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The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism Error

The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism... During the fabrication of quartz crystal resonators (QCRs), parallelism error is inevitably generated, which is rarely investigated. In order to reveal the influence of parallelism error on the working performance of QCRs, the coupled vibration of a non-parallel AT-cut quartz crystal plate with electrodes is systematically studied from the views of theoretical analysis and numerical simulations. The two-dimensional thermal incremental field equations are solved for the free vibration analysis via the coefficient-formed partial differential equation module of the COMSOL Multiphysics software, from which the frequency spectra, frequency–temperature curves, and mode shapes are discussed in detail. Additionally, the piezoelectric module is utilized to obtain the admittance response under different conditions. It is demonstrated that the parallelism error reduces the resonant frequency. Additionally, symmetry broken by the non-parallelism increases the probability of activity dip and is harmful to QCR’s thermal stability. However, if the top and bottom surfaces incline synchronously in the same direction, the influence of parallelism error is tiny. The conclusions achieved are helpful for the QCR design, and the methodology presented can also be applied to other wave devices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mechanica Solida Sinica Springer Journals

The Multi-field Coupled Vibration Analysis of AT-Cut Quartz Crystal Resonators with Parallelism Error

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Publisher
Springer Journals
Copyright
Copyright © The Chinese Society of Theoretical and Applied Mechanics 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0894-9166
eISSN
1860-2134
DOI
10.1007/s10338-023-00384-1
Publisher site
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Abstract

During the fabrication of quartz crystal resonators (QCRs), parallelism error is inevitably generated, which is rarely investigated. In order to reveal the influence of parallelism error on the working performance of QCRs, the coupled vibration of a non-parallel AT-cut quartz crystal plate with electrodes is systematically studied from the views of theoretical analysis and numerical simulations. The two-dimensional thermal incremental field equations are solved for the free vibration analysis via the coefficient-formed partial differential equation module of the COMSOL Multiphysics software, from which the frequency spectra, frequency–temperature curves, and mode shapes are discussed in detail. Additionally, the piezoelectric module is utilized to obtain the admittance response under different conditions. It is demonstrated that the parallelism error reduces the resonant frequency. Additionally, symmetry broken by the non-parallelism increases the probability of activity dip and is harmful to QCR’s thermal stability. However, if the top and bottom surfaces incline synchronously in the same direction, the influence of parallelism error is tiny. The conclusions achieved are helpful for the QCR design, and the methodology presented can also be applied to other wave devices.

Journal

Acta Mechanica Solida Sinica – Springer Journals

Published: Apr 1, 2023

Keywords: Quartz crystal resonators; Parallelism error; Resonant frequency; Mode coupling; Admittance

References

  • Trapped-energy modes in quartz filter crystals
    Shockley, W; Curran, DR; Koneval, DJ
  • Analysis of overtone modes in monolithic crystal filters
    Tiersten, HF
  • Analysis of a monolithic crystal plate acoustic wave filter
    He, HJ; Liu, JX; Yang, JS
  • A two-dimensional model on the coupling thickness-shear vibrations of a quartz crystal resonator loaded by an array spherical-cap viscoelastic material units
    Xie, JM; Hu, YT
  • Thickness-shear vibration of a Z-strip AT-cut quartz crystal plate with nonuniform electrode pairs
    Zhao, ZN; Qian, ZH; Wang, B
  • Thickness-shear and flexural vibrations of crystal plates
    Mindlin, RD
  • Frequency spectra of AT-cut quartz plates with electrodes of unequal thickness
    Wang, JN; Hu, YT; Yang, JS
  • Five-mode frequency spectra of x3-dependent modes in AT-cut quartz resonators
    Chen, GJ; Wu, RX; Wang, J; Du, JK; Yang, JS
  • Coupling vibration analysis of trapped-energy rectangular quartz resonators by variational formulation of Mindlin's theory
    Li, N; Wang, B; Qian, ZH
  • Anharmonic, thickness-twist overtones of thickness-shear and flexural vibrations of rectangular, AT-cut quartz plates
    Mindlin, RD; Spencer, WJ
  • Effect of stepped bi-mesa structures on spurious vibrations of AT-cut quartz plates
    Goka, S; Ishizaki, A; Sekimoto, H; Watanabe, Y
  • Mode decoupling effect of multistepped bi-mesa AT-cut quartz resonators
    Goka, S; Tamura, T; Sekimoto, H; Watanabe, Y; Sato, T; Sato, K
  • Resonances and energy trapping in AT-cut quartz resonators operating with fast shear modes driven by lateral electric fields produced by surface electrodes
    Ma, TF; Wang, J; Du, JK; Yang, JS
  • Composite lateral electric field excited piezoelectric resonator
    Zaitsev, BD; Shikhabudinov, AM; Borodina, IA; Teplykh, AA; Kuznetsova, IE
  • Temperature dependence of the resonant frequency of electroded doubly-rotated quartz thickness-mode resonators
    Tiersten, HF
  • Frequency-temperature behavior of thickness vibrations of doubly rotated quartz plates affected by plate dimensions and orientations
    Lee, PCY; Yong, YK
  • Temperature derivatives of elastic stiffness derived from the frequency–temperature behavior of quartz plates
    Lee, PCY; Yong, YK
  • Equations for small fields superposed on finite biasing fields in a thermoelectroelastic body
    Yang, JS
  • The frequency-temperature analysis equations of piezoelectric plates with Lee plate theory
    Wang, J
  • Multiple quartz crystals connected in parallel for high-resolution sensing of capacitance changes
    Matko, V
  • Temperature behavior of SAW resonators based on LiNbO3/quartz and LiTaO3/quartz substrates
    Naumenko, NF
  • Effects of manufacturing errors on the characteristics of a polymer vertical coupling microring resonator
    Wang, YH; Qin, ZK; Wang, CX
  • Accurate identification of the evolution of MEMS resonant accelerometer residual stresses at the wafer-die-chip level
    Huang, JY; Zhao, Y; Xia, GM; Shi, Q; Qiu, AP
  • The effects of non-parallel plates in a differential capacitive microaccelerometer
    Tay, FEH; Xu, J; Liang, LC; Logeeswaran, VJ; Yao, YF
  • Effects of non-parallel combs on reliable operation conditions of capacitive inertial sensor for step and shock signals
    Dong, LX; Che, LF; Sun, LG; Wang, YL
  • Interferometric straightness measurement system using triangular prisms
    Zhang, J; Cai, L
  • Thickness vibrations of flat piezoelectric plates with massy electrodes of unequal thickness
    Kosinski, JA
  • Effects of a mass layer with gradually varying thickness on a quartz crystal microbalance
    Liu, N; Yang, JS; Chen, WQ
  • Effects of the imperfect interface and viscoelastic loading on vibration characteristics of a quartz crystal microbalance
    Gu, CL; Li, P; Jin, F; Chen, GF; Ma, LS
  • Forced coupling vibration analysis of FBAR based on two-dimensional equations associated with state-vector approach
    Li, N; Qian, ZH; Wang, B
  • Effects of mode couplings on the vibration characteristics of partially electroded thin-film bulk acoustic wave resonators
    Li, N; Wang, B; Qian, ZH
  • Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator
    He, HJ; Yang, JS; Zhang, WP; Wang, J
  • Vibrations of a crystal plate under a thermal bias
    Yang, JS; Zhang, X
  • Effects of thermal stresses on the frequency-temperature behavior of piezoelectric resonators
    Yong, YK; Patel, M; Tanaka, M
  • Electronic activity dip measurement
    Ballato, A; Tilton, R