Accurate reconstruction of permittivity from coaxial transmission line measurements

In the high frequency regime (mega-Hertz to giga-Hertz) accurate permittivity measurements become complicated, as the relation between the measured quantities from which it can be derived and the permittivity itself, becomes highly non-linear. It is common to place the material in a coaxial transmission line [Nguyen 1999] or coaxial-circular wave-guide [Taherian et al. 1991] and [Belhadj-Tahar et al. 1990] and measure the S-parameters of the set-up with a Network Analyser. The S-parameters are then modelled using transmission line, or full-wave theory depending on the type of the sample holder. By means of an optimisation procedure the permittivity is then calculated. However, the coaxial-circular wave-guide technique requires relatively small samples, and so far, no fluid flow through the sample has been achieved. To our knowledge, this is the first time that the full scattering (S-parameter) matrix is modelled with transmission line theory, improving the accuracy of the results. We have designed a coaxial transmission line to perform accurate permittivity measurements in the high frequency regime for relatively large sandy samples. It also allows for simultaneous measurements of capillary pressure, so that electrical properties can be related to the saturationdesaturation history of the sample. In a companion paper [Gorriti et al., 2002] we present the tool and the accuracy of its corresponding forward model. In this paper we present the results obtained for several calibration materials and the limitations of the technique so far.