New Procedure for Computation of Time Delays in Propagation Function Fitting for Transient Modeling of Cables

The solution of traveling-wave equations for transient analysis of transmission lines and cables requires the identification of propagation function and characteristic admittance. A given modal propagation function can be approximated as a rational transfer function associated with an exponential time delay term. Time delays should be properly assigned prior to fitting in order to compensate excessive phase lag and avoid poor fitting results. In this paper, the existing time delay calculation formula of the universal line model (ULM) is first demonstrated using the Bode's magnitude-phase relation and its error source is explained. The underlying assumption is that a modal propagation function is a minimum phase system once a suitable time delay is removed. However, the numerical implementation of the procedure can generate delays that result in high fitting errors. Then, this paper contributes to a new method for estimating time delays and improving propagation function fitting accuracy.