Analysis of microstrip antennas by means of the regularization via Neumann series

Microstrip antennas have become more and more attractive in electromagnetism due to their advantages, such as low profile, low cost, light weight, as far as high gain and wide bandwidth are not of paramount importance. Their field of applications is not limited to telecommunication applications in array configurations: small sources are interesting also as standard electromagnetic probes in low frequencies measurements [Kanda, 1990], and in the evaluation of electromagnetic material properties [Gagnadre et al., 1995]. Moreover, in several fields of applications the very narrow frequency bandwidth may represent an attractive peculiarity. Although a variety of shapes have been considered for the patches etched on the dielectric substrate, most of the microstrip antenna characteristics may be inferred by considering rectangular, circular or elliptical geometries. Due to the increasing interest for microstrip antennas, many methods commonly applied in electromagnetic theory have been used in their analysis, starting from empirical methods, such as Transmission Line Model or Cavity Model, up to full-wave analysis, such as Integral Equation methods, usually, but not necessarily, combined with Finite Element Method or Method of Moments. A quite exhaustive review of the various methods can be found in [Itoh, 1989]. Of course, full-wave analyses are preferable as far as accurate performance prediction is needed, and numerical computation is often too onerous, and sometimes leads to inaccurate or even completely wrong results [Hower et al., 1993], above all in the evaluation of the current distribution. In order to avoid such problems, the Method of Analytical Regularization (MAR) [Nosich, 1999] can be used. This method basically consists of splitting the (integral) operator associated to the problem into two parts, one singular, usually related to an associated problem, and one regular. If it is possible to find a set of orthogonal eigenfunctions for the singular part of the operator, then the Galerkin method, with these functions as a basis, results in a regularized discretization scheme. In this contribution we apply the Neumann series to the regularization of both scalar and vector problems arising in the analysis of planar microstrip antennas. The Neumann series, namely a series of Bessel functions summed over indexes, firstly investigated by Watson [1944], has been widely studied in 60’s by Tranter [1968], and successfully applied in scattering and related problems [Sneddon, 1966]. More recently Eswaran [1990] demonstrated that every function, the Fourier transform of which is of compact support, can be expanded by means of it.