Broadband Measurement of Substrate Complex Permittivity Using Optimized ABCD Matrix

In this paper, a novel two-transmission-line method based on optimized ABCD matrix for broadband and continuous substrate dielectric characterization is presented. The original single-line algorithm is firstly discussed and simulated, while the measurement shows that the extracted parameters are far from the actual values due to the presence of microwave connectors and transition mismatches. Therefore, a modified two-line algorithm based on the optimized ABCD matrix is proposed for ungrounded coplanar waveguide (UGCPW) configuration, which is very suitable for electroplating circuits with a consistent conductor layer on newly developed substrates. A comprehensive procedure to calculate the total line attenuation, phase number, characteristic impedance, substrate dielectric constant, and dielectric loss tangent is described. Since both conductor and radiation losses are taken into account, the extracted results show consistency within a single-digital percentage with the reference values. The analysis of the measurement uncertainty and the related uncertainty budgets for the derived dielectric results are also presented. The proposed method is expected to be applied to any transmission lines with arbitrary characteristic impedance, without a prior knowledge of substrate dielectric constant, and no additional calibrations are required other than the calibration kit for Vector Network Analyzer (VNA).