Distributed parameters for low-frequency dielectric characterization of liquids with open-ended coaxial cell

The theory of distributed parameters is applied at low frequencies to the open-ended coaxial-line dielectric characterization technique. A procedure is proposed to determine the permittivity of liquids when the sample is placed between two dielectric beads to ensure tight closure. The technique leads to a complex transcendental equation that the authors solve. An ad hoc sample holder is built to implement the proposed method. Measurements of both polar and nonpolar liquids demonstrate the adequacy of the method and its advantages with respect to the lumped-circuit theory in the case of polar samples.

I. Introduction

Precise measurements of permittivity in the frequency domain in several frequency ranges require the use of several different experimental setups [1]. In this case, it is desirable to use the same measuring cell in all of them so as to ensure identical sample composition. For this purpose, the sample holder is often an open-ended coaxial cell. Then the circuit theory (lumped circuits) is used at low frequencies, while distributed parameters are used for high frequencies [2]. In certain cases, the sample volume should not be too small to ensure reproducibility of measurements (this can prevent or minimize undesired effects such as the influence of impurities in the sample). In this case, if the circuit theory is applied and the sample is polar, then its electrical length could limit the frequency range below the highest one that the experimental setup would allow. These arguments led to the decision to design and build a coaxial measuring cell and work with distributed parameters on the basis explained in the following sections.