A new tool for accurate S-parameters measurements and permittivity reconstruction

In this paper, we present a tool for permittivity reconstruction. The tool consists of a coaxial transmission line and a novel analytical reconstruction technique. The line is designed for accurate permittivity measurements of soil samples. It allows for single or double phase flow. The full S-parameter matrix is modeled with transmission line theory. We show that for accurate measurements each component of the tool needs careful calibration. We give a method to compute the sensitivity of these measurements to different materials, and we show the accuracy in the determination of the sample permittivity from the measurements based on deviations of the forward model compared to measured results as a function of the error in the sample permittivity. We demonstrate that a maximum error of less than 1% is obtained for the possible permittivity reconstruction from these measurements for wavelengths less than five times the sample holder length. The novel reconstruction technique is based in the propagation matrices method. It consists in rewriting the transmission line model in matrix notation and relating the S-parameters to the total reflection and transmission of the line seen as a two-port network. Thanks to this novel approach, the reconstruction of both permittivity and permeability can be done directly from the measured S-parameters of the line. Due to experimental instabilities the errors are considerable, and we must restrict ourselves to the reconstruction of permittivity. Results on an air sample are within the predicted error of 1%. Computing relative errors for an ethanol sample is not possible due to temperature and purity difference between our experiment and published results; nevertheless, the reconstructed permittivity of ethanol follows the Debye model.