volume | PIER Journals

Abstract

We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green's function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green's function, and the summation of the leading terms is carried out using the fast convergent series.

1. Li, L. and E. Wang, "A hybrid of finite analytic and multi-grid method for calculating electric field distribution," IEEE Transactions on Magnetics, Vol. 42, No. 4, 551-554, Apr. 2006.
doi:10.1109/TMAG.2006.872475 Google Scholar

2. Denno, K., "Computation of electromagnetic lightning response using moments method," IEEE Transactions on Magnetics, Vol. 20, No. 5, Part 2, 1953-1955, Sep. 1984. Google Scholar

3. Sun, K. and Y. Chen, "Spectral-domain analysis of dispersion characteristics of open coupled microstrip lines on YIG/GGG structures," IEEE Transactions on Magnetics, Vol. 31, No. 6, 3458-3460, Nov. 1995. Google Scholar

4. Krempasky, L. and C. Schmidt, "Theoretical analysis of time constant measurements of technical superconductors," IEEE Transactions on Magnetics, Vol. 30, No. 4, Part 2, 2654-2657, Jul. 1994. Google Scholar

5. Mosig, J. R. and A. Alvarez Melcon, "The summation-by-parts algorithm --- A new efficient technique for the rapid calculation of certain series arising in shielded planar structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 1, 215-218, Jan. 2002.
doi:10.1109/22.981269 Google Scholar

6. Tounsi, M., R. Touhami, and M. C. Yagoub, "Analysis of the mixed coupling in bilateral microwave circuits including anisotropy for MICS and MMICS applications," Progress In Electromagnetics Research, Vol. 62, 281-315, Jun. 2006.
doi:10.2528/PIER06020601 Google Scholar

7. Cano, G., F. Mesa, F. Medina, and M. Horno, "Systematic computation of the modal spectrum of boxed microstrip, finline, and coplanar waveguides via an e±cient sda," IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 4, Part 1, 866-872, Apr. 1995. Google Scholar

8. Cano, G., F. Medina, and M. Horno, "On the efficient implementation of SDA for boxed strip-like and slot-like structures," IEEE Transactions on Microwave Theory and Techniques, Vol. 46, No. 11, Part 1, 1801-1806, Nov. 1998. Google Scholar

9. Tsalamengas, J. L. and G. Fikioris, "Rapidly converging spectraldomain analysis of rectangularly shielded layered microstrip lines," IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 6, 1729-1734, Jun. 2003.
doi:10.1109/TMTT.2003.812576 Google Scholar

10. Medina, F. and M. Horno, "Quasi-analytical static solution of the boxed microstrip line embedded in a layered medium," IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 9, 1748-1756, Sep. 1992.
doi:10.1109/22.156601 Google Scholar

11. Medina, F. and M. Horno, "Spectral and variational analysis of generalized cylindrical and elliptical strip and microstrip lines," IEEE Transactions on Microwave Theory and Techniques, Vol. 38, No. 9, 1287-1293, Sep. 1990.
doi:10.1109/22.58655 Google Scholar

12. Tsalamengas, J., "Parallel plate-fed slot antenna loaded by a dielectric semicylinder," IEEE Transactions on Antennas and Propagation, Vol. 44, No. 7, 1031-1040, Jul. 1996.
doi:10.1109/8.504312 Google Scholar

13. Song, J. and S. Jain, "Midpoint summation: A method or accurate and efficient summation of series appearing in electromagnetics," IEEE Antennas and Wireless Propagation Letters, Vol. 9, 1084-1087, Dec. 2010.
doi:10.1109/LAWP.2010.2091488 Google Scholar

14. Fructos, A., R. Boix, and F. Mesa, "Application of kummer's transformation to the efficient computation of the 3-D green's function with 1-D periodicity," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 1, 95-106, Jan. 2010.
doi:10.1109/TAP.2009.2036188 Google Scholar

15. Itoh, T. and R. Mittra, "A technique for computing dispersion characteristics of shielded microstrip lines," IEEE Transactions on Microwave Theory and Techniques, Vol. 22, No. 10, 896-898, Oct. 1974.
doi:10.1109/TMTT.1974.1128375 Google Scholar

16. Collin, R. E., Field Theory of Guided Waves, 2nd Ed., Piscataway, IEEE Press, 1991.

17. Zeng, Z., J. Song, and L. Zhang, "DC limit of microstrip analysis using the spectral domain approach with both transverse and longitudinal currents," IEEE Antennas and Wireless Propagation Letters, Vol. 6, 560-563, Dec. 2007.
doi:10.1109/LAWP.2007.909961 Google Scholar

18. Shu, W., "Electromagnetic waves in double negative metamaterials and study on numerical resonances in the method of moments,", Ph.D. Thesis, Iowa State University, 2008. Google Scholar

19. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1995.

20. Jain, S. and J. Song, "Numerical acceleration of spectral domain approach for shielded microstrip lines by approximating summation with corrected integral," IEEE Electrical Performance of Electronic Packaging and Systems, Oct. 2009. Google Scholar

21. Edwards, H. M., Riemann's Zeta Function, N. Chemsford, Courier Dover Publications, MA, 2001.

22., http://en.wikipedia.org/wiki/Speed of light.. Google Scholar

Dr. Sidharath Jain

Professor Jiming Song