Finite-Element Based Eigenmode Analysis Algorithm for Standard Transmission Lines

This paper presents the development and testing of a finite-element based eigenmode analysis algorithm for standard transmission lines. The descriptions of the mathematical basis of the algorithm and the stages of its operation are given. The calculation of eigenmodes was performed by solving dual scalar wave equations using the Finite Element Method and the Arnoldi method. The Finite Element Method was applied to create equations in matrix form, and the results of their solution by the Arnoldi method are the cutoff frequencies and their corresponding leading components of transverse magnetic and electric waves. The algorithm was implemented in MATLAB and tested on various transmission line structures including rectangular waveguides with different fillings, stripline, differential stripline, microstrip, coplanar waveguide, and grounded coplanar waveguide. The algorithm's results were compared with commercial electromagnetic simulation software. The developed algorithm demonstrates matching cutoff frequencies with commercial electromagnetic simulation software results, while normalized field distributions at these frequencies show agreement with corresponding commercial electromagnetic simulation software field distributions.