Dielectric Characterization Using Reflected Group Delay of a Partially-Filled Coaxial Resonator

Abstract

This paper features an effective and novel method to characterize dielectric materials using the reflected group delay of an over-coupled partially-filled coaxial resonator. The method employs a simple and cost-effective approach by utilizing one-port measurements from a Vector Network Analyzer to determine the dielectric constant and loss tangent of a dielectric material filled inside a coaxial resonator. Simulations using Advanced Design System by PathWave and ANSYS Electronics Desktop are done to test the mathematical model under different scenarios. Based on the results obtained from simulations, the proposed method can determine the dielectric constant and loss tangent with an error of less than 2% and 30% respectively, when operated to have a coupling coefficient in the range of 2.5 to 10. A region of confidence is derived by taking into account the effect of systematic errors to determine the maximum expected error in the calculated values of dielectric constant and loss tangent. The region of confidence describes that the resonator when filled to more than 50% of its capacity to have coupling coefficient greater than 2.5 can determine the dielectric constant and loss tangent of a material with an error of less than 5% and 80% respectively. However, by limiting the value of coupling coefficient the error in the loss tangent can be restricted under 30%. A coaxial resonator is designed and fabricated, and Teflon is tested in order to validate the proposed method. A hollow Teflon rod is tested twice for different values of coupling capacitance to confirm the repeatability of the method. Soil samples with different moisture contents are tested to confirm the capacity of the method in testing different types of materials. Each of the soil sample is tested three times and standard deviation in the calculated values of the dielectric properties re-confirmed the repeatability of the method. The proposed method is considered appropriate to test the dielectric properties of solid materials which can be machined to fit inside the hollow cavity of the resonator and other materials like soils, fine particle solids, grains and liquids.

Keywords

• Coaxial resonator
• dielectric materials
• dielectric measurements
• microwave filters
• one-port measurement
• reflected group delay