Analytical transmission line model for complex dielectric constant measurement of thin substrates using T-resonator method

This work presents a new analytical transmission line model for microstrip T-resonator dielectric constant measurement method in order to simplify the extraction of the complex dielectric permittivity of the substrate and increase its accuracy. The proposed new formula, which is based on the T-matrix equivalent circuit of the structure, is only dependent on the propagation and attenuation constants of the stub line. Two new formulas to determine the end effect of open-ended stub and the propagation constant parameters are also presented. As an example, a T-resonator is implemented on a 31 mil RO4003C substrate, and it is simulated and measured S-parameter results in the range of 1 MHz-8 GHz are used to calculate a complex dielectric constant of the substrate at each resonance frequency. A full-wave simulation is also used to confirm the accuracy of the proposed model. The comparison between the simulated and the measured S-parameters demonstrates a relative error of <1% over the frequency range.