Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

Defoort, Martial; Hentz, Sébastien; Shaw, Steven W.; Shoshani, Oriel

doi:10.1038/s42005-022-00861-y

Cited by 12 publications

(3 citation statements)

References 47 publications

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“…The micromechanical resonant accelerometer is sensitive to acceleration caused by the frequency, and the frequency's stability determines the resolution [27,28]. At the same time, it has been reported that a large vibration amplitude will lead to the coupling of amplitude and resonant frequency [29], so it is necessary to quickly and accurately analyze the stability of the steady-state vibration amplitude and the resonant frequency [30].…”

Section: Analysis and Experiments Of Output Stabilitymentioning

confidence: 99%

Closed-Loop Control and Output Stability Analysis of a Micromechanical Resonant Accelerometer

Liu

2022

Micromachines

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In this study, a dynamic equation for a micromechanical resonant accelerometer based on electrostatic stiffness is analyzed, and the parameters influencing sensitivity are obtained. The sensitivity can be increased by increasing the detection proof mass and the area facing the detection capacitor plate and by decreasing the stiffness of the fold beams and the initial distance between the plate capacitors. Sensitivity is also related to the detection voltage: the larger the detection voltage, the greater the sensitivity. The dynamic equation of the closed-loop self-excited drive of the accelerometer is established, and the steady-state equilibrium point of the vibration amplitude and the stability condition are obtained using the average period method. Under the constraint conditions of the PI controller, when the loading acceleration changes, the vibration amplitude is related to the reference voltage and the pre-conversion coefficient of the interface circuit and has nothing to do with the quality factor. When the loading voltage is 2 V, the sensitivity is 321 Hz/g. Three Allan variance analysis methods are used to obtain the frequency deviation of 0.04 Hz and the amplitude deviation of 0.06 mVwithin 30 min at room temperature. When the temperature error in the incubator is ±0.01 °C, the frequency deviation decreases to 0.02Hz, and the resolution is 56ug. The fully overlapping Allan variance analysis method (FOAV) requires a large amount of data and takes a long time to implement but has the most accurate stabilityof the three methods.

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Section: Analysis and Experiments Of Output Stabilitymentioning

confidence: 99%

Closed-Loop Control and Output Stability Analysis of a Micromechanical Resonant Accelerometer

Liu

2022

Micromachines

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“…Micro/nanomechanical resonator sensing technology has substantially advanced as driven by the ever-growing comprehension and utilization of fundamental physical phenomena. Various intrinsic physical phenomena, such as internal resonance [1][2][3][4] , phase synchronization [5][6][7] , phononcavity [8][9][10][11] , and mode localization [12][13][14] , have been developed and employed to overcome the sensing resolution of the resonator(s). Among these nonlinear physics explorations, notable achievements include noise reduction and stability enhancement, along with quality factor improvement through internal resonance and phase synchronization 1 .…”

Section: Introductionmentioning

confidence: 99%

A decouple-decomposition noise analysis model for closed-loop mode-localized tilt sensors

Wang,

Xiong,

Wang

et al. 2023

Microsyst Nanoeng

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The development of mode-localized sensors based on amplitude output metrics has attracted increasing attention in recent years due to the potential of such sensors for high sensitivity and resolution. Mode-localization phenomena leverage the interaction between multiple coupled resonant modes to achieve enhanced performance, providing a promising solution to overcome the limitations of traditional sensing technologies. Amplitude noise plays a key role in determining the resolution of mode-localized sensors, as the output metric is derived from the measured AR (amplitude ratio) within the weakly coupled resonator system. However, the amplitude noise originating from the weakly coupled resonator’s closed-loop circuit has not yet been fully investigated. This paper presents a decouple-decomposition (DD) noise analysis model, which is applied to achieve high resolution in a mode-localized tilt sensor based on a weakly coupled resonator closed-loop circuit. The DD noise model separates the weakly coupled resonators using the decoupling method considering the nonlinearity of the resonators. By integrating the decoupled weakly coupled resonators, the model decomposes the weakly coupled resonator’s closed-loop circuit into distinct paths for amplitude and phase noise analyses. The DD noise model reveals noise effects at various circuit nodes and models the system noise in the closed-loop circuit of the weakly coupled resonators. MATLAB/Simulink simulations verify the model’s accuracy when compared to theoretical analysis. At the optimal operating point, the mode-localized tilt sensor achieves an input-referred instability of 3.91 × 10-4° and an input-referred AR of PSD of 2.01 × 10-4°⁄√Hz using the closed-loop noise model. This model is also applicable to other varieties of mode-localized sensors.

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“…Recently, the vibrations of micro-and nano-electromechanical resonators have provided a new realm of applications for nonlinear vibrations [1][2][3][4]. Many significant advances have been made in theory [5][6][7], experiments [8][9][10], and applications [11][12][13], including exploring new phenomena uncovered in previously unattainable parameter regimes [14][15][16]. The dynamics of these systems range from simple Duffing responses [17][18][19] to more exotic responses, sometimes involving two or more interacting vibration modes [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

2022

Self Cite

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Models for nonlinear vibrations commonly employ polynomial terms that arise from series expansions about an equilibrium point. The analysis of symmetric systems with cubic terms is very common, and the inclusion of asymmetric quadratic terms is known to modify the effective cubic nonlinearity in weakly nonlinear systems. The net effect is a monotonic dependence of the vibration frequency on the amplitude squared in both cases. However, in many applications, such a monotonic dependence is not observed, necessitating the use of techniques for strongly nonlinear systems or the inclusion of higher-order terms in a weakly nonlinear formulation. In either case, the analysis involves very tedious and/or numerical approaches for determining the system response. In the present work, we propose a method that is a hybrid of the methods of averaging and harmonic balance, which provides, with relatively straightforward calculations, good approximations for the amplitude-frequency dependence and for the steady-state response of damped, driven vibrations, including information about overtone harmonics and stability. The method is described, and general results are obtained for an asymmetric system with up to quintic nonlinear terms. The results are applied to a numerical example and validated using simulations. This approach will be useful for analyzing various systems with higher-order polynomial nonlinearities.

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Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

Cited by 12 publications

References 47 publications

Closed-Loop Control and Output Stability Analysis of a Micromechanical Resonant Accelerometer

Closed-Loop Control and Output Stability Analysis of a Micromechanical Resonant Accelerometer

A decouple-decomposition noise analysis model for closed-loop mode-localized tilt sensors

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

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