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Rogowski coil
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<h2 id="advantages">Advantages</h2> <p>This type of coil has advantages over other types of <a href="/facts/Current_transformer/w5JaY0oc">current transformers</a>. </p> <ul><li>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. However, positioning of the measured conductor is important in that case: It has been shown that, with flexible sensors, the effect of the position on the accuracy ranges from 1 to 3%. Another technique uses two rigid winding halves with a precise locking mechanism.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></li> <li>Due to its low <a href="/facts/Inductance/oIxj7JxX">inductance</a>, it can respond to fast-changing currents, down to several nanoseconds.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></li> <li>Because it has no iron core to saturate, it is highly linear even when subjected to large currents, such as those used in <a href="/facts/Electric_power_transmission/I9w3lRmM">electric power transmission</a>, <a href="/facts/Welding/6EJ62mYV">welding</a>, or <a href="/facts/Pulsed_power/BTJN8xg5">pulsed power</a> applications.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a> This linearity also enables a high-current Rogowski coil to be calibrated using much smaller reference currents.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a></li> <li>No danger of opening the secondary winding.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a></li> <li>Lower construction costs.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a></li> <li>Temperature compensation is simple.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a></li> <li>For larger currents conventional current transformers require an increase of the number of secondary turns, in order to keep the output current constant. Therefore, a Rogowski coil for large current is smaller than an equivalent rating current transformer.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a></li></ul> <h2 id="disadvantages">Disadvantages</h2> <p>This type of coil also has some disadvantages over other types of <a href="/facts/Current_transformer/w5JaY0oc">current transformers</a>. </p> <ul><li>The output of the coil must be passed through an integrator circuit to obtain the current waveform. The integrator circuit requires power, typically 3 to 24Vdc, and many commercial sensors obtain this from batteries.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a></li> <li>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 <a href="/facts/N%C3%A9el_effect/NcokQwUb">Néel effect</a> coils for DC). However, they can measure very slow changing currents with frequency components down to 1 Hz and less.<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a></li> <li>Constant DC current cannot be measured. The Rogowski coil samples the field, generating a voltage as the field changes.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a></li></ul> <h2 id="applications">Applications</h2> <p>Rogowski coils are used for current monitoring in precision welding systems, arc melting furnaces, or electromagnetic launchers. They are also used in short-circuit testing of electric generators and as sensors in protection systems of electrical plants. Another field of usage is the measurement of harmonic current content, due to their high linearity.<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> Also for lightning research. </p> <h2 id="formulae">Formulae</h2> <p>The voltage produced by a Rogowski coil is </p> v ( t ) = − A N μ 0 l d I ( t ) d t , {\displaystyle v(t)={\frac {-AN\mu _{0}}{l}}{\frac {dI(t)}{dt}},} <p>where </p> <ul><li> A = π r 2 {\displaystyle A=\pi r^{2}} is the area of one of the small loops,</li> <li> N {\displaystyle N} is the number of turns,</li> <li> l = 2 π R {\displaystyle l=2\pi R} is the length of the winding (the circumference of the ring),</li> <li> d I ( t ) d t {\displaystyle {\frac {dI(t)}{dt}}} is the rate of change of the current threading the loop,</li> <li> μ 0 = 4 π × 10 − 7 {\displaystyle \mu _{0}=4\pi \times 10^{-7}} <a href="/facts/Volt/KF18MXP2">V</a>·<a href="/facts/Second/jtFxnJXx">s</a>/(<a href="/facts/Ampere/MScqkCgz">A</a>·<a href="/facts/Meter/hPhzc1CV">m</a>) is the <a href="/facts/Permeability_of_free_space/nKxRk6J1">magnetic constant</a>,</li> <li> R {\displaystyle R} is the major radius of the toroid,</li> <li> r {\displaystyle r} is its minor radius.