Enhancing output linearity of weakly coupled resonators by simple algebraic operations

Abstract The mode-localized weakly coupled resonators (WCRs) based on amplitude ratio modulation exhibit great advantages in relative mechanical sensitivity and ambient robustness compared with traditional frequency-modulated resonators. However, due to the inherent strong nonlinearity across the veering point, the further high-performance application of mode localized sensors is still limited. In this paper, for the first time, a new output metric based on the subtraction of reciprocal amplitude ratios (SRAR) is proposed to enhance the output linearity of WCRs. The implementation of this proposal only requires an additional algebraic operation module in subsequent signal processing without changing the device architecture. The linearity of SRAR-based readout is theoretically proven to be significantly better than that of amplitude ratio readout, whether in a vacuum or non-vacuum circumstance. Besides, the numerical calculations and simulations indicate that our proposal maintains superior linearity in the presence of structural non-ideal errors. Finally, the linearity enhancement of the SRAR-based output metric is experimentally verified based on the fabricated prototype of a mode localized accelerometer.