Behavioural modelling of MEMS oscillators and phase noise simulation

Papin, G.; Lévy, R.; Lissorgues, Gaëlle; Poulichet, Patrick; Masson, Stève; Marechal, Baptiste; Guérard, Jean; Janiaud, D.; Traon, O. Le

doi:10.1007/s10470-012-9853-4

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…However, the higher motional resistance, non-linearity and in some cases high operating frequencies increase the design complexity of the sustaining electronics. In addition, the mechanical noise of the resonator is an important factor to consider when designing an integrated circuit and several works have attempted to model it [ 221 , 226 , 227 , 228 ]. This section focuses on the particularities of MEMS resonator-based oscillators, and discusses the circuitry that is interfaced with MEMS resonators in order to implement them.…”

Section: Applicationsmentioning

confidence: 99%

“…For instance, mechanical noise can impact performance depending on the relative noise performance of the sustaining amplifier [ 225 ]. Moreover, resonant non-linear behavior can also cause close-in offset noise degradation and a higher than 30 dB phase noise slope [ 222 , 226 , 227 ]. This degradation of phase-noise, notably at low frequency offsets has pushed most MEMS oscillator designs to employ automatic gain control in the sustaining amplifier in order to reduce the non-linear behavior of the MEMS resonator, and ensure optimal close-in offset performance [ 209 , 231 , 237 , 238 ].…”

Section: Applicationsmentioning

confidence: 99%

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Micromachined Resonators: A Review

et al. 2016

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This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

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Section: Applicationsmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Micromachined Resonators: A Review

et al. 2016

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“…The LTI models are useful as a starting point but they fail to capture several important effects including the interaction of nonlinearities on noise performance, experimental observations of the up-conversion of low frequency noise and the interaction between amplitude noise and phase noise [8]. These LTI models have been extended using semi-empirical approaches but these approaches do not reveal insight into the underlying physics or enable significant design optimisation studies [5], [9]- [11].…”

Section: Introductionmentioning

confidence: 99%

An analytical formulation for phase noise in MEMS oscillators

Agrawal

Seshia

2014

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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In recent years, there has been much interest in the design of low-noise MEMS oscillators. This paper presents a new analytical formulation for noise in a MEMS oscillator encompassing essential resonator and amplifier nonlinearities. The analytical expression for oscillator noise is derived by solving a second-order nonlinear stochastic differential equation. This approach is applied to noise modeling of an electrostatically addressed MEMS resonator-based square-wave oscillator in which the resonator and oscillator circuit nonlinearities are integrated into a single modeling framework. By considering the resulting amplitude and phase relations, we derive additional noise terms resulting from resonator nonlinearities. The phase diffusion of an oscillator is studied and the phase diffusion coefficient is proposed as a metric for noise optimization. The proposed nonlinear phase noise model provides analytical insight into the underlying physics and a pathway toward the design optimization for low-noise MEMS oscillators.

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“…The behavioral model of the vibrating beam accelerometer shown in figure 3 has been presented in previous papers [2,3], it includes:…”

Section: Behavioural Modeling Of the Oscillatormentioning

confidence: 99%

A high resolution vibrating beam accelerometer working in nonlinear region for seismic ground sensor application

Lévy¹,

Papin²,

Traon³

et al. 2014

2014 Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP)

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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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Behavioural modelling of MEMS oscillators and phase noise simulation

Cited by 4 publications

References 16 publications

Micromachined Resonators: A Review

Micromachined Resonators: A Review

An analytical formulation for phase noise in MEMS oscillators

A high resolution vibrating beam accelerometer working in nonlinear region for seismic ground sensor application

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