Abstract
The goal of this paper is to approximate the natural frequencies of symmetric multiconductor transmission lines (MTLs). The MTLs consist of multiple parallel thin wires above the ground with a long horizontal section in the middle. The wire trajectories at the terminals can be arbitrary as long as the wires are identical. Then, the vector containing the wire currents can be expressed as a function of the current reflection coefficient matrices from the two ports. The reflection coefficient matrices are analytically approximated with an iterative approach. The iterative approach includes high-frequency phenomena and respects the nonuniformity of the wires. These effects are not considered with the classical transmission line theory. In the end, the natural frequencies of the coupled wires are approximated via fixed-point iteration. Frequency splitting, which is common for coupled resonant systems, is observed. This phenomenon is explained using common and differential modes. All analytic results are compared to a numerical reference. Very good agreement is observed.
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