TIME-DOMAIN SIMULATION OF MULTICONDUCTOR TRANSMISSION-LINES WITH FREQUENCY-DEPENDENT LOSSES

This paper presents a method for the time-domain simulation of multiconductor transmission lines with frequency-dependent conductor (skin effect) and dielectric losses. The method is based on a traveling-wave solution of the transmission line equations in the frequency domain, which reduces to the conventional modal solution for lossless lines when no losses are present. Time-domain simulation for the lossy case is achieved by convolving the transmission line terminal voltages with describing time-domain input and transfer impulse responses for the multiconductor line, which are easily computed from the frequency-domain solution. Attention must be given to careful formulation of the frequency-dependent conductor and dielectric losses to assure causality in the transmission line responses. The excessive numerical burden of discrete-time convolution is avoided by approximating the transmission line responses with exponential series, which may be convolved recursively, making the transmission line solution feasible and practical for large simulations. An implementation of the solution algorithm in the circuit simulation program SPICE is described. Examples are included for coupled lossy stripline and microstrip configurations, and comparisons are made to the lossless case and to the case where only constant (dc) conductor losses are present.