Coplanar waveguides loaded with symmetric and asymmetric pairs of slotted stepped impedance resonators : modeling, applications, and comparison to SIR-loaded CPWS

This article is focused on the analysis and modeling of coplanar waveguide (CPW) transmission lines loaded with pairs of slotted stepped impedance resonators (S-SIRs), etched in the ground planes. These structures may be described by a pair of parallel-connected transmission lines, each one loaded with a series-connected parallel resonator, and with mutual capacitive coupling between such resonators. If the structures are symmetric, the transmission coefficient exhibits a single transmission zero, related to the fundamental resonance of the SIRs, though perturbed by the effects of mutual coupling. However, if symmetry is disrupted, two notches appear, separated a distance that depends on the level of asymmetry, coupling, and CPW length. Therefore, these structures may be useful for the implementation of differential sensors and comparators. It is shown that if the S-SIR-loaded CPWs are electrically small, the structures can be modeled by a lumped element equivalent circuit. Using this model, the resonance frequencies are obtained analytically. The proposed lumped element model is validated through electromagnetic simulation and experiment, and a prototype comparator loaded with dielectric samples is fabricated and measured. Finally, the circuit model of the structure is compared to that of SIR-loaded CPW transmission lines. Despite the fact that the lumped element equivalent circuits of these structures are completely different, the equations providing the transmission zeros are formally identical.