Improvement of Transmission/Reflection Method for Permittivity Measurement Using Long Fixtures With Time-Domain Analysis Approach

A transmission/reflection (T/R) method using a coaxial fixture is conventionally employed for permittivity measurements of high-loss materials. However, in this method, ripples often appear in the frequency characteristics of the measured permittivities owing to the reflections at the fixture ends. Although gating analysis for the time-domain signals have been employed to reduce these ripples, it cannot be applied to conventional T/R methods at microwave frequencies because of the short distance of the time interval between the required signal and unwanted signals to be eliminated in the gating process. To deal with the problem of eliminating the reflection effects at fixture interfaces, we used a long air line as a fixture, and analyzed the measured S-parameters by using the improved gating analysis in the time domain, where unwanted reflection signals in S-parameters in the time domain were eliminated while maintaining the continuity of the waveforms. We demonstrated its efficacy by performing numerical calculations, as well as using actual measurement data for polytetrafluoroethylene obtained with a PC-7 air line with the length of 30 cm. Furthermore, we developed a new algorithm for a rigorous uncertainty analysis of the time-domain analysis of S-parameters that considers the correlations between the measured S-parameters at different frequencies. By applying this algorithm, we evaluated the uncertainty of the proposed method for permittivity measurements.