Accuracy of bulk electrical conductivity measurements with time domain reflectometry

Abstract

Accurate determination of bulk electrical conductivity with time domain reflectometry (TDR) requires calibration or direct measurement of the probe constant and the cable resistance. The aims of this study were threefold. First, the accuracy of an analytical expression for the direct determination of the probe constant was evaluated for three TDR probe designs by comparing the analytical result with the probe constant obtained by calibration to TDR measurements in solutions with varying electrical conductivity. Second, the accuracy of direct measurement of cable resistance was compared with the accuracy that can be achieved by calibrating this resistance. The uncertainty in directly measured and calibrated probe and cable properties was determined in a Monte Carlo analysis. The results showed that the analytical expression for the probe constant and calibration of the probe constant do not provide significantly different estimates when the uncertainty in both approaches is considered; however, the uncertainty in the calibrated probe constants was lower than or similar to the uncertainty in the direct measurements. Directly measured and calibrated cable resistance differed, which was attributed to recording time issues. It was concluded that calibration of probe and cable parameters should be preferred over direct measurements to achieve accurate bulk electrical conductivity measurements. The final aim of this study was to quantify how the various sources of uncertainty identified in this study affect the accuracy of TDR bulk conductivity measurements. This uncertainty analysis showed that the accuracy of TDR ranges between 0.6 and 1.2% of the bulk electrical conductivity if the reflection coefficient varies between -0.75 and 0.75. Outside this range, the accuracy of the bulk electrical conductivity measurements made with TDR is lower.