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ARS Home » Plains Area » Fort Collins, Colorado » Center for Agricultural Resources Research » Water Management and Systems Research » Research » Publications at this Location » Publication #333284
Title: Improved theory of time domain reflectometry with variable coaxial cable length for electrical conductivity measurements

Author
item SHUAI, XIUFU - Central China Normal University
item Green, Timothy
item Logsdon, Sally

Submitted to: Soil Science Society of America Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/23/2017
Publication Date: 8/17/2017
Publication URL: https://handle.nal.usda.gov/10113/6579851
Citation: Shuai, X., Green, T.R., Logsdon, S.D. 2017. Improved theory of time domain reflectometry with variable coaxial cable length for electrical conductivity measurements. Soil Science Society of America Journal. 81(4):723-733. doi:10.2136/sssaj2016.09.0297.
DOI: https://doi.org/10.2136/sssaj2016.09.0297

Interpretive Summary: A mechanistic model is needed for estimating electrical conductivity (EC) using time domain reflectometery (TDR) with variable lengths of coaxial cable. The goals of this study are to: (1) derive a mathematical model based on theory to estimate EC using TDR readings; and (2) test this new model with laboratory experiments of variable EC solutions and coaxial cable length, then compare the current results with four previous empirical models that are based on observation rather than theory. The new mechanistic model simulates a transmission line comprised of a TDR probe, coaxial cable and cable tester to describe the relationship between EC and the steady-state reflection of an electromagnetic wave. Five parameters (cable length, series resistance, series inductance, and bypass or shunt conductance and capacitance) describe the coaxial cable section. The new model requires an open-air and a short-circuit measurement, but no other calibration measurements. Experimental results showed that the measured EC values of test solutions were very close to the values measured by a standard conductivity meter, and the mechanistic model performed as well as the three best empirical models without calibration.

Technical Abstract: Although empirical models have been developed previously, a mechanistic model is needed for estimating electrical conductivity (EC) using time domain reflectometry (TDR) with variable lengths of coaxial cable. The goals of this study are to: (1) derive a mechanistic model based on multisection transmission line theory to estimate EC using TDR readings; and (2) test this new mechanistic model with laboratory experiments of variable EC solutions and coaxial cable length, and compare the results with four previous empirical 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-ohm source impedance. The new model requires an open and a short-circuit measurement to measure the series resistance and series inductance 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 the mechanistic model performed as well as the three best empirical models without calibration.