Model for the Evaluation of the Loss Tangent of a Dielectric Material with a Scanning Split-Ring Resonator Probe

Recently an approach for fast quantitative surface scanning of dielectric permittivity at microwave frequency using a single split ring resonator (SRR) was presented [1]. While an analytical solution for retrieving the dielectric permittivity from raw measurement data was developed and experimentally verified, the quantification of the dielectric loss evaluated using the same technique remains an unsolved problem. Here we propose a model for estimation of the complex dielectric properties of materials from the experimental measurements of the transmission coefficient determined by the SRR probe. The relative permittivity and the loss tangent of a dielectric substrate are evaluated from the resonant frequency and Q-factor of the SRR probe placed in contact with the substrate. The response of the SRR test probe is related theoretically to the complex permittivity by considering an equivalent circuit in terms of the capacitance and radiation resistance of the SRR.