2000 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

IEEE Transactions on Microwave Theory and Techniques
Volume 48 Number 12, December 2000

Novel Closed-Form Green's Function in Shielded Planar Layered Media

Page 2225.

Abstract:

A new method is proposed for the construction of closed-form Green's function in planar, stratified media between two conducting planes. The new approach does not require the a priori extraction of the guided-wave poles and the quasi-static part from the Green function spectrum. The proposed methodology can be easily applied to arbitrary planar media without any restriction on the number of layers and their thickness. Based on the discrete solution of one-dimensional ordinary differential equations for the spectral-domain expressions of the appropriate vector potential components, the proposed method leads to the simultaneous extraction of all Green's function values associated with a given set of source and observation points. Krylov subspace model order reduction is used to express the generated closed-form Green's function representation in terms of a finite sum involving a small number of Hankel functions. The validity of the proposed methodology and the accuracy of the generated closed-form Green's functions are demonstrated through a series of numerical experiments involving both vertical and horizontal dipoles.

References

1. J. R. Mosig, "Integral equation techniques,"in Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, T. Itoh, Ed. New York: Wiley, 1988.
2. K. A. Michalski and D. Zheng, "Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, Part I: Theory", IEEE Trans. Antennas Propagat., vol. 38, pp.  335-344, Mar.  1990.
3. W. C. Chew, Waves and Fields in Inhomogeneous Media, Piscataway, NJ: IEEE Press, 1995.
4. Y. L. Chow, J. J. Yang, D. G. Fang and G. E. Howard, "A closed-form spatial Green's function for the thick microstrip substrate", IEEE Trans. Microwave Theory Tech., vol. 39, pp.  588-592, Mar.  1991.
5. M. I. Aksun, "A robust approach for the derivation of closed-form Green's functions", IEEE Trans. Microwave Theory Tech., vol. 44, pp.  651-658, May  1996.
6. C. Tai, Dyadic Green Functions in Electromagnetic Theory, Piscataway, NJ: IEEE Press, 1993.
7. D. C. Chang and J. X. Zhang, "Electromagnetic modeling of passive circuit elements in MMIC", IEEE Trans. Microwave Theory Tech., vol. 40, pp.  1741-1747, Sept.  1992.
8. F. Alonso-Monferrer, A. A. Kishk and A. W. Glisson, "Green's functions analysis of planar circuits in a two-layer grounded medium", IEEE Trans. Antennas Propagat., vol. 40, pp.  690-696,  June  1992.
9. M. J. Tsai, F. D. Flaviis, O. Fordham and N. G. Alexopoulos, "Modeling planar arbitrary shaped microstrip elements in multilayered media", IEEE Trans. Microwave Theory Tech., vol. 45, pp.  330-337, Mar.  1997.
10. Q.-H. Liu and W. C. Chew, "Application of the conjugate gradient fast Fourier Hankel transfer method with an improved fast Hankel transform algorithm", Radio Sci. , vol. 29, pp.  1009-1022, July-Aug.  1994.
11. R. C. Hsieh and J. T. Kuo, "Fast full-wave analysis of planar microstrip circuit elements in stratified media", IEEE Trans. Microwave Theory Tech., vol. 46, pp.  1291-1297, Sept.  1998.
12. T. J. Cui and W. C. Chew, "Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects", IEEE Geosci. Remote Sensing, vol. 37, pp.  887-900, Mar.  1999.
13. D. G. Fang, J. J. Yang and G. Y. Delisle, "Discrete image theory for horizontal electric dipole in a multilayer medium", Proc. Inst. Elect. Eng. H, vol. 135, pp.  297-303, Oct.  1988.
14. J. J. Yang, Y. L. Chow, G. E. Howard and D. G. Fang, "Complex images of an electric dipole in homogenious and layered dielectrics between two ground planes", IEEE Trans. Microwave Theory Tech., vol. 40, pp.  595-600, Mar.  1992.
15. F. Ling, D. Jiao and J. M. Jin, "Efficient electromagnetic modeling of microstrip structures in multilayered media", IEEE Trans. Microwave Theory Tech., vol. 47, pp.  1810-1818, Mar.  1999.
16. T. K. Sarkar and O. Pereira, "Using the matrix pencil method to estimate the parameters of a sum of complex exponentials", IEEE Antennas Propagat. Mag., vol. 37, pp.  48-55, Feb.  1995.
17. M. L. Van Blaricum and R. Mittra, "A technique for extracting the poles and residues of a system directly from its transient response", IEEE Trans. Antennas Propagat., vol. AP-23, pp.  777-781, Nov.  1975.
18. B. Hu and W. C. Chew, "Fast inhomogeneous plane wave algorithm for electromagnetic solutions in layered medium structures-2D case", Radio Sci., vol. 35, no. 1, 2000 .
19. F. Ling, "Fast electromagnetic modeling of multilayer microstrip antennas and circuits", Ph.D. dissertation, Univ. of Illinois, Urbana-Champaign, 2000.
20. E. J. Grimme, "Krylov projection methods for model reduction", Ph.D. dissertation, Univ. of Illinois, Urbana-Champaign, 1997.
21. M. Abramovitz and I. Stegun, Handbook of Mathematical Functions, Dover U.K.: 1965.
22. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipies in Fortran 77, Cambridge: U.K.: Cambridge Univ. Press, 1992.
23. R. Freund, "Reduced-order modeling techniques based on Krylov subspaces and their use in circut simulation,"in Numer. Anal. Manuscript 98-3-02, Murray Hill, NJ: Bell Laboratories, Feb. 1998.
24. A. Odabasioglu, M. Celik and L. Pileggi, "PRIMA: Passive reduced-order interconnect macromodeling algorithm", IEEE Trans. Computer-Aided Design, vol. 17, pp.  645-654, Aug.  1998.
25. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, New York: Oxford Univ. Press, 1985.