Improved Equivalent Circuit Model for Complementary Split Ring Resonators

Complementary split ring resonators (CSRRs) have been used in many applications for several years, such as sensors or structures for filter-size reduction. In the literature, different equivalent circuit models for CSRRs are found. We study those approaches and analyze which circuit topology gives the highest modeling accuracy. For this purpose, we use a least squares error metric to quantify the difference between the scattering matrices (S-matrices) of different equivalent circuits and the CSRRs simulated in a 3-D full-wave simulation (FWS). To identify the best circuit topology, we consider both a wide frequency range and variations of the CSRR’s size. Firstly, for each geometry, the “reference” S-matrix of the structure is found with the FWS Ansys HFSS. Secondly, the different equivalent circuits’ elements are derived by means of least mean square error minimization. Plotting the resulting errors of each investigated equivalent circuit topology over the CSRR’s size reveals which model performs best. As a next step, the best model is studied in detail and its circuit parameters’ dependencies on the CSRR’s geometry are discussed.