, where the measured charge directly corresponds to the number of ions deposited on a substrate, assuming the charge state of the

ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conven ...

s is known. The two current-carrying electrical leads must to be connected to the

ion source An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines. Electron ionization Electron ...

and the substrate, closing the

electric circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...

which in part is given by the ion beam.

In software

* Integrators may also be software components. * In some

computational physics Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, ...

computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...

s, such as

numerical weather prediction Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in th ...

molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the ...

flight simulator A flight simulator is a device that artificially re-creates aircraft flight and the environment in which it flies, for pilot training, design, or other purposes. It includes replicating the equations that govern how aircraft fly, how they rea ...

reservoir simulation Reservoir simulation is an area of reservoir engineering in which computer models are used to predict the flow of fluids (typically, oil, water, and gas) through porous media. The creation of models of oil fields and the implementation of ca ...

noise barrier A noise barrier (also called a soundwall, noise wall, sound berm, sound barrier, or acoustical barrier) is an exterior structure designed to protect inhabitants of sensitive land use areas from noise pollution. Noise barriers are the most effecti ...

design,

architectural acoustics Architectural acoustics (also known as building acoustics) is the science and engineering of achieving a good sound within a building and is a branch of acoustical engineering. The first application of modern scientific methods to architectura ...

, and

electronic circuit simulation Electronic circuit simulation uses mathematical models to replicate the behavior of an actual electronic device or circuit. Simulation software allows for modeling of circuit operation and is an invaluable analysis tool. Due to its highly accurat ...

, an integrator is a numerical method for integrating trajectories from forces (and thereby accelerations) that are only calculated at discrete time steps.

Mechanical integrators

Mechanical integrators were key elements in the mechanical

differential analyser The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operat ...

, 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 The ball-and-disk integrator is a key component of many advanced mechanical computers. Through simple mechanical means, it performs continual integration of the value of an input. Typical uses were the measurement of area or volume of material in ...

were used both for computation in differential analysers and as components of instruments such as naval gun directors, flow totalizers and others. A

planimeter A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape. Construction There are several kinds of planimeters, but all operate in a similar way. The precise way in whic ...

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 An Integraph is a mechanical analog computing device for plotting the integral of a graphically defined function. History Gaspard-Gustave de Coriolis first described the fundamental principal of a mechanical integraph in 1836 in the ''Journal ...

is used to plot the indefinite integral of a function given in graphical form.

Drawbacks of ideal integrator

* Bandwidth is very small and used for only small range of input frequencies. * For dc input (''f'' = 0), the reactance of the capacitance, ''X'', is infinite. Because of this op-amp goes into open loop configuration. In open loop configuration the gain is infinite and hence the small input offset voltages are also amplified and appears at output as error. This is referred as false triggering and must be avoided. Due to all such limitations, an ideal integrator needs to be modified. Some additional components are used along with ideal integrator circuit to reduce the effect of an error voltage in practice. This modified integrator is referred as practical integrator.

Practical integrator (lossy integrator)

Frequency response of ideal and practical integrator

The gain of an integrator at low frequency can be limited to avoid the saturation problem, therefore to avoid saturation of the op amp the feedback capacitor is shunted by a resistor Rf. The parallel combination of Rf and C behaves like a practical capacitor which dissipates power, unlike an ideal capacitor. For this reason this circuit is also called a lossy integrator. The resistor Rf limits the low frequency gain to (-Rf/R), generally f=10*R1and thus provides DC stabilisation.

Applications

* Op-amp integrating amplifiers are used to perform calculus operations in analogue computers. * Integrating circuits are most commonly used in analogue-to-digital converters, ramp generators and also in wave shaping applications. * Another application would be to integrate a signal representing water flow, producing a signal representing the total quantity of water that has passed by the flow meter. This application of an integrator is sometimes called a totalizer in the industrial instrumentation trade.

References

External links

Wolfram Online IntegratorCalc.Matthen Online Integrator, can do definite integrals