Transmission Lines Loaded With Pairs of Stepped Impedance Resonators: Modeling and Application to Differential Permittivity Measurements

Abstract

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.

Configurations of Splitter/Combiner Microstrip Sections Loaded with Stepped Impedance Resonators (SIRs) for Sensing Applications

“…This latter case is the preferred one in terms of sensitivity optimization. By choosing $\theta$ 1 = $\pi$ we achieve a similar performance as the one of the cascaded configuration [12]. …”

“…However, differential sensors can be also implemented by means of a single transmission line loaded with a pair of resonant elements [11,12], or with a pair of resonators coupled to it [13,14,15]. In this latter type of sensors, the sensing principle is based on frequency splitting.…”

“…The first implementation of such sensors was presented in [11], where the sensing element consisted of a microstrip line loaded with a pair of SIRs placed at the same position in the line (parallel configuration, see Figure 1a). In this configuration, the SIRs are inductively coupled, and this causes sensitivity degradation at small perturbations, as discussed in [11,12]. One solution to prevent inter-resonator coupling is to place the SIRs at different positions along the line (cascade connection, see Figure 1b [12]).…”

“…In this configuration, the SIRs are inductively coupled, and this causes sensitivity degradation at small perturbations, as discussed in [11,12]. One solution to prevent inter-resonator coupling is to place the SIRs at different positions along the line (cascade connection, see Figure 1b [12]). In this case, the transmission zeros are given by the intrinsic resonance frequencies of both resonators, and it was argued in [12] that by spacing the SIRs λ /2, where λ is the guided wavelength at SIR resonance, the equivalent circuit model is the one of the parallel configuration but without inter-resonator coupling.…”

Extremely Sensitive Microwave Sensor for Evaluation of Dielectric Characteristics of Low-Permittivity Materials

“…The main advantages of SRR-and CSRR-based sensors are the small size with high sensitivity, lower cost with robustness, and high precision. The performance of the planar microwave sensor depends on the resonating structure as well as the hosting transmission line [43][44][45][46][47][48].…”