Estimation of conductive losses in complementary split ring resonator (CSRR) loading an embedded microstrip line and applications

In this paper, a simple method to estimate the conductive losses in complementary split ring resonators (CSRRs) is proposed. It is based on the measurement of the transmission coefficient (insertion loss) in an embedded microstrip line with the CSRR under consideration etched in the ground plane, beneath the conductor strip. It is assumed that losses are due to the substrate (dielectric losses) and CSRR (ohmic and dielectric losses) since conductive losses in the strip of the line are negligible. By considering the circuit model of the CSRR-loaded line, including the substrate conductance plus the conductive (ohmic resistance) and dielectric losses of the CSRR, it is possible to infer from the insertion loss the real part of the shunt impedance at resonance. From this value, and assuming that the loss tangent of the considered substrate is known, the ohmic resistance of the CSRR can be estimated. Once this resistance is known, it is possible to use these CSRR-loaded structures to estimate the complex permittivity of dielectric samples and liquids.