Complex Dielectric Permittivity Measurements Using a Rational Functional Method with Arbitrary Open-Ended Coaxial Probes

In this paper, we present a rational function method (RFM) in order to measure complex dielectric parameters (CDP) with an open ended coaxial probe. The scattered field data is measured on the aperture of the open ended coaxial probe. Then admittance of material under test (MUT) is calculated and used as the data of the inversion scheme. The relation between the CDP and the admittance of MUT is performed via RFM. RFM presents this relation as a polynomial function and the root of polynomial consist of CDP of MUT. Although these approximation is well known and applied in previous works, the determination of required model parameters for arbitrary open ended coaxial probes (different filled coaxial lines and diameters) is detailed. In addition, these coefficients for an specific commercial probe (DAK) is found and given in tables. Moreover, validation of these coefficients are checked by comparing the rational approximation with integral formula of impedance. At the end, CDP of a reference liquid dimethyl sulfoxide (DMSO) is determined from an experimental setup and results are compared with literature. The results demonstrated that RFM method is capable of retived CDP of MUT by using the presented coefficients with DAK probes.