Simultaneous reconstruction of two parameters from the transient response of a nonuniform LCRG transmission line

Abstract

A time-domain method to determine two of the physical parameters L, C, R, and G of a nonuniform transmission line, from the knowledge of the remaining two parameters and the transient response of the line, is presented. The method is based on the recently introduced compact Green functions approach. It is shown that any pair of the parameters can be reconstructed if L and C are considered in terms of the characteristic impedance Z and the wavefront speed c. The impedance is assumed to be continuous along the nonuniform line, but may be discontinuous at the end. It is shown that a discontinuity at the end both simplifies the reconstruction and makes the reconstruction less sensitive to noise. The parameters R and G, which both represent losses, are the most difficult to reconstruct. It is found that reconstructions involving c as well as reconstructions of R and G fail under certain conditions, at certain points along the line. The method is tested numerically for all combinations of parameters, and the failure to determine the parameters at some points is illustrated. The influence of noise is also illustrated. The present method should be useful as a fast analysis tool for time domain reflectometer measurements.