# A Discussion on Sensitivity Optimization in Reflective-Mode Phase-Variation Permittivity Sensors Based on Semi-Lumped Resonators

## TL;DR

This paper discusses how to optimize the sensitivity of permittivity sensors using semi-lumped resonators by identifying the best operating frequency.

## Contribution

The paper identifies the optimal frequency for sensitivity optimization, which lies between the resonance and maximum phase slope frequencies.

## Key findings

- The optimal frequency for sensitivity is between the resonance and maximum phase slope frequencies.
- High-Q resonators show that these frequencies tend to coincide.
- Results are validated through electromagnetic simulations and experiments.

## Abstract

Typically, the operating frequency in single-frequency reflective-mode phase-variation permittivity sensors based on semi-lumped resonators (e.g., step-impedance resonators—SIRs) is set to the resonance frequency of the sensing resonator when it is loaded with the so-called reference (REF) material, f0,REF. For the case of an SIR-based sensor, if the ratio between the inductance and the capacitance is high (corresponding to a high-Q resonator), the sensitivity in the limit of small perturbations of the dielectric constant (in the vicinity of that of the REF material) is also high. However, the optimum frequency for sensitivity optimization in the limit of small perturbations neither corresponds to the resonance frequency nor coincides with the frequency of maximum phase slope. Such frequencies are calculated in this paper, and it is shown that the optimum frequency for sensitivity optimization is located between the frequency of maximum phase slope and the resonance frequency, although such frequencies tend to coincide for high-Q sensing resonators. This aspect is validated in this paper from electromagnetic simulation and experiment.