Time delay identification for transmission line modeling

Frequency dependent transmission line models of the traveling wave type requires to approximate the propagation function by a rational function plus a time delay. It is shown that to simply use the time delay of lossless propagation can lead to significant loss of accuracy of the rational approximation. A procedure is shown which optimizes the time delay together with the poles and residues of the rational approximation. This is achieved by combining Brent's method with vector fitting.