PIER M
 
Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 22 > pp. 191-203

EFFICIENT AND ACCURATE APPROXIMATION OF INFINITE SERIES SUMMATION USING ASYMPTOTIC APPROXIMATION AND FAST CONVERGENT SERIES

By S. Jain and J.-M. Song

Full Article PDF (432 KB)

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.

Citation:
S. Jain and J.-M. Song, "Efficient and Accurate Approximation of Infinite Series Summation Using Asymptotic Approximation and Fast Convergent Series," Progress In Electromagnetics Research M, Vol. 22, 191-203, 2012.
doi:10.2528/PIERM11100810

References:
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

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.

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.

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.

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

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

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 eĀ±cient sda," IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 4, Part 1, 866-872, Apr. 1995.

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.

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

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

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

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

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

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

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

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

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.

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

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

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


© Copyright 2010 EMW Publishing. All Rights Reserved