# On the Unique Determination of Modal Multiconductor Transmission-Line Properties

## TL;DR

This paper presents a novel method to uniquely determine modal transmission-line properties by relating voltage and current transformations through physical power equivalence, resolving longstanding non-uniqueness issues.

## Contribution

It introduces a new relation between voltage and current transformation matrices based on physical principles, enabling unambiguous extraction of modal properties.

## Key findings

- Successfully derives unique modal properties for various conductor systems.
- Validates the method with multiple practical examples.
- Overcomes limitations of previous arbitrary normalization approaches.

## Abstract

Some modal (or decoupled) transmission-line properties such as per-unit-length impedance, admittance, or characteristic impedance have long been held to be, in general, non-unique. This ambiguity arises from the nature of the similarity transformations used to relate the terminal and modal domains, for which the voltage transformation matrix has been shown to be only loosely related to the corresponding current transformation matrix. Modern methods have attempted to relate the two, but these relations typically rely on arbitrary normalizations, leading to strictly incorrect and/or non-unique results. This work introduces relations between the two transformations, derived from the physical equivalence of total power and currents between the two domains, by which the transformation matrices can be unambiguously related to each other, and the modal properties uniquely solved. This technique allows for the correct extraction of the modal transmission-line properties for any arbitrary system of conductors. Multiple examples are studied to validate the proposed solution process.