Clarification and calibration of reflection coefficient for electrical conductivity measurement by time domain reflectometry

Abstract

Measurement of electrical conductivity by time domain reflectometry (TDR) requires knowledge of the source step voltage, which is often implicitly accounted for in the measured reflection coefficient. Errors may arise, however, from imperfect amplitude calibration when transforming the voltage signal into the reflection coefficient signal. This instrument error was identified as a considerable source of error in addition to cable resistance for TDR electrical conductivity measurements. The effect of the instrument error due to imperfect amplitude calibration was theoretically examined by the direct current circuit model and experimentally verified. The instrument error resulted in an overestimation of electrical conductivity while the cable resistance led to an underestimation. We clarified that the series resistors model for correction of cable resistance is accurate if the measured reflection coefficient is corrected for the instrument error. A calibration (correction) method for the measured reflection coefficient was proposed to account for both the instrument error and the effect of cable resistance, leading to a simple, accurate, and theoretically sound procedure for TDR electrical conductivity measurements.