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Modal Analysis of Weakly Coupled Electromagnetic Systems Using Tridiagonal Toeplitz Matrices

Jose Brandao Faria(1*)

(1) Department of Electrical Engineering , Instituto de Telecomunicações Instituto Superior Técnico University of Lisbon, Portugal
(*) Corresponding author



In the analysis of weakly coupled electromagnetic systems, consisting of several identical equidistant components, the coupling matrix is often approximated by tridiagonal Toeplitz matrices, whose eigenvalues and eigenvectors can be determined in closed-form. The theory of tridiagonal Toeplitz matrices is not new, it can be found in several linear algebra articles and math books, but its presentation is usually very dense and far from appealing to the electrical engineer. This paper has two goals. The first is of tutorial nature —we present a concise review of the modal analysis of tridiagonal matrices. The second goal is to call the reader’s attention to the inherent fragilities of the tridiagonal matrix approximation —we discuss and work out application examples, dealing with multiconductor transmission line systems, where the approximation is shown to clearly fail.
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Matrix Methods; Multiconductor Transmission Lines; Multimodal Propagation; Weakly Coupled Systems

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