A coaxial transmission line for accurate permittivity measurements from 300 MHz to 3 GHz

The permittivity of porous media is usually measured from very low frequencies up to the giga- Hertz region, where it becomes constant for most natural materials and which is also the range of interest for field applications using geo-radar techniques. On the low frequency regime, up to hundreds of mega-Hertz, the so-called direct methods are being used. Generally, the material is placed between two parallel plates and the impedance or admittance of this capacitor is measured so that the permittivity is calculated directly from these measured quantities, see for i.e. [Bona et al. 1998] and [Shen et al. 1987]. On the high frequency regime, the relation between the permittivity and the measured quantities is no longer linear for reasonably sized sample holders and more complex set-ups have to be implemented. It is common to place the material in a coaxial transmission line [Shen 1985] and [Nguyen 1999] or coaxial-circular wave guide [Taherian et al. 1991] and measure the S-parameters of the set-up with a Network Analyser. The S-parameters are then modelled using transmission line theory. By means of an optimisation procedure the permittivity is calculated, or when possible, the S-parameters of the section of the line filled with the material are extracted [Shen 1985, Compensation Parameters method] and then the permittivity is calculated directly from an explicit analytic expression [Weir 1974]. We have designed our tool such that the same material can be characterised over the whole frequency range, so that it can work as a coaxial capacitor in the low frequency regime and as a coaxial transmission line in the high frequency regime. Moreover, we want to test which of the two existing methods to calculate permittivity from the S-parameters lead to the best results. The method known as the Compensation Parameters was not satisfactory because it suffers from many resonant frequencies at which the calculated parameters are unstable. In this paper we present the tool and its forward model, in a companion paper [Gorriti et al., 2002] we present the results obtained for several materials and the limitations of the technique.