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

Abstract

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.

Spatial time domain reflectometry and its application for the measurement of water content distributions along flat ribbon cables in a full‐scale levee model

“…Another possibility is to develop inversion algorithms based on a straightforward calculation of the wave propagation along the transmission line due to an incident voltage step. Here the response of the transmission line can be calculated either in the time domain [Lundstedt and Stroem, 1996;Lundstedt and He, 1996;Feng et al, 1999;Oswald, 2000;Todoroff and Lan Sun Luk, 2001;Lundstedt and Norgren, 2003;Rahman and Marklein, 2005;Greco, 2006] or in the frequency domain [Norgren and He, 1996;Heimovaara et al, 2004;Lambot et al, 2004;Leidenberger et al, 2006;Scheuermann and Huebner, 2009].…”

Fractionally Spaced Constant Modulus Algorithm for Wireless Channel Equalization

“…This combination of CMA & FSE used to implement blind adaptive algorithm for equalizer [18]. Figure 4 shows the frequency response of the microwave channel taken for simulation [16,17]. Fig.…”

Acoustic wave propagation in a macroscopically inhomogeneous porous medium saturated by a fluid

“…where c 0 is the sound speed in air, p + corresponds to right-going waves and p − corresponds to left-going waves, the sum of which equals p. This is the so-called Wave Splitting description, which was mainly used in scattering problems in the time domain in electromagnetism [17] and then adapted to the frequency domain [3]. It can be seen as a change of variables from (p, ∂ x p) to (p + , p − ).…”

“…The reflected and transmitted pressure fields are calculated from a known incident plane wave impinging at normal incidence using a Wave SplittingGreen's functions approach (WS-GF) [3]. The method can be extended to include oblique incidence by working on the appropriate component of the wavevectors.…”

“…Green's function approach.-The initialization of the procedure described above requires that p ± must be determined at x = L. To avoid this calculation, a Green's function approach [17,3] can be used. Two Green's functions…”