Nonlinear Operation of Resonant Sensors Based On Weakly Coupled Resonators: Theory and Modeling

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Jerome JuillardPietro Maris Ferreira

Abstract

This theoretical work investigates the properties of nonlinearly operated weakly coupled resonators (WCRs) for resonant sensing applications. We propose an analysis framework for mutually injection-locked oscillators (MILOs) and mode-localized oscillators (MOLOs), subject to nonlinear restoring and damping forces. Under some simplifying assumptions, three sensor architectures are investigated and compared, highlighting several common features, such as: 1) the insensitivity of the amplitude ratio output metric to the A-f effect and 2) the instability of one oscillation state above a threshold amplitude. These results are illustrated and validated using transient simulations. Their range of validity is then discussed with finite perturbations, finite bandwidth, measurement noise, and nonlinear dissipation-fluctuation.

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