Paolo Castiglione and Jon Wraith. Montana State University, 818 Leon Johnson Hall, Bozeman, MT 59715
TDR measurements of electrical conductivity rely on knowledge of the cell constant (Kp), a quantity characteristic of the probe which can be determined through calibration in electrolyte solutions of known conductivity or indirectly from estimates of the probe characteristic impedance. The cell constant is considered a non-variable quantity, determined solely by the probe geometry. However, for a homogeneous medium of given conductivity, the sample resistance and therefore Kp is determined by the electrical field distribution in the plane transverse to the probe rods. Any perturbation to the electrical field results in a change of the effective cell constant, which may deviate from the calibration value and result in conductivity measurement errors. TDR probes for soils applications are typically open designs to allow for mass flow through the region of measurement sensitivity. As a consequence, the electric field extends beyond the outer rods, and is subject to perturbation by external factors. We found that the response to external constraint or interference strongly depends on the probe geometry. Common sources of interference for TDR EC measurements include the presence of additional probes connected to common multiplexers, and insulating boundaries within the probe's electric field. The dependence of the cell constant on the electric field distribution is derived explicitly, and analytical expressions for Kp are provided for common probe geometries. In particular, an approximate expression for the common three-rod configuration is derived. A simple numerical procedure is also presented, which permits calculation of the (effective) cell constant for arbitrary geometry and boundary conditions. A series of experiments carried out in electrolyte solutions and soils confirms the theoretical results within 2% accuracy.
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