Accurate time domain reflectometry measurement of electrical conductivity accounting for cable resistance and recording time

Abstract

Methods accounting for cable resistance in time domain reflectometry (TDR) based electrical conductivity measurements remain controversial, and the effect of TDR recording time has been underrated when long cables are used. A comprehensive full waveform model and the direct current (DC) analysis were used to show the correct method for taking cable resistance into account and guidelines for selecting proper recording time. The Castiglione-Shouse scaling method was found to be incorrect because the effect of cable resistance on the steady-state reflection coefficient is nonlinear. To account for cable resistance, the series resistors model is theoretically sound and should be used. The characteristic impedance of the lead cable has a frequency-dependent increase due to cable resistance, resulting in a rising step pulse and multiple reflections within the cable section. Hence, reaching the steady state takes much longer time than conventionally thought when long cables are used, in particular at very low and very high electrical conductivities. To determine the electrical conductivity accurately, the recording time should be taken after 10 multiple reflections within the probe and three multiple reflections within the lead cable.