A Novel Scaling Process for the Computation of Multiconductor Transmission-Line Modal Properties Using the Basis Invariance of Total Current and Power

It is generally regarded that some properties of the characteristic modes of multiconductor transmission lines, such as per-unit-length impedance, admittance, or characteristic impedance, cannot be meaningfully computed analytically. This inability arises from the nature of the definition of the modes – sets of relative voltages and/or currents – which in the prevailing understanding may be arbitrarily scaled. Several methods with which to compute scaling factors have been proposed, but often – and as demonstrated in this work – the results of these processes do not agree with values determined directly from field quantities or experiments. This work begins by examining several facets of multiconductor-transmission-line modes under the approximation of ideal TEM propagation: firstly, that transmission-line modes are normal, and secondly, that as a result of possessing this property, it is postulated that total currents in the terminal domain may be directly equated to those in the modal domain. It is then shown that these relations allow the scaling factors to be determined to within a sign, and as a result, modal properties may be directly computed. This technique allows for the extraction of the modal transmission-line properties for any arbitrary system of conductors. Multiple examples are studied numerically, in which it is shown that the proposed process results in much stronger agreement with field solution than other proposed processes, and further validation of the proposed process is provided though experimentally obtained data.