Role of dispersive effects in determining probe and electromagnetic parameters by Time Domain Reflectometry

Time domain reflectometry (TDR) measurements, performed in a cylindrical tube filled with air, glass beads, and water, are analyzed in the time and frequency domains. In the time domain, air and water provide contrasting results of the probe length if the standard tangent line fitting procedure is used. An alternative method, based on the time derivative of the TDR response, is introduced. Its application suggests that the anomalous result provided by the tangent method in water is explained by dispersion effects. To account for the frequency dependence of the permittivity, an analysis in the frequency domain is performed. The problems of the input function choice and of the noise control are investigated. This allows us to correct the experimental scatter function S(n) and to perform the best fit of its parameterized expression, which is theoretically evaluated from the Debye model of the permittivity. Consistent values of the probe length are derived. It is concluded that the tangent method cannot be applied for determining the geometrical and electromagnetic parameters of a probe filled by dispersive media. As an application, the calibrated probe is used for measuring the TDR trace of glass beads, which simulate sandy soils, and for deriving the frequency-dependent permittivity within the Debye model.