Novel complex dielectric permittivity measurement methods with open ended coaxial probes

Abstract

Nowadays, microwave dielectric spectroscopy is a popular research topic for scientists with use in a broad area. Microwave dielectric spectroscopy is realized with various methods. The most commonly applied methods are coaxial probe methods, transmission line methods, free space methods, resonant methods, and parallel plate capacitor methods. The open-ended coaxial probe method differs from microwave dielectric spectroscopy by being broadband, non-destructive technique. In addition, it is suitable for measuring lossy materials. The open-ended coaxial probe techniques are based on retrieving the complex dielectric permittivity (CDP) from the aperture admittance of the probe. This process is carried out by using the reflection coefficients from the vector network analyzer. These are realized in two steps. In the first step, real reflection coefficients are determined from the measured reflection coefficients from the calibration procedure. Next step, by using the relation between the aperture admittance and CDP, electrical properties are obtained. The main weakness of the technique is a high error rate that prevents accurate and stable results. This thesis first gives a brief overview of the realization of microwave dielectric measurement with an open-ended coaxial probe. It will then describe one of the previous methods, the rational functional model, for an open-ended probe technique. Validation of the method is tested in both simulation and measurement setups. Moreover, the effectiveness of methods is shown in retrieving the biological sample. In addition, the mentioned technique for a commercial probe improved in the third section. In the following section, a new method to reduce the error rate of dielectric measurements of the open-ended coaxial probe has been developed. This method takes advantage of the observation that electrical properties of materials variations are continuous functions of frequency. In particular, we derive a mathematical model that enforces spectral continuity by directly incorporating the Debye relaxation model. In addition, the robustness of the proposed methods is tested with a low-sensitive pocket network analyzer. Finally, a novel approximation in which measurement uncertainty and experimental noise are addressed in determining the CDP processes is presented. However, these effects are not considered in previous open-ended coaxial probe measurement studies. Take advantage of this extra information to enhance the improving measurement accuracy and results in similar problems. Benefit from statistical information; we define a new cost function based on maximum-likelihood estimation. The obtained results have been compared with the values given in the literature. The results of that studies demonstrated that mentioned methods are achievable in reducing errors. In addition to the open-ended coaxial probe, the proposed approach can accurately obtain the Debye parameters of the MUT. Furthermore, extending the method for different relaxation models is straightforward by introducing additional partial derivatives of the new parameters.