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Introduction
Over the past years microstrip resonators have been widely used over the range of microwave frequencies. In general, these structures are poor radiators, but by proper design the radiation performance can be improved and these structures can be used as antenna elements ([1] Damiano and Papiernik, 1994). In recent years microstrip patch antennas have became one of the most popular antenna types for use in aerospace vehicles, telemetry and satellite communication.
For the analysis and the design of microstrip antennas there have been several techniques developed such as the cavity model and the transmission line model ([1] Damiano and Papiernik, 1994; [2] Mirshekar-Syahkal, 1990). However, the accuracy of these approximate models (simple analytical methods) is limited and only suitable for analyzing simple, regularly shaped antenna or thin substrates. The spectral domain approach is extensively used in microstrip analysis and design ([2] Mirshekar-Syahkal, 1990). In such an approach, the spectral dyadic Green's function relates the tangential electric fields and currents at various conductor planes.
For a rigorous solution to the problem of a rectangular microstrip antenna, which is the most widely used configuration because its shape readily allows theoretical analysis, Galerkin's method is employed in the spectral domain with two sets of patch current expansions. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other employs Chebyshev polynomials with the proper edge condition for the patch currents ([3] Tulintsef et al. , 1991). The use of the asymptotic currents for the analysis of the microstrip antennas is new. A number of results using the asymptotic forms of the current by a combination of Chebyshev polynomials, and the asymptotic forms of the entire domain sinusoid basis function with and without edge condition, are presented and compared.
Theory
Consider a perfectly conducting rectangular patch of dimensions a ×b on a grounded uniaxial dielectric substrate of a uniform thickness h , shown in Figure 1 [Figure omitted. See Article Image.].
At low frequencies, the analysis for this structure can be done by using either the transmission model or a cavity model ([2] Mirshekar-Syahkal, 1990). However, for high-frequency operation in the millimeter-wave range, the thin substrate approximation of low frequencies is not valid and a rigorous analysis is necessary for...