Vol. 8
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2008-06-25
A Numerical Solution for the Round Disk Capacitor by Using Annular Patch Subdomains
By
Progress In Electromagnetics Research B, Vol. 8, 179-194, 2008
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
Che-Young 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