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THE CAPACITANCE OF THE CIRCULAR PARALLEL PLATE CAPACITOR OBTAINED BY SOLVING THE LOVE INTEGRAL EQUATION USING AN ANALYTIC EXPANSION OF THE KERNEL
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-9241-8030
KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.ORCID iD: 0000-0001-7269-5241
2009 (English)Article in journal (Refereed) Published
Abstract [en]

The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of the Sine and Cosine integrals. Hence, we can, in the approximation of the kernel, use considerably larger matrices, resulting in improved numerical accuracy for the capacitance. In order to improve the accuracy at the smallest separations, we develop a heuristic extrapolation scheme that takes into account the convergence properties of the algorithm. Our results are compared with other numerical results from the literature and with the Kirchhoff result. Error estimates are presented, from which we conclude that our results is a substantial improvement compared with earlier numerical results.

Place, publisher, year, edition, pages
2009. Vol. 97, 357-372 p.
Keyword [en]
disk capacitors
Identifiers
URN: urn:nbn:se:kth:diva-18938DOI: 10.2528/pier09092503ISI: 000271569600021Scopus ID: 2-s2.0-70350646857OAI: oai:DiVA.org:kth-18938DiVA: diva2:336985
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2011-01-13Bibliographically approved

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Norgren, MartinJonsson, B. Lars G.

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