Study of Equivalent Circuits for Open-Ring Resonators in Coplanar Waveguide Technology

A study of open-ring resonators (ORRs) is performed in terms of equivalent circuits. This resonant particle can be intrinsically described by a simple LC equivalent circuit. The resonance is due to the behaviour of the ORR as a microstrip lambda_g/2 open end stub, so it has a distributed nature. When this particle is inserted on the back-plane of a coplanar waveguide (CPW), and combined with short-circuiting wires on the top-plane, the overall structure exhibits a pass-band where backward waves are generated. The left-handed behaviour is proved through the analysis of the phase of different length transmission lines. 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 based on different analytical approaches