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| [[Image:Rogowsky coil.png|thumb|
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| A Rogowski coil is a [[toroid]] of wire used to measure an alternating current ''i(t)'' through a cable encircled by the toroid. The above picture shows a coil encircling a current-carrying cable, with its output terminals ''v(t)'' connected to an integrator circuit, to obtain a voltage ''V<sub>out</sub>(t)'' proportional to ''i(t)''.
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| A '''Rogowski coil''', named after [[Walter Rogowski]], is an electrical device for [[Electrical measurements|measuring]] [[alternating current]] (AC) or high speed current pulses. It consists of a [[helix|helical]] [[coil]] of [[wire]] with the [[lead (electronics)|lead]] from one end returning through the centre of the coil to the other end, so that both [[Terminal (electronics)|terminal]]s are at the same end of the coil. The whole assembly is then wrapped around the straight [[conductor (material)|conductor]] whose current is to be measured. Since the [[voltage]] that is induced in the coil is proportional to the rate of change ([[derivative]]) of current in the straight conductor, the output of the Rogowski coil is usually connected to an electrical (or electronic) [[integrator]] circuit to provide an output signal that is proportional to the current.
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| ==Advantages==
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| This type of coil has advantages over other types of [[current transformer]]s.
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| * It is not a closed loop, because the second terminal is passed back through the center of the toroid core (commonly a plastic or rubber tube) and connected along the first terminal. This allows the coil to be open-ended and flexible, allowing it to be wrapped around a live conductor without disturbing it.
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| * It has an air core rather than an [[iron]] core, it has a low [[inductance]] and can respond to fast-changing currents.
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| * Because it has no iron core to saturate, it is highly linear even when subjected to large currents, such as those used in [[electric power transmission]], [[welding]], or [[pulsed power]] applications.
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| * The full-scale output of a properly designed Rogowski coil is typically a few hundred millivolts. Although a correctly formed Rogowski coil, with equally spaced windings, is largely immune to [[electromagnetic interference]], the integrator circuitry it requires may not be.
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| ==Disadvantages==
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| This type of coil also has some disadvantages over other types of [[current transformer]]s.
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| * The output of the coil must be passed through an integrator circuit to obtain the current waveform. The integrator circuit requires power, typically +/-15Vdc. Traditional split-core current transformers do not require integrator circuits. The integrator is lossy, so the Rogowski coil does not have a response down to DC; neither does a conventional current transformer (see [[Néel effect]] coils for DC).
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| Due to these disadvantages, Rogowski coils are primarily used when ease-of-installation is a high priority. Traditional or split-core current transformers are used when accuracy, noise immunity, and currents during power quality events are a high priority.{{cn|date=October 2012}}
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| ==Formulae==
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| [[File:RC PULSE.png|thumb|Example waveform of R.C. output for [[Switched-mode power supply|switched-mode load]]. As explained above the output waveform - CH4 (green) - represents the [[derivative]] of the current waveform - CH2 (Blue). CH1 (Yellow) is 230V AC Mains waveform]]
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| The voltage produced by a Rogowski coil is
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| <math>V = \frac{-AN\mu_0}{l} \frac{dI}{dt}</math>,
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| where <math>A= \pi a^2</math> is the area of one of the small loops, N is the number of turns, and <math>l=2 \pi R</math> is the length of the winding (the circumference of the ring). <math>\frac{dI}{dt}</math> is the rate of change of the current threading the loop. This formula assumes the turns are evenly spaced and that these turns are small relative to the radius of the coil itself. At high frequencies, the Rogowski coil's [[inductance]] will decrease its output. The inductance of a toroid is
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| <math>L = \mu_0 N^2 (R - \sqrt{R^2-a^2})</math>
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| <math>\mu_0 = 4 \pi \times 10^{-7}</math> [[Volt|V]]·[[Second|s]]/([[Ampere|A]]·[[Meter|m]]) is the [[permeability of free space|magnetic constant]], <math>R</math> is the major radius of the toroid, and <math>a</math> is its minor radius.
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| ==Similar devices==
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| A device similar to the Rogowski coil was described by [[Arthur Prince Chattock]] of [[Bristol University]] in 1887.<ref>"On a magnetic potentiometer", ''Philosophical Magazine and Journal of Science'', vol. XXIV, no. 5th Series, pp. 94–96, Jul-Dec 1887</ref> Chattock used it to measure [[magnetic field]]s rather than currents. The definitive description was given by Walter Rogowski and W. Steinhaus in 1912.<ref>Walter Rogowski and W. Steinhaus in "Die Messung der magnetischen Spannung", ''Archiv für Elektrotechnik'', 1912, 1, Pt.4, pp. 141–150.</ref>
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| More recently, low-cost current sensors based on the principle of a Rogowski coil have been developed.<ref>Patent for a planar Rogowski current sensor {{US patent|6414475}}, granted 2 Jul 2002.</ref> These sensors share the principles of a Rogowski coil, measuring the rate of change of current using a transformer with no magnetic core. The difference from the traditional Rogowski coil is that the sensor can be manufactured using a planar coil rather than a toroidal coil. In order to reject the influence of conductors outside the sensor's measurement region, these planar Rogowski current sensors use a concentric coil geometry instead of a toroidal geometry to limit the response to external fields. The main advantage of the planar Rogowski current sensor is that the coil winding precision that is a requirement for accuracy can be achieved using low-cost [[printed circuit board]] manufacturing.
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| ==See also==
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| * [[Current (electricity)|Current]]
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| * [[Current transformer]]
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| * [[List of electronics topics]]
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| * [[Pulsed power]]
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| * [[Toroidal inductors and transformers]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://homepage.ntlworld.com/rocoil/Pr9.pdf Rogowski Coils], [http://homepage.ntlworld.com/rocoil/Pr7o.pdf Using Rogowski Coils for Transient Current Measurements], [http://homepage.ntlworld.com/rocoil/principle.htm Rocoil Ltd] Operating Principle
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| * [http://www.pacw.org/fileadmin/doc/AutumnIssue07/prot_rogowski_autumn07.pdf Rogowski Coil Designs], PAC World, Autumn 2007, protection relaying applications
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| * [http://www.powertekuk.com/cwtmini.htm Miniature Wideband Current Probe] sensor using this principle
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| * [http://www.pemuk.com/publications.aspx PEM UK] Rogowski current transducer theory
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| {{DEFAULTSORT:Rogowski Coil}}
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| [[Category:Electromagnetic coils]]
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| [[Category:Electrical test equipment]]
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