Study of equivalent circuits for open-ring and split-ring resonators in coplanar waveguide technology

A study of open-ring resonators and split-ring resonators is performed in terms of equivalent circuits. The resonant particles can be intrinsically described by simple LC circuits; even if their resonant behaviours are caused by conceptually different phenomena, either distributed or quasi-static resonances can be attributed for designs with similar geometrical dimensions. When inserted on the back-plane of a coplanar waveguide, and combined with short-circuiting wires on the top-plane, the periodic structures designed so far exhibit a certain pass-band where backward waves are generated. The left-handed behaviour is proved through the analysis of the phase of different length transmission lines and can be observed for both types of resonators. Full-wave simulations and experimental results performed on manufactured prototypes validate the overall good performance of the proposed equivalent circuits. Detailed models for the different elements of the unit-cells are provided on the basis of different analytical approaches.