Improvement of Self-Inductance Calculations for Circular Coils of Rectangular Cross Section
In this paper, an improvement for calculating the self-inductance of circular coils of rectangular cross section is presented. An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral wi...
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| Veröffentlicht in: | IEEE transactions on magnetics 2013-03, Vol.49 (3), p.1249-1255 |
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| creator | Luo, Yao Chen, Baichao |
| description | In this paper, an improvement for calculating the self-inductance of circular coils of rectangular cross section is presented. An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. Furthermore, the asymptotic behaviors of the special coils which tend to be a circular ring are obtained and numerically validated. |
| doi_str_mv | 10.1109/TMAG.2012.2228499 |
| format | Article |
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An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. Furthermore, the asymptotic behaviors of the special coils which tend to be a circular ring are obtained and numerically validated.</description><identifier>ISSN: 0018-9464</identifier><identifier>EISSN: 1941-0069</identifier><identifier>DOI: 10.1109/TMAG.2012.2228499</identifier><identifier>CODEN: IEMGAQ</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Acceleration ; Accuracy ; Algorithms ; Circular coils ; Coils ; Cross-disciplinary physics: materials science; rheology ; Educational institutions ; Exact sciences and technology ; Inductance ; Magnetism ; Materials science ; Other topics in materials science ; Physics ; self-inductance ; Shape ; Solenoids ; special functions ; Studies</subject><ispartof>IEEE transactions on magnetics, 2013-03, Vol.49 (3), p.1249-1255</ispartof><rights>2014 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Mar 2013</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c323t-e5a2626cd83d96500e5dde6901a53f838539573602ae7831490318340b46a3ac3</citedby><cites>FETCH-LOGICAL-c323t-e5a2626cd83d96500e5dde6901a53f838539573602ae7831490318340b46a3ac3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/6359946$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/6359946$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27129761$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Luo, Yao</creatorcontrib><creatorcontrib>Chen, Baichao</creatorcontrib><title>Improvement of Self-Inductance Calculations for Circular Coils of Rectangular Cross Section</title><title>IEEE transactions on magnetics</title><addtitle>TMAG</addtitle><description>In this paper, an improvement for calculating the self-inductance of circular coils of rectangular cross section is presented. An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. Furthermore, the asymptotic behaviors of the special coils which tend to be a circular ring are obtained and numerically validated.</description><subject>Acceleration</subject><subject>Accuracy</subject><subject>Algorithms</subject><subject>Circular coils</subject><subject>Coils</subject><subject>Cross-disciplinary physics: materials science; rheology</subject><subject>Educational institutions</subject><subject>Exact sciences and technology</subject><subject>Inductance</subject><subject>Magnetism</subject><subject>Materials science</subject><subject>Other topics in materials science</subject><subject>Physics</subject><subject>self-inductance</subject><subject>Shape</subject><subject>Solenoids</subject><subject>special functions</subject><subject>Studies</subject><issn>0018-9464</issn><issn>1941-0069</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kEFLxDAQhYMouK7-APFSEI9dZ5ImbY5SdF1YEXQ9eQgxTaVLt12TVvDfm9BlT0km772Z-Qi5RlgggrzfvDwsFxSQLiilRSblCZmhzDAFEPKUzACwSGUmsnNy4f02PDOOMCOfq93e9b92Z7sh6evk3bZ1uuqq0Qy6MzYpdWvGVg9N3_mk7l1SNi4WwqVvWh8tbzZqv6ei670PISYaLslZrVtvrw7nnHw8PW7K53T9ulyVD-vUMMqG1HJNBRWmKlglBQewvKqskICas7pgBWeS50wA1TYvGGYSGBYsg69MaKYNm5PbKTds8jNaP6htP7outFRIJQrIBWNBhZPKxBmdrdXeNTvt_hSCigxVZKgiQ3VgGDx3h2TtjW5rF5g0_mikecjPBQbdzaRrrLXHb8G4DMjZP8rxeNM</recordid><startdate>20130301</startdate><enddate>20130301</enddate><creator>Luo, Yao</creator><creator>Chen, Baichao</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. 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| source | IEEE Electronic Library (IEL) |
| subjects | Acceleration Accuracy Algorithms Circular coils Coils Cross-disciplinary physics: materials science rheology Educational institutions Exact sciences and technology Inductance Magnetism Materials science Other topics in materials science Physics self-inductance Shape Solenoids special functions Studies |
| title | Improvement of Self-Inductance Calculations for Circular Coils of Rectangular Cross Section |
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