Drive level dependency in quartz resonators

Mihir S. Patel, Yook Kong Yong, Masako Tanaka, Tsutomu Imai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations


Common piezoelectric resonators such as the quartz resonators have a very high Q and ultra stable resonant frequency. However, due to small material nonlinearities in the quartz crystal, the resonator is drive level dependent, that is, the resonator level of activity and its frequency are dependent on the driving, or excitation, voltage. The size of these resonators will be reduced to one fourth of their current sizes in the next few years, but the electrical power which is applied will not be reduced as much. Hence, the applied power to resonator size ratio will be larger, and the drive level dependency may play a role in the resonator designs. We study this phenomenon using the Lagrangian nonlinear stress equations of motion and Piola-Kirchhoff stress tensor of the second kind. Solutions are obtained using FEMLAB for the AT-cut, BT-cut, SC-cut and other doubly rotated cut quartz resonators and the results compared well with experimental data. The phenomenon of the drive level dependence is discussed in terms of the voltage drive, electric field, power density and current density. It is found that the drive level dependency is best described in terms of the power density. Experimental results for the AT-, BT- and SC-cut resonators in comparison with our model results are presented. Results for new doubly rotated cuts are also presented.

Original languageEnglish (US)
Title of host publication2005 Joint IEEE International Frequency Controlo Symposium (FCS) and Precise Tome and Time INterval (PTTI) Systems and Applications Meeting
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages9
ISBN (Print)0780390539, 9780780390539
StatePublished - 2005
Event2005 Joint IEEE International Frequency Control Symposium (FCS) and Precise Time and Time Interval (PTTI) Systems and Applications Meeting - Vancouver, BC, Canada
Duration: Aug 29 2005Aug 31 2005

Publication series

NameProceedings of the IEEE International Frequency Control Symposium and Exposition


Other2005 Joint IEEE International Frequency Control Symposium (FCS) and Precise Time and Time Interval (PTTI) Systems and Applications Meeting
CityVancouver, BC

All Science Journal Classification (ASJC) codes

  • General Engineering


  • AT-cut
  • BT-cut
  • Doubly rotated cuts
  • Drive level dependency
  • MEMS
  • Nonlinear phenomenon
  • Piezoelectric resonators
  • Quality factor
  • Quartz
  • SC-cut


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