A Closed-Form Spatial Green’s Function for the Thick Microstrip Substrate: The Meshless Interpolation Approach
Keywords:
Microstrip, integral equation, IQ, RBF, Sommerfeld integralAbstract
In this paper the Green’s functions (GFs) of a thick microstrip in the spatial-domain is computed based on expanding the corresponding spectral-domain functions over inverse quadric (IQ) radial basis functions (RBFs). The scattered data interpolation ability of RBFs is exploited for efficient sampling of the Sommerfeld integration path (SIP), passing from close vicinity of singularities in the complex k? plane. By this, the information content of spectral-domain GFs is preserved, which makes it possible to compute the far-fields accurately. Thus, the method can be applied to the analysis of electrically large structures near layered media. The proposed method is direct with only one approximation level.
Downloads
References
A. Taflove and S. Hagness, Computational Electrodynamics, Third Edition. Artech House, 2005.
J. Jin, The Finite Element Method in Electromagnetics, 2nd John Wiley & Sons, 2002.
J. G. Van Bladel, Singular Electromagnetic Fields and Sources. Wiley-IEEE Press, 1996.
R. Bancroft, Understanding Electromagnetic Scattering Using the Moment Method. Artech House, 1996.
W. C. Chew, Waves and Fields in Inhomogeneous Media. IEEE Press, 1995.
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, no. 3, pp. 588- 592, 1991.
M. I. Aksun, “A robust approach for the derivation of closed-form Green’s functions,” IEEE Trans. Microwave Theory Tech., vol. 44, no. 5, pp. 651- 658, 1996.
F. Ling and J. Jin, “Discrete complex image method for Green’s functions of general multilayer media,” IEEE Microwave and Guided Wave Letters, vol. 10, no. 10, pp. 400-402, 2000.
Y. Ge and K. P. Esselle, “New closed-form Green’s functions for microstrip structures theory and results,” IEEE Trans. Microwave Theory Tech., vol. 50, no. 6, pp. 1556-1560, 2002.
M. Yuan, T. K. Sarkar, and M. Salazar-Palma, “A direct discrete complex image method from the closed-form Green’s functions in multilayered media,” IEEE Trans. Microwave Theory Tech., vol. 54, no. 3, pp. 1025-1032, 2006.
V. N. Kourkoulos and A. C. Cangellaris, “Accurate approximation of Green’s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1568-1576, 2006.
A. G. Polimeridis, T. V. Yioultsis, and T. D. Tsiboukis, “A robust method for the computation of Green’s functions in stratified media,” IEEE Trans. Microwave Theory Tech., vol. 55, no. 7, pp. 1963-1969, 2007.
M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antennas Propagat., vol. 58, no. 1, pp. 88-94, 2010.
J. W. Brown, R. V. Churchill, Complex Variables and Applications. McGraw-Hill, 1996.
R. W. Hamming, Numerical Methods for Scientists and Engineers. Dover Publications, 1987.
Y. Hua and T. K. Sarkar, “Generalized pencil-offunction method for extracting poles of an EM system from its transient response,” IEEE Trans. Antennas. Propagat., vol. 37, no. 2, pp. 229-234, 1989.
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, no. 3, pp. 48-55, 1995.
B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,” IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, 1999.
B. Fornberg and C. Piret, “On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere,” Elsevier J. Comput. Phys., vol. 227, pp. 2758-2780, 2008.
M. J. D. Powell. “The theory of radial basis function approximations in 1990,” Advances in Numerical Analysis: Wavelets, Subdivision Algorithms, and Radial Basis Functions, vol. 2. W. Light, Ed. USA: Oxford University Press, pp.105- 210, 1992.
G. R. Liu, Mesh Free Methods. CRC Press, 2003.
G. R. Liu and Y. T. Gu, An Introduction to MeshFree Methods and Their Programming, Springer, 2005.
A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space, Pergamon, 1966.
