Search search
Publication Date
to
Vol. 22
Latest Volume
All Volumes
PIERM 139 PIERM 138 PIERM 137 PIERM 136 PIERM 135 PIERM 134 PIERM 133 PIERM 132 PIERM 131 PIERM 130 PIERM 129 PIERM 128 PIERM 127 PIERM 126 PIERM 125 PIERM 124 PIERM 123 PIERM 122 PIERM 121 PIERM 120 PIERM 119 PIERM 118 PIERM 117 PIERM 116 PIERM 115 PIERM 114 PIERM 113 PIERM 112 PIERM 111 PIERM 110 PIERM 109 PIERM 108 PIERM 107 PIERM 106 PIERM 105 PIERM 104 PIERM 103 PIERM 102 PIERM 101 PIERM 100 PIERM 99 PIERM 98 PIERM 97 PIERM 96 PIERM 95 PIERM 94 PIERM 93 PIERM 92 PIERM 91 PIERM 90 PIERM 89 PIERM 88 PIERM 87 PIERM 86 PIERM 85 PIERM 84 PIERM 83 PIERM 82 PIERM 81 PIERM 80 PIERM 79 PIERM 78 PIERM 77 PIERM 76 PIERM 75 PIERM 74 PIERM 73 PIERM 72 PIERM 71 PIERM 70 PIERM 69 PIERM 68 PIERM 67 PIERM 66 PIERM 65 PIERM 64 PIERM 63 PIERM 62 PIERM 61 PIERM 60 PIERM 59 PIERM 58 PIERM 57 PIERM 56 PIERM 55 PIERM 54 PIERM 53 PIERM 52 PIERM 51 PIERM 50 PIERM 49 PIERM 48 PIERM 47 PIERM 46 PIERM 45 PIERM 44 PIERM 43 PIERM 42 PIERM 41 PIERM 40 PIERM 39 PIERM 38 PIERM 37 PIERM 36 PIERM 35 PIERM 34 PIERM 33 PIERM 32 PIERM 31 PIERM 30 PIERM 29 PIERM 28 PIERM 27 PIERM 26 PIERM 25 PIERM 24 PIERM 23 PIERM 22 PIERM 21 PIERM 20 PIERM 19 PIERM 18 PIERM 17 PIERM 16 PIERM 14 PIERM 13 PIERM 12 PIERM 11 PIERM 10 PIERM 9 PIERM 8 PIERM 7 PIERM 6 PIERM 5 PIERM 4 PIERM 3 PIERM 2 PIERM 1
All Journals
PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2011-12-20
Efficient and Accurate Approximation of Infinite Series Summation Using Asymptotic Approximation and Fast Convergent Series
By
Sidharath Jain,

    Dr. Sidharath Jain

    R&D Engineer

    Microsoft Corporation

    USA

    Homepage

Jiming Song

    Professor Jiming Song

    Electrical and Computer Engineering

    Iowa State University

    USA

    Homepage

Progress In Electromagnetics Research M, Vol. 22, 191-203, 2012
doi:10.2528/PIERM11100810 | Google Scholar

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.
Download Full Article (839) View Full Article volume
Citation
Sidharath Jain, and Jiming 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        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

Download Full Article (839) View Full Article volume


The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.