Complex Resonances of a Circular Patch in a Multi-layered Medium: A Regularized Analysis

Antennas and resonators based on microstrip technology have been widely studied due to their attractive properties such as low weight and cost, conformability and ease of manufacturing, resulting in a huge number of applications including mobile satellite communications, direct broadcast satellite services and nondestructive testing sensors in permittivity and porosity measurements. Full wave methods are commonly used for the analysis of microstrip circuits and structures in stratified media, as they can take into account the effect of the electromagnetic coupling, surface waves, and radiation losses. Consequently they are more accurate than quasi-static methods and other simplified equivalent models. Of course, the drawback is a greater complexity of the overall method. Among the possible full-wave techniques used to analyse non-shielded structures, spectral domain integral equation formulations are probably the most common when dealing with cylindrical structures or planar surfaces involving stratified media. In general, the obtained integral equation in the spectral domain does not admit a closed form solution, but it can be suitably recast into a well-posed matrix operator equation by means of the method of analytical preconditioning [1]. It consists of the discretization of the integral equation by means of Galerkin's method with a suitable set of expansion functions leading to a matrix equation at which Fredholm's or Steinberg's theorems can be applied. In literature, it has been widely shown that this goal can be fully reached by selecting expansion functions reconstructing the physical behaviour of the fields on the involved objects with a closed-form spectral domain counterpart [2]. With such a choice, few expansion functions are needed to achieve highly accurate results and the convolution integrals are reduced to algebraic products. The aim of this paper is the introduction of a new accurate and efficient analytical technique to study the complex resonances of a circular patch in a multilayered medium. The problem is formulated as an EFIE in the spectral domain and is discretized by means of functions reconstructing the expected physical behaviour of the curl-free and divergence-free contributions [3] of the surface current density, which form a complete set of orthogonal eigenfunctions of the most singular part of the integral operator. In such a way, the overall problem is analytically regularized.