Comparison between Frequency Domain and Time Domain Methods for Parameter Reconstruction on Nonuniform Dispersive Transmission Lines

In this paper, we present two methods for the inverse problem of reconstructing a parameter profile of a nonuniform and dispersive transmission line — one frequency domain and one time domain method. Both methods are based on the wave splitting technique, but apart from that the methods are mathematically very different. The time domain analysis leads to hyperbolic partial differential equations and an inverse method based on solving implicit equations. The frequency domain analysis leads instead to Riccati differential equations and an inverse method based on optimization. The two methods are compared numerically by simulating a reconstruction of a soil moisture profile along a flat band cable. A heuristic model of the dispersion characteristics of a flat band cable in moist sand is derived. We also simulate the effect parasitic capacitances at the cable ends has on the reconstructions. The comparison shows that neither method outperforms the other. The time domain method is numerically much faster whereas the frequency domain method is much faster to implement. An important conclusion is also that it is crucial to model the connector parasitic capacitances correctly — especially if there are impedance mismatches at the connectors. 2 Lundstedt and Norgren