Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By W. C. Chew and L. Jiang

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In the past, coupling capacitances between conductors was extracted using charge distributions directly. In this paper a set of new generalized variational formulas are derived. They are complete since they are valid not only for self-capacitances, but also for mutual capacitances. As for the realistic numerical implementation, elastance matrices become asymmetrical because of numerical method used. Then a more general variational formula is derived to account for the asymmetrical elastance matrix case. By these novel formulas the computational accuracy can be significantly improved compared to the conventional capacitance extraction method.

W. C. Chew and L. Jiang, "A Complete Variational Method for Capacitance Extractions," Progress In Electromagnetics Research, Vol. 56, 19-32, 2006.

1. Smythe, W. R., Static and Dynamic Electricity, Mcgraw-Hill Book Co., Inc., 1950.

2. Walker, M., Schwarz-Christoffel Transformation and Its Applications: A Simple Exposition, Dover Publications, New York, 1964.

3. Kirchhoff, G. and Monatsb. Deutsch. Akad. Wiss., 144, Berlin, 1877.

4. Ignatowsky, W. and Akad. Nauk SSSR Mat. Inst. Trudy, Chapter 2, 1, 1932.

5. Nomura, Y., "The electrostatic problems of two equal parallel circular plates," Proc. Phys. Math. Soc., Vol. 3, 1941.

6. Polya, G. and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, NJ, 1951.

7. Leppington, F. and H. Levine, "On the capacity of the circular disc condenser at small separation," Proc. Cambridge Philos. Soc., Vol. 68, 1970.

8. Shaw, S., "Circular-disk viscometer and related electrostatic problems," Phys. Fluid, Vol. 13, 1970.

9. Itoh, T. and R. Mittra, "A new method of calculating the capacitance of a circular disk for microwave integrated circuits," IEEE Trans. Micro. Theory Tech., Vol. 21, 431-432, 1973.

10. Borkar, S. R. and R. F. M. Yang, "Capacitance of a circular disk for applications in microwave integrated circuits," IEEE Trans. Micro. Theory Tech., Vol. 23, 588-591, 1975.

11. Chew, W. C. and J. A. Kong, "Effects of fringing field on the capacitance of a circular microstrip disk," IEEE Trans. Microwave Theory Tech., Vol. 28, 98-104, 1980.

12. Poh, S. Y., W. C. Chew, and J. A. Kong, "Approximate formulas for line capacitance and characteristic impedance of microstrip line," IEEE Trans. Microwave Theory Tech., Vol. 29, 135-142, 1981.

13. Chew, W. C. and J. A. Kong, "Asymptotic formula for the capacitance of two oppositely charged discs," Math. Proc. Camb. Philos. Soc., Vol. 89, 373-384, 1981.

14. Chew, W. C. and J. A. Kong, "Microstrip capacitance for a circular disk through matched asymptotic expansions," SIAM J. Appl. Math., Vol. 42, 302-317, 1982.

15. Nabors, K., S. Kim, and J. White, "Fast capacitance extraction of general three-dimensional structures," IEEE Trans. Microwave Theory Tech., Vol. 40, 1496-1506, 1992.

16. Le Coz, Y. L., H. J. Greub, and R. B. Iverson, "Performance of random-walk capacitance extractors for IC interconnects: a numerical study," Solid-State Electronics, Vol. 42, 581-588, 1998.

17. Shi, W. P., J. G. Liu, N. Kankani, and T. J. Yu, "A fast hierarchical algorithm for 3-D capacitance extraction," IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, Vol. 21, 3, 2002.

18. Jandhyala, V., Y. Wang, D. Gope, and R. Shi, "A surfacebased integral equation formulation for coupled electromagnetic and circuit simulation," Microwave Optical Technology Letters, Vol. 34, 103-106, 2002.

19. Pan, Y. C., W. C. Chew, and L. X. Wan, "A fast multipole method based calculation of the capacitance matrix for multiple conductors above stratified media," IEEE Trans. Microwave Theory Tech., Vol. 49, 480-490, 2001.

20. Pan, Y. C. and W. C. Chew, "A hierarchical fast-multipole method for stratified media," Microwave and Optical Technology Letters, Vol. 27, 2002.

21. Chew, W. C., J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Inc., 2001.

22. Galerkin, B. G., "Series occurring in various questions concerning the elastic equilibrium of plates," Eng. Bull. (Vestn. Inzh. Tech.), Vol. 19, 897-908, 1915.

23. Harrington, R. F., Field Computation by Moment Methods, The IEEE/OUP Series on Electromagnetic Wave Theory, IEEE Press, 1993.

24. Jackson, J. D., Classical Electrodynamics, Third Edition, Wiley, New York, 1999.

25. Collin, R. E., Field Theoryof Guided Waves, McGraw-Hill, New York, 1999.

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