</li></ul> <p>This formula assumes the turns are evenly spaced and that these turns are small relative to the radius of the coil itself. </p><p>The output of the Rogowski coil is proportional to the derivative of the wire current. The output is often integrated so the output is proportional to the wire's current: </p> V out = ∫ v d t = − A N μ 0 l I ( t ) + C integration . {\displaystyle V_{\text{out}}=\int v\,dt={\frac {-AN\mu _{0}}{l}}I(t)+C_{\text{integration}}.} <p>In practice, an instrument will use a lossy integrator with a time constant much less than the lowest frequency of interest. The lossy integrator will reduce the effects of offset voltages and set the constant of integration to zero. </p><p>At high frequencies, the Rogowski coil's <a href="/facts/Inductance/oIxj7JxX">inductance</a> will decrease its output. </p><p>The inductance of a toroid is<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> </p> L = μ 0 N 2 ( R − R 2 − r 2 ) . {\displaystyle L=\mu _{0}N^{2}\left(R-{\sqrt {R^{2}-r^{2}}}\right).} <h2 id="similar-devices">Similar devices</h2> <p>A device similar to the Rogowski coil was described by <a href="/facts/Arthur_Prince_Chattock/mR15crKG">Arthur Prince Chattock</a> of <a href="/facts/Bristol_University/naU7Gvlc">Bristol University</a> in 1887.<a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> Chattock used it to measure <a href="/facts/Magnetic_field/Ta8Ev588">magnetic fields</a> rather than currents. The definitive description was given by Walter Rogowski and W. Steinhaus in 1912.<a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> </p><p>More recently, low-cost current sensors based on the principle of a Rogowski coil have been developed.<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a> 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 <a href="/facts/Printed_circuit_board/muSR2p43">printed circuit board</a> manufacturing. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Balisor/uLEmwreg">Balisor</a>, a device that gets energy from the electric field, instead of the magnetic field</li> <li><a href="/facts/Current_(electricity)/Dc1xdnUX">Current</a></li> <li><a href="/facts/Current_transformer/w5JaY0oc">Current transformer</a></li> <li><a href="/facts/Index_of_electronics_articles/VTrwvXxp">Index of electronics articles</a></li> <li><a href="/facts/Pulsed_power/BTJN8xg5">Pulsed power</a></li> <li><a href="/facts/Toroidal_inductors_and_transformers/RfElL6kX">Toroidal inductors and transformers</a></li> <li><a href="/facts/Current_sensing/xHEQuzpS">Current sensing</a></li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="http://homepage.ntlworld.com/rocoil/Pr9.pdf">Rogowski Coils</a> <a href="https://web.archive.org/web/20090920070139/http://homepage.ntlworld.com/rocoil/Pr9.pdf">Archived</a> 2009-09-20 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a>, <a href="http://homepage.ntlworld.com/rocoil/Pr7o.pdf">Using Rogowski Coils for Transient Current Measurements</a> <a href="https://web.archive.org/web/20160304102532/http://homepage.ntlworld.com/rocoil/Pr7o.pdf">Archived</a> 2016-03-04 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a>, <a href="http://homepage.ntlworld.com/rocoil/principle.htm">Rocoil Ltd Operating Principle</a> <a href="https://web.archive.org/web/20160304084646/http://homepage.ntlworld.com/rocoil/principle.htm">Archived</a> 2016-03-04 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li> <li><a href="http://www.pacw.org/fileadmin/doc/AutumnIssue07/prot_rogowski_autumn07.pdf">Rogowski Coil Designs</a> <a href="https://web.archive.org/web/20181215130311/http://www.pacw.org/fileadmin/doc/AutumnIssue07/prot_rogowski_autumn07.pdf">Archived</a> 2018-12-15 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a>, PAC World, Autumn 2007, protection relaying applications</li> <li><a href="http://www.powertekuk.com/cwtmini.htm">Miniature Wideband Current Probe</a> sensor using this principle</li> <li><a href="http://www.pemuk.com/publications.aspx">PEM UK</a> Rogowski current transducer theory</li> <li><a href="http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F1AC8F9A99D59E6EEB9EE13009CBA3AF?doi=10.1.1.473.9903&rep=rep1&type=pdf">An Overview of Rogowski Coil Current Sensing Technology</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>D.G. Pellinen, M.S. DiCipua, S.E. Sampayan, H. Gerbracht, and M. Wang, "Rogowski coil for measuring fast, highlevel pulsed currents," Rev.Sci.Instr. 