Analysis of transmission lines loaded with pairs of coupled resonant elements and application to sensors

This paper is focused on the analysis of transmission lines loaded with pairs of magnetically coupled resonators. We have considered two different structures: (i) a microstrip line loaded with pairs of stepped impedance resonators (SIRs), and (ii) a coplanar waveguide (CPW) transmission line loaded with pairs of split ring resonators (SRRs). In both cases, the line exhibits a single resonance frequency (transmission zero) if the resonators are identical (symmetric structure with regard to the line axis), and this resonance is different to the one of the line loaded with a single resonator due to inter-resonator coupling. If the structures are asymmetric, inter-resonator coupling enhances the distance between the two split resonance frequencies that arise. In spite that the considered lines and loading resonators are very different and are described by different lumped element equivalent circuit models, the phenomenology associated to the effects of coupling is exactly the same, and the resonance frequencies are given by identical expressions. The reported lumped element circuit models of both structures are validated by comparing the circuit simulations with extracted parameters with both electromagnetic simulations and experimental data. These structures can be useful for the implementation of microwave sensors based on symmetry properties.