Abstract
The analysis of the electromagnetic scattering at discontinuities between equilateral triangular waveguides is studied. The complete electromagnetic solution is derived using analytical closed form expressions for the mode spectrum of the equilateral waveguide. The mathematical formulation of the electromagnetic scattering problem is based on the quasi-analytical Mode-Matching method. This method benefits from the electromagnetic field division into symmetries as well as from the plane wave formulation presented for the expressions involved. The unification of the surface integrals used in the method thanks to the plane wave formulation is revealed, leading to expressions that are very well suited for its implementation in an electromagnetic analysis and design code. The obtained results for some cases of interest (building blocks for microwave components for communication systems) are verified using other numerical methods included in a commercial software package, showing the potential of the presented approach based on quasi-analytic expressions.
Highlights
Nowadays radiofrequency systems are widely used for very diverse applications
This paper focuses on the latter type of methods, in the ModeMatching method [6]
This paper addresses the Mode-Matching method applied to the equilateral triangular geometry, giving a flexible mathematical formulation based on well-known plane waves
Summary
Nowadays radiofrequency systems are widely used for very diverse applications. The GPS system for positioning, the LTE system for mobile communications, the DBS system for digital broadcasting, and ground penetrating radar or remote security screening are some examples of the usage of the electromagnetic spectrum that extends from some GHz to several hundred GHz [1, 2]. In order to accomplish such designs, CAD (Computer Aided Design) tools have experienced a strong development over the last decades [3, 4] These tools solve Maxwell equations using numerical approaches or quasi-analytical methods [5]. This paper addresses the Mode-Matching method applied to the equilateral triangular geometry, giving a flexible mathematical formulation based on well-known plane waves. This formulation simplifies the surface integrals of the method and allows a very easy generalization to other problems involving waveguides whose modes can be written as a plane wave. In order to validate the formulation, several case studies are presented and compared with the results given by other different numerical methods from commercial software
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