A Higher Order B-Splines 1-D Finite Element Analysis of Lossy Dispersive Inhomogeneous Planar Layers

Document Type : Research Article

Authors

Electrical Engineering Department, Amirkabir University of Technology (Tehran polytechnic), Tehran, Iran

Abstract

In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and transmission from inhomogeneous layer. Moreover we obtain both electric and magnetic fields in the inhomogeneous layers. The method employs a set of spline-harmonic basis functions and leads to one-dimensional integrals for system matrix elements. This fact along with the higher order nature of the basis functions provides an accurate method for the analysis of the aforementioned dispersive lossy inhomogeneous layers. The accuracy and the convergence behavior of the method are studied through several numerical examples and the results are compared with the exact solutions to establish the validity of the proposed method.

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[1]F. Bilotti, A. Toscano, and L. Vegni, “Very fast design formulas for microwave nonhomogeneous media filters,” Microw. Opt. Tech. Letters, pp.218–221, 1999.
[2]A. Toscano, L. Vegni, and F. Bilotti, “A new efficient method of analysis for inhomogeneous media shields and filters,” IEEE Trans. Electromagn. Compat., pp. 394–399, Aug. 2001.
[3] L. Sossi, “A method for the synthesis of multilayer dielectric interference coatings,” Izv, Akad. Nauk Est. SSSR Fiz. Mat., vol. 23, no. 3, pp.223–237, 1974
[4] A. Toscano, L. Vegni, and F. Bilotti, “A new efficient method of analysis for inhomogeneous media shields and filters,” IEEE Trans. Electromagn. Compat., pp. 394–399, Aug. 2001.
[5] Urbani, F., L. Vegni, and A. Toscano, “Inhomogeneous layered planar structures: An analysis of the reflection coefficients,” IEEE Trans. Magn., 2771–2774, Sep. 1998.
[6] Vegni, L. and A. Toscano, “Full-wave analysis of planar stratified with inhomogeneous layers,” IEEE Trans. Antennas Propag., Vol. 48, No. 4, 631–633, Apr. 2000.
[7] Khalaj-Amirhosseini, M., “Analysis of lossy inhomogeneous planar layers using Taylor’s series expansion,” IEEE Trans. Antennas and Propagation, Vol. 54, No. 1, 130– 135, Jan. 2006.
[8] Khalaj-Amirhosseini, M., “Analysis of lossy inhomogeneous planar layers using fourier series expansion,” IEEE Trans. Antennas and Propagation, Vol. 55, No. 2, 489–493, Feb. 2007.
[9] Khalaj-Amirhosseini, M., “Analysis of lossy inhomogeneous planar layers using method of moment,” J. of Electromagn. Waves and Appl., Vol. 21, No. 14, 1925–1937, 2007
[10] A. Hatamkhani and E. Khodapanah., “effect of substrate dielectric inhomogeneity in the dispersion characteristics of a microstrip lines,” Microw. Opt. Tech. Letters, Vol. 56, No. 8, pp.1819–1822, August 2014
[11] E. Khodapanah and S. Nikmehr., “a higher order analysis of a class of inhomogeneously filled conducting waveguide,” Progress In Electromagnetics Research, Vol. 118, 223-241, 2011 .
[12] W. C. Chew, Waves and Fields in Inhomogeneous Media, New York,IEEE Press, 1995.
[13] L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Hoboken, New Jersey: John Wiley & Sons, 2003.
[14] C. de Boor, A Practical Guide to Splines, New York: Springer-Verlag,1978.