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This paper is focused on the analysis and modeling of transmission lines loaded with pairs of shunt connected stepped impedance resonators (SIRs), and their application to differential sensors for dielectric characterization, and for diagnosis and quality control of material samples by comparison to a reference. It is demonstrated that by placing the SIR junctions in the same position of the line, the SIRs are magnetically coupled. Such coupling has significant influence on the sensitivity of the sensor, determined by the split in frequency caused by an asymmetric dielectric loading of the SIRs. The circuit model of the structure, including magnetic coupling between SIRs, is proposed and validated through electromagnetic simulations and measurements. Finally, the principle of sensing is experimentally validated by a proof-of-concept demonstrator. Index Terms -Circuit modeling, stepped impedance resonator (SIR), microstrip technology, microwave sensor.

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Differential techniques are widely used in communication and sensor systems, as these techniques have been shown to improve the performance. This paper shows how differential sensing of permittivity can be conducted in a simple way. For that purpose, a microstrip line loaded with a pair of stepped impedance resonators is used in two different resonator connections: parallel and cascade. Each resonator is individually perturbed dielectrically so that: (i) when the two individual permittivities are identical, the structure exhibits a single resonance frequency; (ii) when the permittivies are different, resonance frequency splitting occurs, giving rise to two resonances (all these resonances are seen in the form of transmission zeros). The two sensing approaches are successfully validated through electromagnetic simulations and experiments. By virtue of a differential measurement, robustness against changing ambient factors that may produce sensor miscalibration is expected.

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