Measurement of Dielectric Properties Using Reflected Group Delay of an Over-Coupled Resonator

A method is proposed to determine the dielectric properties of a material placed inside a capacitively coupled coaxial transmission line resonator. The proposed method requires measured values of the magnitude of the reflection coefficient, reflected group delay and the reactance of the input impedance, all at the resonant frequencies of the empty and dielectric-filled coaxial transmission line resonator. Maintaining the lossy resonator in an over-coupled state allows for the use of the reflected group delay in the measurement of dielectric properties using the proposed method. Equations developed from ideal circuit and transmission line theory are used to estimate the dielectric constant and loss tangent of the material filling the coaxial resonator. A resonator is designed and fabricated, and the proposed method is validated through the dielectric characterization of Teflon.