Complex permittivity determination only with reflection coefficient in partially filled waveguides

In this study, dielectric measurement of homogeneous materials partially loaded in rectangular waveguides is presented utilizing multi-frequency reflection coefficient (ΓM) data measured via a vector network analyser. The relation between ΓM and the complex permittivity of the material, of which the frequency behavior in the considered band is analytically modelled with a one-pole Debye relaxation model, is constructed through integral equations associated with the Dyadic Green's function of the hollow waveguide. The integral equations are then inverted to determine the complex permittivity via a root search routine based on the multivariate Newton-Raphson method, which is applied to calculate the model parameters valid for the considered frequency band. Finally, sensitivity and convergence analysis are performed for different scenarios.