51, 1535 (1980); http://dx.doi.org/10.1063/1.1136119. <a href="https://dx.doi.org/10.1063/1.1136119" target="_blank">https://dx.doi.org/10.1063/1.1136119</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>John G. Webster, Halit Eren (ed.), Measurement, Instrumentation, and Sensors Handbook, Second Edition: Electromagnetic, Optical, Radiation, Chemical, and Biomedical Measurement, CRC Press, 2014, ISBN 1-439-84891-2, pp. 16-6 to 16-7. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Klaus Schon, High Impulse Voltage and Current Measurement Techniques: Fundamentals – Measuring Instruments – Measuring Methods, Springer Science & Business Media, 2013, ISBN 3-319-00378-X, p. 193. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>John G. Webster, Halit Eren (ed.), Measurement, Instrumentation, and Sensors Handbook, Second Edition: Electromagnetic, Optical, Radiation, Chemical, and Biomedical Measurement, CRC Press, 2014, ISBN 1-439-84891-2, pp. 16-6 to 16-7. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>D.G. Pellinen, M.S. DiCipua, S.E. Sampayan, H. Gerbracht, and M. Wang, "Rogowski coil for measuring fast, highlevel pulsed currents," Rev.Sci.Instr. 51, 1535 (1980); http://dx.doi.org/10.1063/1.1136119. <a href="https://dx.doi.org/10.1063/1.1136119" target="_blank">https://dx.doi.org/10.1063/1.1136119</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Klaus Schon, High Impulse Voltage and Current Measurement Techniques: Fundamentals – Measuring Instruments – Measuring Methods, Springer Science & Business Media, 2013, ISBN 3-319-00378-X, p. 193. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Slawomir Tumanski, Handbook of Magnetic Measurements, CRC Press, 2011, ISBN 1-439-82952-7, p. 175. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Slawomir Tumanski, Handbook of Magnetic Measurements, CRC Press, 2011, ISBN 1-439-82952-7, p. 175. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>John G. Webster, Halit Eren (ed.), Measurement, Instrumentation, and Sensors Handbook, Second Edition: Electromagnetic, Optical, Radiation, Chemical, and Biomedical Measurement, CRC Press, 2014, ISBN 1-439-84891-2, pp. 16-6 to 16-7. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Slawomir Tumanski, Handbook of Magnetic Measurements, CRC Press, 2011, ISBN 1-439-82952-7, p. 175. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>Slawomir Tumanski, Handbook of Magnetic Measurements, CRC Press, 2011, ISBN 1-439-82952-7, p. 175. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>John G. Webster, Halit Eren (ed.), Measurement, Instrumentation, and Sensors Handbook, Second Edition: Electromagnetic, Optical, Radiation, Chemical, and Biomedical Measurement, CRC Press, 2014, ISBN 1-439-84891-2, pp. 16-6 to 16-7. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Stephen A. Dyer, Wiley Survey of Instrumentation and Measurement, John Wiley & Sons, 2004, ISBN 0-471-22165-1, p. 265. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>Krzysztof Iniewski, Smart Sensors for Industrial Applications, CRC Press, 2013, ISBN 1-466-56810-0, p. 346. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>Klaus Schon, High Impulse Voltage and Current Measurement Techniques: Fundamentals – Measuring Instruments – Measuring Methods, Springer Science & Business Media, 2013, ISBN 3-319-00378-X, p. 193. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>"What is Rogowski Coils and How Does it Work?". aimdynamics. July 28, 2023. Retrieved September 26, 2023. <a href="https://aimdynamics.com/rogowski-coils" target="_blank">https://aimdynamics.com/rogowski-coils</a> <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>Krzysztof Iniewski, Smart Sensors for Industrial Applications, CRC Press, 2013, ISBN 1-466-56810-0, p. 346. <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>"Toroid Inductor Formulas and Calculator". <a href="http://www.nessengr.com/technical-data/toroid-inductor-formulas-and-calculator/" target="_blank">http://www.nessengr.com/technical-data/toroid-inductor-formulas-and-calculator/</a> <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>"On a magnetic potentiometer", Philosophical Magazine and Journal of Science, vol. XXIV, no. 5th Series, pp. 94–96, Jul-Dec 1887 <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>Walter Rogowski and W. Steinhaus in "Die Messung der magnetischen Spannung", Archiv für Elektrotechnik, 1912, 1, Pt.4, pp. 141–150. <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>Patent for a planar Rogowski current sensor U.S. patent 6,414,475, granted 2 Jul 2002. <a href="https://patents.google.com/patent/US6414475" target="_blank">https://patents.google.com/patent/US6414475</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> </ol>