Highly Sensitive Transmission-Mode Phase-Variation Permittivity Sensor Based on Resonance and Antiresonance

This article presents a strategy for implementing highly sensitive planar microwave permittivity sensors operating in transmission and based on the measurement of the phase of the transmission coefficient at a single frequency. The idea is to shunt-connect a sensitive element to the host line exhibiting a zero (resonance) and a pole (antiresonance) closely spaced. By this means, the phase of the transmission coefficient experiences a significant variation between the zero and the pole, and the sensitivity can be boosted up by tuning the frequency of operation to the pole frequency. The specific implementation consists of a shunt-connected step-impedance resonator (SIR) in parallel with an inductive strip. The effects of coupling between both elements are analyzed in detail. It is shown that such coupling (magnetic) limits the achievable sensitivity. Thus, a method to circumvent such coupling between the SIR and the inductive strip, thereby enhancing the sensitivity, is presented. The maximum sensitivity in the optimized prototype, without coupling, is $S_{\max } = - 86.18^{\circ }$ , and the figure of merit (FoM), defined as the ratio between $S_{\max }$ and the area of the sensing region expressed in terms of the squared wavelength, is FoM =17380°/ $\lambda ^{2}$ .