Frequency-Dependent Multiconductor Transmission Line Model With Collocated Voltage and Current Propagation

Abstract

This paper reviews the classical multiconductor transmission line (MTL) equations and proposes additional constraints on these equations. A fundamental physical constraint is that the voltage and current waves must be collocated and travel together with the same propagation function. Based on this condition, the Revised Multiconductor Transmission Line (RMTL) equations are proposed. As opposed to the classical MTL equations that require complex frequency-dependent transformation matrices for their diagonalization, the RMTL equations can be diagonalized very accurately using a single real constant transformation matrix. A new Frequency-Dependent Line Model (FDLM) is proposed based on the RMTL equations. FDLM is compared with the two most accepted frequency-dependent line models in the Electromagnetic Transients Program (EMTP): The JMARTI model (fdLine) that uses a constant transformation matrix as an approximation, and the phase-coordinates Universal Line Model (ULM) that fits the frequency dependence of the transformation matrices. These time-domain models are compared with a reference frequency-domain solution for a double-circuit vertical line.