Reference-plane invariant transmission-reflection method for measurement of constitutive parameters of liquid materials

We propose a new transmission-reflection method for measuring constitutive parameters of liquid samples inside an asymmetric measurement cell (a sample over a low-loss holder in vertical position inside an empty waveguide section). We derived reference-plane invariant expressions for constitutive parameters measurement of liquid samples from reference-plane dependent scattering parameters. In addition, we also applied a simple approach for unique determination of transformation factor and reference-plane distances. After, we also investigated how the performance of the proposed method could be improved by performing a differential uncertainty analysis. From this analysis, we found the following key results: (a) the accuracy of the proposed method could be enhanced for low-loss liquid samples by using thicker samples, and (b) the effect of constitutive parameters and the length of the (low-loss) sample holder on constitutive parameters measurements of liquid samples by the proposed method is a key parameter in increasing the accuracy of the measurements. Finally, we performed constitutive parameter measurements of distilled water and methanol to validate the proposed method and compared the proposed method with similar methods in the literature. From the measurements, we note that our method is especially useful for liquid sample measurements when the reference-plane transformation factors are not known a priori and/or if the measurements are carried out over a high frequency range.