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A NUMERICAL SOLUTION FOR THE ROUND DISK CAPACITOR BY USING ANNULAR PATCH SUBDOMAINS

By C.-Y. Kim

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Abstract:
A numerical method is presented for determining the static charge distribution and capacitance of a round disk capacitor. Based on equivalent surface charge distributions, an integral equation subject to the boundary conditions is transformed into an algebraic equation by using the method of moments. In the proposed scheme to eliminate the discretizing errors often encountered in other techniques, annular patch subdomains are introduced, not only to improve the accuracy of solutions, but also to reduce the matrix size of the resultant equation. By solving the transformed algebraic equation, the charges per unit area on the interfaces are numerically determined. With use of the free charge on plates obtained by using annular patches, the capacitance is more accurately calculated. The equipotential lines around a round disk capacitor are also calculated.

In order to show the usefulness of this method, the employed scheme is applied to a single circular disk with an exact solution, and to the dielectric filled capacitor partially covered by plates. Those results are examined and discussions are also made to support the validity of the presented scheme.

Citation:
C.-Y. Kim, "A Numerical Solution for the Round Disk Capacitor by Using Annular Patch Subdomains," Progress In Electromagnetics Research B, Vol. 8, 179-194, 2008.
doi:10.2528/PIERB08052102

References:
1. Farrar, A. and A. T. Adams, "Matrix methods for microstrip three-dimensional problem," IEEE Trans. Microwave Theory Tech., Vol. 20, 497-504, Aug. 1972.
doi:10.1109/TMTT.1972.1127796

2. Benedex, P. and P. Silvester, "Capacitance of parallel rectangular plates separated by a dielectric sheet," IEEE Trans. Microwave Theory Tech., Vol. 20, 504-510, Aug. 1972.
doi:10.1109/TMTT.1972.1127797

3. Itoh, T. and R. Mittra, "A new method for calculating the capacitance of a circular disk for microwave integrated circuit," IEEE Trans. Microwave Theory Tech., Vol. 21, 431-432, 1973.
doi:10.1109/TMTT.1973.1128023

4. Shen, L. C., S. A. Long, M. R. Allerding, and M. D. Walton, "“Resonator frequency of a circular disk, printed circuit antenna," IEEE Trans. Antennas Propagat., Vol. 25, 595-596, July 1977.
doi:10.1109/TAP.1977.1141643

5. Pyati, V. P., "Capacitance of a circular disk placed over a grounded substrate," Journal of Electromagnetic Waves and Applications, Vol. 1, No. 11, 1013-1025, 1997.
doi:10.1163/156939397X00387

6. Jiang, L. J. and W. C. Chew, "A complete variational method for capacitance extractions," Progress In Electromagnetics Research, Vol. 56, 19-32, 2006.

7. Harrington, R. F., Field Computation by Moment Methods, N.Y. Macmillan Co., 24-28, 1968.

8. Ghosh, S. and A. Chakrabarty, "Capacitance evaluation of arbitrary-shaped multiconducting bodies using rectangular subareas," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 14, 2091-2102, 2006.
doi:10.1163/156939306779322666

9. Reitan, D. K., "Accurate determination of the capacitance of rectangular parallel-plate capacitor," Journ. Appl. Phys., Vol. 30, No. 2, 172-176, Feb. 1959.
doi:10.1063/1.1735128

10. Harrington, R. F., "Matrix methods for field problems," Proc. IEEE, Vol. 55, No. 2, 136-149, Feb. 1967.
doi:10.1109/PROC.1967.5433

11. Wei, C. W., R. F. Harrington, J. R. Mautz, and T. K. Sarkar, "Multiconductor transmission lines in multilayered dielectric media," IEEE MTT, Vol. 32, No. 4, 439-450, Apr. 1984.
doi:10.1109/TMTT.1984.1132696

12. Stratton, J. A., Electromagnetic Theory, 183-185, N.Y. McGraw-Hill, 1941.

13. Griffiths, D. J. and Y. Li, "Charge density on a conducting needle," Am. J. Phys., Vol. 64, No. 6, 706-714, June 1996.
doi:10.1119/1.18236

14. Liang, C. H., H. B. Yuan, and K. B. Tan, "Method for largest extended circle for the capacitance of arbitrarily shaped conducting plates," Progress In Electromagnetics Research Letters, Vol. 1, 51-60, 2008.
doi:10.2528/PIERL07112101

15. Rao, S. M., A. W. Glisson, D. R. Wilton, and B. S. Vidula, "A simple numerical solution procedure for static problems involving arbitrary-shaped surfaces," IEEE Trans. Antennas Propagat., Vol. 27, No. 5, 604-608, Sept. 1979.
doi:10.1109/TAP.1979.1142171


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