FULL FREQUENCY-DEPENDENT PHASE-DOMAIN TRANSMISSION-LINE MODEL

This paper presents a new model (Z-Line) for the representation of fre quency-dependent multicircuit transmission lines in time-domain transi ent solutions. The model is formulated directly in phase coordinates t o avoid the problems associated with frequency-dependent transformatio n matrices. The main obstacle in phase-domain modelling, which is the superposition of travelling times in the coupled-phase waves, is circu mvented by separating the wave propagation into two parts: ideal propa gation at the speed of light and pulse shaping by the losses. The loss es are represented by a frequency-dependent impedance matrix [Z(loss)( omega)] which is synthesized in the phase-domain by rational function approximations. A new coordinated-fitting procedure is introduced to e nsure numerically stable fitting functions. The model is accurate, eff icient, and numerically stable, and is specially suited for strongly a symmetrical line configurations where conventional models can give ver y inaccurate results.