The Role of Probe Attenuation in the Time-Domain Reflectometry Characterization of Dielectrics

The influence of the measurement set-up on the estimation of dielectric permittivity spectra from time-domain reflectometry responses is investigated. The analysis is based on a simplified model of the time-domain reflectometry measurement set-up, where an ideal voltage step is applied to an ideal transmission line that models the probe. The main result of this analysis is that the propagation in the probe has an inherent band limiting effect, and the estimation of the high-frequency permittivity parameters is well conditioned only if the wave attenuation for a round-trip propagation in the dielectric sample is small. This is a general result, holding for most permittivity model and estimation schemes. It has been verified on real estimation problems by estimating the permittivity of liquid dielectrics and soil samples via an high-order model of the time-domain reflectometry set-up and a parametric inversion approach.