Microstrip Configurations of Reflective-Mode Phase-Variation Permittivity Sensors Based on Weakly Coupled Step Impedance Resonators (SIR): An Analysis to the Light of Circuit Duality

This paper presents and experimentally validates various topologies of one-port reflective-mode phase-variation permittivity sensors based on weakly coupled step impedance resonators (SIRs), the sensing elements, implemented in microstrip technology. The differences between such topologies concern the specific configuration, either series or parallel, of the SIR driven by the feeding (harmonic) signal, and the type of coupling, either electric or magnetic, between the SIRs. Thus, four different sensor topologies result. These sensors are modeled by lumped element circuits that describe their behavior to a very good approximation and are useful to predict the sensitivity in the limit of small perturbations. It is shown that the models of one of the pairs of these four sensors are circuit duals, and such circuit duality applies also to the models of the other pair. In all cases, a high (maximum) sensitivity is achievable provided the coupling (either electric or magnetic) between the SIRs pair is weak. Since the sensing regions in the reported sensors are also small, the resulting figures of merit (FoM), or ratio between the maximum sensitivity and the area of the sensing region expressed in squared guided wavelengths, are very competitive.