Amplitude ratio calibration in mode-localized sensors with nonlinear amplitude variations

Mode-localized sensors based on weakly coupled resonators offer high sensitivity by leveraging the amplitude ratio as their output metric. In practice, however, the ideal linearity of the amplitude ratio is compromised by nonlinear amplitude variations in the resonators, compounded by noise and feedthrough interference. This paper presents a comprehensive investigation into amplitude ratio calibration of weakly coupled resonators in mode-localized sensors characterized by nonlinear amplitude variations of its internal resonators. A theoretical framework that links the dynamics of resonator amplitudes to deviations in the amplitude ratio is established, demonstrating that diminishing signal-to-noise ratios and increasing feedthrough interference distort the amplitude ratio output under large stiffness perturbations. To address these challenges, the paper introduces calibration methods, including adjustments of the DC bias voltage and a novel feedthrough cancellation algorithm designed to extract the true resonator signal from the measured composite output. The proposed calibration methods effectively restore the linearity in the amplitude ratio measurement, thereby enhancing the overall reliability for precision applications in mode-localized sensors.