SCIENCE CHINA Information Sciences, Volume 64 , Issue 4 : 142401(2021) https://doi.org/10.1007/s11432-020-2974-9

Resolution limit of mode-localised sensors

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  • ReceivedFeb 22, 2020
  • AcceptedJul 2, 2020
  • PublishedNov 25, 2020


In recent years, the mode localisation phenomenon of weakly coupled resonators has been successfully utilised to improve the sensitivity of microelectromechanical system (MEMS) sensors. However, controversy remians about the resolution limits of mode-localised sensors. This paper asks two questions of the community: what are the resolution limits of the mode-localised sensors, and can the resolution improvement be obtained using mode-localised sensing? To answer these questions, we report a series of resolution models of mode-localised sensors. We conclude that mode-localised sensing can realise a higher measuring resolution by orders of magnitude when more than three resonators are weakly coupled, and this will lay the theoretical foundation for a breakthrough for the MEMS sensors industry.


This work was supported by National Key Research and Development Program of China (Grant No. 2018YFB2002600), National Natural Science Foundation of China (Grant No. 51575454), and Fundamental Research Funds for the Central Universities (Grant No. 3102019JC002). The author would like to show grateful acknowledgment to H. Kang and J. Yang for their helpful discussion.


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  • Figure 1

    (Color online) Schematic diagram of thermomechanical noise mechanism of a resonator.

  • Figure 2

    (Color online) Schematic diagram of 2-DoF WCRs.

  • Figure 3

    (Color online) Schematic diagram of multi-DoF WCRs.

  • Table 1  

    Table 1Comparison of resolution limit model of 2-DoF WCRs

    Resolution limit model
    This model $R_{AR}\approx2\sqrt{2}\kappa\frac{N}{F}\Delta~f^{1/2}=2\sqrt{2}\kappa\frac{\sqrt{4k_BTc\Delta~f}}{F}$
    A. Seshia [21] $R_{AR}\approx8\kappa\sqrt{\frac{E_{\rm~th}\Delta~f}{2E_cQ\omega_{\rm~eff}}}=8\kappa\sqrt{\frac{k_BTC_c^{\rm~eff}\Delta~f}{(m_r^{\rm~eff})^2(\omega_{\rm~eff})^4(X_r^0)^2}}$
    Jérôme Juillard [24] $R_{AR}=\frac{2N}{QF}\Delta~f^{1/2}$
  • Table 2  

    Table 2Comparison of resolution limit model using frequency and AR output metrics

    Resolution limit model
    Frequency output metric $~\frac{1}{Q}~\frac{N}{F}~\Delta~f^{1/2}$
    2-DoF $~2\sqrt{2}\kappa\frac{N}{F}\Delta~f^{1/2}$
    AR output metric 3-DoF $~\frac{2\sqrt{2}\kappa^2}{a-1}\frac{N}{F}\Delta~f^{1/2}$
    4-DoF $~\frac{2\sqrt{2}\kappa^3}{(a-1)^2}\frac{N}{F}\Delta~f^{1/2}$