Circuit Analysis of a Coplanar Waveguide (CPW) Terminated With a Step-Impedance Resonator (SIR) for Highly Sensitive One-Port Permittivity Sensing

This paper presents a single-frequency reflective-mode phase-variation microwave sensor devoted to the dielectric characterization of materials. The device is implemented in coplanar waveguide (CPW) technology and consists of two parts: (i) the sensing region, a step-impedance resonator (SIR) as termination of a CPW transmission line, and (ii) the design region, a cascade of high/low impedance quarter-wavelength inverters, used to boost up the sensitivity. By placing the so-called material under test (MUT) on top of the sensing region, the capacitance of the SIR is altered due to the effects of the dielectric constant of the MUT. This modifies the phase of the reflection coefficient seen from the input port, the output variable. From a circuit analysis, it is demonstrated that the sensitivity for small perturbations in the vicinity of the dielectric constant of a reference (REF) material can be optimized by setting the operation frequency of the sensor to the resonance frequency of the SIR loaded with such REF material. The maximum sensitivity in one of the reported sensors is as high as 66.5°, and the main figure of merit, defined as the ratio between the maximum sensitivity and the area of the sensing region expressed in terms of the squared guided wavelength, is $\text {FoM} = 3643^{\circ }/\lambda ^{2}$ . Such figure of merit represents a significant improvement as compared to the one of the equivalent sensor implemented by means of an open-ended quarter-wavelength sensing line. Such equivalence between the semi-lumped element (i.e., SIR-based) sensor and the fully distributed counterpart is also analyzed in the paper.