MEMS frequency references and MEMS vibrating sensors, based on a resonator vibrating at its resonance frequency, offer interesting prospects in terms of miniaturization, cost and precision but their design optimization is difficult because multiple physical domains must be taken into account, as well as the associated nonlinearities that limit the carrier power. Once the model is set up, the simulation of the accurate phase noise that limits the sensor's precision is also a difficult matter. In this work, a behavioural model in Verilog-A is presented, that allows multi-physic simulations : mechanical, piezoelectric, electrostatic and electrical analytic descriptions including the associated nonlinear behaviours are derived. Transient and phase noise analysis are then performed with this model through the dedicated CADENCE PSS (Periodic Steady State) and Pnoise (Periodic Noise) analysis and compared to the analytical expression of the nonlinear critical amplitude, and to the standard Leeson analytical expression for phase noise. This work is the first step to improve the performances of such MEMS oscillators.

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The Vibrating Beam Accelerometer (VBA) consists in a vibrating micro beam anchored on one side and linked to a proof mass on the other side. The beam is maintained at resonance by means of an oscillator circuit, and when the proof mass is submitted to acceleration, compressive or tensile stresses are applied on the vibrating beam modifying its resonance frequency. The output of the accelerometer is a frequency measurement, its resolution is determined by the phase noise integrated over the sensor bandwidth, and its bias stability is determined by the close to carrier phase noise or frequency stability. If the beam resonator is actuated with increased force amplitude high enough to operate in the nonlinear region, far from carrier phase noise is decreased improving the sensor resolution while the close to carrier phase noise is increased deteriorating the resolution and bias stability.For inertial applications, the acceleration measurement is twice integrated to calculate the position, and as a consequence the bias stability is crucial. The bias stability is deteriorated when the beam resonator operates in the nonlinear region, this is the reason why VBAs work in the linear region for inertial applications. Concerning seismic ground sensor applications the bias stability is not considered and the important parameter is the resolution at the bandwidth determined by the frequency of the seismic waves. In this case it is then better to operate the beam resonator in the nonlinear region to improve the sensor resolution.Previous work have presented a behavioral model of the vibrating beam accelerometer including the beam resonator and the oscillator circuit taking into account the nonlinear terms. The transient and phase noise simulations are presented to show the improvement of the far from carrier phase noise and the degradation of the close to carrier phase noise while increasing the vibration amplitude in nonlinear region. These simulations are then compared to experimental measurements of the VIA vibrating beam accelerometer developed at ONERA. Finally these accelerometer noise is calculated from the phase noise simulations and the accelerometer resolution is optimized.

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