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Phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator

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Abstract

Phase feedback is commonly utilized to set up a synchronized MEMS oscillator for high performance sensor application. It is a consensus that the synchronization region varies with phase delay with an ‘Anti-U’ mode. In this paper, phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator is investigated analytically and experimentally. The analytical expression for predicting the synchronization bandwidth with phase delay is derived based on the mathematic model. An additional dynamic extreme point of synchronization bandwidth actuated by nonlinearity is observed, which leads to three different types (‘U’, ‘Anti-U’ and ‘M’) of variation pattern of synchronization bandwidth as feedback tuning. The variation of frequency stability along phase delay is also studied. The synchronization bandwidth and the frequency stability have exactly opposite variation pattern with phase delay in linear oscillators while they are totally consistent in nonlinear oscillators. Experimental results validate the analytical observations. Our work provides a precise way for achieving best performance of a synchronized MEMS oscillator in the sensor application.

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Data availability statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was financially supported by the National Key Research and Development Program of China (2018YFB2002303), National Natural Science Foundation of China (11772293, 52075432) and Key research and development program of Shaanxi Province (2018ZDCXL-GY-02-03).

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Authors and Affiliations

  1. Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Zhan Shi, Dong Pu, Xuefeng Wang & Ronghua Huan

  2. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Zhuangde Jiang & Xueyong Wei

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  1. Zhan Shi
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Correspondence to Ronghua Huan or Xueyong Wei.

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Shi, Z., Pu, D., Wang, X. et al. Phase-delay induced variation of synchronization bandwidth and frequency stability in a micromechanical oscillator. Nonlinear Dyn 105, 2981–2994 (2021). https://doi.org/10.1007/s11071-021-06783-8

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