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



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 $~\frac{2\sqrt{2}\kappa^3}{(a-1)^2}\frac{N}{F}\Delta~f^{1/2}$

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