An integrator in measurement and control applications is an element whose output signal is the time
integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
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 principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
and
scientific 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 computers and charge amplifiers. Integration is also performed by digital computing algorithms.
In signal processing circuits
:''See also
Integrator at op amp applications''
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 ''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 movi ...
, 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 res ...
. A
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.
In software
* Integrators may also be software components.
* In some
computational physics 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 deter ...
s, such as
numerical weather prediction,
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 th ...
,
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 re ...
s,
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 design,
architectural acoustics, 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, 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.
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)
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.
See also
*
Differentiator
*
Digital differential analyzer
A digital differential analyzer (DDA), also sometimes called a digital integrating computer, is a digital implementation of a differential analyzer. The integrators in a DDA are implemented as accumulators, with the numeric result converted bac ...
*
Fractional-order integrator
A fractional-order integrator or just simply fractional integrator is an integrator device that calculates the fractional-order integral or derivative (usually called a differintegral) of an input. Differentiation or integration is a real or co ...
*
Integrating ADC
An integrating ADC is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its basic implementation, the dual-slope converter, the unknown input voltage is ...
*
Lowpass filter
*
Operational amplifier
*
Signal processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, ...
References
External links
Wolfram Online IntegratorCalc.Matthen Online Integrator, can do definite integrals
Further reading
* {{cite book, url= https://books.google.com/books?id=yDef8POEwIQC&pg=PA85, title=Transistor Circuits for Spacecraft Power System, author=Keng C. Wu , pages=85–87 , publisher=Springer , year=2002 , isbn=978-1-4020-7261-1
Mathematical tools