Highly Sensitive Coplanar Waveguide (CPW) Reflective-Mode Phase-Variation Permittivity Sensors Based on Weakly Coupled Step-Impedance Resonators (SIRs)
Pau Casacuberta, Paris Vélez, Jonathan Muñoz-Enano, Lijuan Su, Ferran Martı́n
Abstract
This article presents a small-sized and highly sensitive planar microwave permittivity sensor based on a pair of weakly coupled step-impedance resonators (SIRs), the sensing elements. The sensor, a one-port structure, is implemented in coplanar waveguide (CPW) technology, and it operates in the reflection mode. The sensing principle is the variation in the phase of the reflection coefficient at the operating frequency, the output variable, caused by the changes in the dielectric constant of the material under test (MUT). This article demonstrates that the maximum sensitivity is inversely proportional to the square of the electric coupling coefficient between the sensing SIRs. Thus, the sensitivity can be unprecedentedly enhanced by merely separating enough the coupled SIRs (thereby reducing their mutual coupling). Since the sensing area is circumscribed to the region occupied by the square (capacitive) patches of the SIRs, it follows that the proposed sensor exhibits also a very high figure of merit ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\text {FoM} = 26\,551^{\circ} /\lambda ^{2}}$ </tex-math></inline-formula> ), or ratio between the maximum sensitivity and the size of the sensing area expressed in terms of the squared guided wavelength, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda ^{2}$ </tex-math></inline-formula> .