Extraction of the Complex Relative Permittivity from the Characteristic Impedance of Transmission Line by Resolving Discontinuities

Abstract

This paper describes a material complex permittivity extraction technique based on four measurements of two identical coaxial (circular and rectangular) lines, distinguished by their lengths. The paper presents a combination of propagation parameters through mixing the eigenvalue principle and the lines’ characteristic impedance to improve the extraction techniques of intrinsic material parameters. However, the accuracy of some material parameters is insufficient, as the discontinuities at the feedline–ideal line interface are not adequately solved. In these cases, a new formulation of the complex effective permittivity is suggested, associating the propagation constant and the characteristic impedance for a homogeneous structure. Next, uncertain errors that can negatively impact the method are removed from the mathematical expression. Then, a characteristic impedance expression is developed in the second stage to improve the mathematical formulation. Finally, a correction coefficient in tune with reality and a polynomial function to amend the behavior of some of the curves are provided. The approach’s novelty lies in its ability to extract and correct the characteristic impedances despite discontinuity impedances at the ideal line–feedline interface. Several materials are tested with circular and/or rectangular coaxial fixtures to confirm the performance of the suggested method. The test cells are homogeneous, full, and long, at 80 mm and 100 mm (50 mm for the circular one). Determining the propagation constant from the eigenvalue of the wave cascading matrix (WCM) is a fundamental step in this method. Knowing the propagation constant helps to automatically compute a correction coefficient that depends on the fixture and the material being tested. Experimental validation is performed in the frequency range from some MHz to 10 GHz, 13.5 GHz, and 20 GHz, according to the tested material. Both test fixtures are filled with the sample material, with a vacuum considered as a reference parameter. The method’s accuracy is better than 5% on the relative permittivity parameter throughout the frequency range. All the tested samples are compared with the results using the filled two-transmission-line technique (FTTL), using only the eigenvalue determination principle. The trapper cells are coaxially circular and rectangular.