Full frequency-dependent phase-domain transmission line model

This paper presents a new model (Z-Line) for the representation of frequency-dependent multicircuit transmission lines in time-domain transient solutions. The model is formulated directly in phase coordinates to avoid the problems associated with frequency-dependent transformation matrices. The main obstacle in phase-domain modelling, which is the superposition of travelling times in the coupled-phase waves, is circumvented by separating the wave propagation into two parts: ideal propagation at the speed of light and pulse shaping by the losses. The losses are represented by a frequency-dependent impedance matrix [Z^loss(ω)] which is synthesized in the phase-domain by rational function approximations. A new coordinated-fitting procedure is introduced to ensure numerically stable fitting functions. The model is accurate, efficient, and numerically stable, and is specially suited for strongly asymmetrical line configurations where conventional models can give very inaccurate results