Generalized Exponential Matrix Technique Application for the Evaluation of the Dispersion Characteristics of a Chiro-Ferriteshielded Multilayered Microstrip Line

Abstract

Abstract-In this work, a new analytical matrix formulation approach for the characterization of a microwave planar structure printed on a complex medium is detailed. The approach is based on the Generalized Exponential Matrix Technique (GEMT) combined with the Method of Moments (MoM)and Galerkin's procedure. The mathematical calculation development is a robust approach that exclusively uses matrix formulations starting from Maxwell's equations until the derivation of a compact form of the Green's tensor of the studied structure. Reduced complexity and calculation simplicity foundation of the applied approach have actually incited the authors to consider the case study of a complex bianisotropic lossy chiral substrate medium. The complexity of the medium is expressed by full tensors form of all four constitutive parameters: permittivity, permeability and magnetoelectric parameters, each is represented by a nine-element tensor. To investigate the electromagnetic behavior of complex media, results of particular bianisotropy cases are presented and discussed. Original results of the biaxial chiral anisotropy case are carried out, discussed and compared with data available in literature.

Complex Bianisotropy Effect on the Propagation Constant of a Shielded Multilayered Coplanar Waveguide Using Improved Full Generalized Exponential Matrix Technique

“…The considered structure is based on a complex bianisotropic medium (region 1) characterized by full 3 × 3-magneto-electric tensors expressing the cross coupling between electric and magnetic fields. Bianisotropic materials, in their general form, are characterized by the following constitutive relations [30,41,45].…”

“…Starting from Maxwell's equations and using the GEMT in the spectral domain, we come to four coupled first-order differential equations for the transverse electromagnetic field components as functions of their derivatives [40,41] given in the Fourier domain:…”

“…This paper introduces a mathematical modeling of complex media characterized by full 3 × 3 bianisotropic tensors of permittivity, permeability and magneto-electric parameters. The objective of this work is to sufficiently develop predictive mathematical models to judiciously characterize the propagation of electromagnetic waves in a suspended shielded bianisotropic three-layer CPW structure using a Full-GEM technique [28,40,41]. Three primary considerations have been exploited to accomplish new and promising results.…”

“…The efficient spectral Galerkin-based method of moments (SGMoM) is extensively used to analyze microwave planar structures [18,22,25,27,29,30,[41][42][43][44][45][46][47][48]. In our recent work [42], we presented an analytical modeling of a shielded microstrip line based on an anisotropic medium with full 3 × 3 permittivity and permeability tensors.…”

“…The herein considered complex medium is bianisotropic with non-zero magneto-electric tensors (ξ 0 and η 0 at the same time). Our previous study, presented in [41], did not treat the case of bianisotropic media with both magneto-electric tensors; only one tensor was considered non zero. The relative simplicity of this case of medium does not require a more complex resolution technique or longer calculation time.…”