A Method to Measure Complex Dielectric Permittivity with Open-Ended Coaxial Probes

This work presents a new method to measure the complex dielectric permittivity (CDP) variation of materials under test (MUTs) with open-ended coaxial probes. The CDP variation of an MUT is a continuous function of frequency as modeled with various dielectric relaxation models. Hence, the accuracy and the repeatability of CDP measurements can be improved by enforcing such spectral continuity. Here, we derive a new formulation that explicitly enforces the spectral continuity via the Debye relaxation model. In particular, we construct a cost functional based on an admittance integral at the tip of an open-ended coaxial probe. The Debye model parameters are substituted into the admittance integral to form a set of nonlinear equations. Later, these equations are iteratively minimized by a Gauss-Newton-based minimization scheme, for measured reflection coefficients when the tip of the probe is in contact with the MUT. The presented method differs from the conventional CDP measurement techniques in two aspects. First, the method looks for a global solution across the investigated frequency spectrum instead of solving CDP values individually at each frequency step. Second, the Debye parameters are directly retrieved without any data-fitting. The presented method is experimentally verified with various liquid samples, and the accuracy of obtained results is compared against the literature.