volume | PIER Journals

2009-10-20

The Capacitance of the Circular Parallel Plate Capacitor Obtained by Solving the Love Integral Equation Using an Analytic Expansion of the Kernel

Martin Karl Norgren,

Dr. Martin Karl Norgren

School of Electrical Enginering

Royal Institute of Technology

Sweden

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Lars Jonsson

Dr. Lars Jonsson

Electromagnetic Engineering

Royal Institute of Technology

Sweden

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Progress In Electromagnetics Research, Vol. 97, 357-372, 2009

doi:10.2528/PIER09092503

Abstract

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.

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Martin Karl Norgren, and Lars Jonsson, "The Capacitance of the Circular Parallel Plate Capacitor Obtained by Solving the Love Integral Equation Using an Analytic Expansion of the Kernel," Progress In Electromagnetics Research, Vol. 97, 357-372, 2009.
doi:10.2528/PIER09092503

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