Coplanar Waveguides Loaded with S-Shaped Split-Ring Resonators: Modeling and Application to Compact Microwave Filters

This letter studies the transmission characteristics of coplanar waveguides (CPWs) loaded with single-layer S-shaped split-ring resonators (S-SRRs) for the first time. Two structures are analyzed: 1) a CPW simply loaded with an S-SRR, and 2) a CPW loaded with an S-SRR and a series gap. The former exhibits a stopband functionality related to the resonance of the S-SRR excited by the contra-directional magnetic fluxes through the two connected resonator loops; the latter is useful for the implementation of compact bandpass filters. In both cases, a lumped-element equivalent circuit model is proposed with an unequivocal physical interpretation of the circuit elements. These circuits are then validated by comparing the circuit response with extracted parameters to full-wave electromagnetic simulations. The last part of the letter illustrates application of the S-SRR/gap-loaded CPW unit cell to the design of a bandpass filter. The resulting filter is very compact and exhibits competitive performance.