Transmission lines loaded with pairs of magnetically coupled stepped impedance resonators (SIRs): Modeling and application to microwave sensors

Abstract

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.

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

“…2. Even for wide (low impedance) host microstrip lines, the coupling between SIRs cannot be neglected and it has been found that such coupling is magnetic and negative [32], as indicated in Fig. 2(b).…”

“…9, this asymmetry produces two notches in the transmission coefficient, which can be easily detected. The experimental validation of this sensing principle was reported in [32], where a conductor backed CPW transmission line loaded with a pair of symmetric SIRs was tested with and without the presence of a piece of glass on the top of one of the SIRs. As expected, a frequency response with two notches in the transmission coefficient, similar to those depicted in Fig.…”

“…Therefore, we will consider the more general case of CPWs with asymmetric SRR loading (i.e., with different SRRs forming the pair, including different inductive coupling between the line and the resonators). Moreover, since microstrip lines loaded with pairs of shunt connected stepped impedance resonators (SIRs) have been found to be useful for sensing purposes [32], we will also study in detail these lines, where coupling between resonators is also present. It is important to highlight that, in spite that SRR-loaded CPWs and SIR-loaded microstrip lines are described by distinct lumped element circuits, the phenomenology associated to inter-resonator coupling is roughly the same in both structures, and the resonance frequencies predicted by the respective models are given by identical expressions.…”

Symmetry-Related Electromagnetic Properties of Resonator-Loaded Transmission Lines and Applications

“…Like in the strategy based on single resonators, symmetry rupture by adding inclusions to the structure using paired resonators may be useful for the implementation of differential sensors and comparators [34]. Potential applications are dielectric characterization, quality control (e.g., defect detection in samples by comparison to a reference), biosensors, etc.…”

“…However, the proof-of-concept comparator illustrated in this section, firstly reported in [34], is based on a pair of shunt-connected stepped-impedance resonators (SIRs) loaded to a CPW or microstrip transmission line. Like in CPWs loaded with pairs of SRRs, there is magnetic coupling between the SIRs loaded in pairs [34]. Indeed, the expression providing the resonance frequencies is identical to that reported in Section 3.3 (Equation (2)).…”