Modelagem de estruturas planas no domínio espectral e aplicação de técnica numérica para obtenção dos modos de propagação em meios estratificados

Abstract

This document presents the electromagnetic modeling of simple and multilayer plane structures and the use of a numerical technique to obtain the propagation modes in different types of microwave laminates, as well as to obtain the radiated electric fields. For this purpose, the equivalent circuit method is applied in the analysis of stratified structures to determine the relationship between electromagnetic fields and surface current densities in the spectral domain, which relationship results in dyadic Green’s function. Through this function it is possible to determine the modes of propagation in the investigated structures through the application of a numerical method. In this work, the Newton-Raphson technique was implemented in Matlab and used to determine the roots of the characteristic equation, also known as the transcendental equation, obtained from dyadic Green’s function. Each root found numerically corresponds to a TE or TM mode. The study is applied to slab type structures for commercial laminates. Among the evaluated dielectrics are: Rogers RT/Duroid 5870, RO4003C, Kappa 438, TMM6, TMM10i, TMM13i and Taconic Cer 10. In a structure composed of a single dielectric layer, it is found that the TM0 mode is always present, and the other modes (example: TE1, TM1, TE2, TM2, etc.) depend on the constitutive parameters of the laminate to be established, such as electrical permittivity, magnetic permeability and dielectric thickness. The electric field scattered by the structure is determined from the dyadic Green’s function and the surfasse electric current density. In this way, sinusoidal functions with segmented edge condition are used to represent the current density present in the structure, and application of the stationary phase method to obtain the radiated electric field. Finally, the validation of this work occurs from the comparison with solutions found in the classical literature and through simulations carried out in the software Ansys Designer.