TY - GEN
T1 - Drive level dependency in quartz resonators
AU - Patel, Mihir S.
AU - Yong, Yook Kong
AU - Tanaka, Masako
AU - Imai, Tsutomu
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
KW - AT-cut
KW - BT-cut
KW - Doubly rotated cuts
KW - Drive level dependency
KW - MEMS
KW - Nonlinear phenomenon
KW - Piezoelectric resonators
KW - Quality factor
KW - Quartz
KW - SC-cut
UR - http://www.scopus.com/inward/record.url?scp=33846611080&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846611080&partnerID=8YFLogxK
U2 - 10.1109/FREQ.2005.1574036
DO - 10.1109/FREQ.2005.1574036
M3 - Conference contribution
AN - SCOPUS:33846611080
SN - 0780390539
SN - 9780780390539
T3 - Proceedings of the IEEE International Frequency Control Symposium and Exposition
SP - 793
EP - 801
BT - 2005 Joint IEEE International Frequency Controlo Symposium (FCS) and Precise Tome and Time INterval (PTTI) Systems and Applications Meeting
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2005 Joint IEEE International Frequency Control Symposium (FCS) and Precise Time and Time Interval (PTTI) Systems and Applications Meeting
Y2 - 29 August 2005 through 31 August 2005
ER -