Parametric resonance: Amplification and damping in MEMS gyroscopes

The attainable resolution of inertial sensors is ultimately limited by the cumulated noise level generated in both the mechanical domain (mechano-thermal noise) and the frontend of the electrical readout circuit, provided that deterministic errors, such as quadrature errors in the case of gyroscopes, are kept under control. Improving the resolution performance of MEMS structures mounts to being able to either increase the minimum detectable signal through an increased sensitivity, or to improve the signal-to-noise ratio (SNR). This paper reports on parametric amplification and damping employed in a MEMS gyroscope. Experiments confirm that parametric modulation through electro-mechanical coupling leads to both an increase in spectral selectivity and a reduction of the equivalent input noise angular rate (from 0.0046∘/(sHz) to 0.0026∘/(sHz) for a parametric gain of 5). In a more general analysis of a MEMS resonant structure, electro-mechanical parametric amplification decreases the mechano-thermal noise associated with the resonant mode motion – the equivalent input noise acceleration was diminished from 0.033 m s−2 to 0.022 m s−2 for a parametric gain of 5. Either signal amplification or an attenuation of undesired signal components can be achieved by tuning the phase difference between the driving force and the parametric coupling. Therefore, the technique can be applied as well to reduce the quadrature error signal, which strongly constrains the maximum gain of the sensing circuit. Our experiments show a 2.2 improvement factor in SNR using a parametric amplification with a gain of 25.