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arXiv · 2504.01599

Frequency-Domain Bounds for the Multiconductor Telegrapher's Equation

Daniel Selvaratnam·Alessio Moreschini·Amritam Das·Thomas Parisini·Henrik Sandberg
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Abstract

We establish mathematical bounds on the chain, ABCD and immittance matrices of a multiconductor transmission line, based on the Telegrapher's equation. Closed-form expressions for those matrices are also presented. Existing results that hold on the imaginary axis are extended to the complex plane, without reliance on a diagonalizability assumption that is prevalent in the literature. Therefore, the results remain valid under arbitrary arrangements of the conducting wires, which include electrical faults. The analysis ultimately reveals important system-theoretic implications of the Telegrapher's equation, which are of general relevance to control, power systems, and signal processing involving multiconductor transmission lines.

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Daniel Selvaratnam, Alessio Moreschini, Amritam Das, Thomas Parisini, Henrik Sandberg. 2025-04-02. Frequency-Domain Bounds for the Multiconductor Telegrapher's Equation. https://arxiv.org/abs/2504.01599

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