Losses Assisted Sensitivity Enhancement in Reflective-Mode Phase-Variation Permittivity Sensors Based on Weakly Coupled Distributed Resonators

This letter demonstrates that losses [including substrate losses and losses in the material under test (MUT)] can be beneficial to boost the sensitivity in one-port reflective-mode phase-variation planar permittivity sensors based on a pair of weakly coupled quarter-wavelength resonators (the sensing elements). It is shown that the key aspect of optimizing the sensitivity in the limit of small perturbations of the dielectric constant of the MUT in the vicinity of the reference dielectric constant is to achieve a high slope in the phase of the reflection coefficient at the operating frequency and the output variable. Depending on the level of losses, such phase slope can be either negative (low-loss regime) or positive (high-loss regime). Nevertheless, the relevant aspect is that, regardless of its sign, the magnitude of the phase slope can be arbitrarily high by adequately designing the sensor considering the device and MUT losses. Thus, losses do not necessarily degrade sensitivity; instead, they can be strategically utilized to achieve unprecedented sensitivities in this type of sensor, which operates based on the measurement of the reflection coefficient phase.