Effects of Losses on the Sensitivity of Reflective-Mode Phase-Variation Liquid Sensors

This article is focused on the analysis of the effects of losses on the sensitivity of reflective-mode phase-variation liquid sensors implemented by means of an open-ended (either quarter-wavelength or half-wavelength) transmission line distributed resonator (the sensing element) cascaded to a set of high/low impedance inverters (implemented by means of quarter-wavelength line sections). The device operates at a single frequency, and the working principle is the variation of the phase of the reflection coefficient (the output variable) caused by changes in the dielectric properties of the material under test (MUT), a liquid in this study. Since liquids are lossy samples, it is expected that the sensitivity of the sensor is influenced by losses, an aspect demonstrated in this article. It is shown that two operation regimes can be distinguished: 1) the low-loss regime, where the sensitivity is influenced by MUT losses, but the behavior is similar to the one of the lossless case and 2) the high-loss regime, where losses not only play a key role on the sensitivity but also modify the dependence of the output variable with the dielectric constant of the liquid under consideration compared to the lossless case. Nevertheless, contrary to general belief, with an adequate sensor design, losses might be beneficial in order to boost the sensitivity in the limit of small perturbations (this is the main contribution of this article). Validation is carried out by considering different types of oil samples and various sensing devices operating either in the low-loss regime or the high-loss regime.