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Improved Theory of Time Domain Reflectometry with Variable Coaxial Cable Length for Electrical Conductivity Measurements

Xiufu Shuai, Timothy R. Green, Sally Logsdon
Soil Science Society of America journal 2017 v.81 no.4 pp. 723-733
air, capacitance, dielectric permittivity, electrical conductivity, laboratory experimentation, mechanistic models, potassium chloride, time domain reflectometry
Core Ideas A new multisection transmission line model estimates soil bulk electrical conductivity. The new model depends on known impedances and lengths of TDR instrument components. Cable effects were corrected with lab measured steady‐state reflection coefficients. The model can be applied without fitting any empirical parameters. Although models have been developed previously, a mechanistic model is needed to estimate electrical conductivity (EC) using time domain reflectometry (TDR) with variable lengths of coaxial cable. The goals of this study are to: (i) derive a mechanistic model based on multisection transmission line theory to estimate EC using TDR readings; and (ii) test this new mechanistic model with laboratory experiments of variable EC solutions and coaxial cable length, and compare the results with four previous models. A new mechanistic model was derived from the zero‐frequency response of the reflection scatter function of a multisection transmission line comprised of a TDR probe, coaxial cable and cable tester to describe the relationship between EC and the steady state reflection coefficient. The length, reference impedance, and complex dielectric permittivity describe the sections in the TDR probe. Five parameters (length, series resistance, series inductance, shunt conductance and shunt capacitance) describe the coaxial cable section. The cable tester includes a coaxial cable and 50‐Ω source impedance. The new model requires an open and a short‐circuit measurement to measure the shunt conductance and series resistance of coaxial cable, respectively. An implementation model was further derived to measure EC based on the steady state reflection coefficients when the TDR probe is in air, short circuit, and test media. Experimental results showed that the measured EC values of KCl solutions were very close to the values measured by a standard conductivity meter, and without calibration the new mechanistic model performed as well as the three best calibrated models.