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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.

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