TY - GEN
T1 - Frequency-temperature behavior of quartz resonators affected by transient and steady state temperature changes
AU - Yong, Yook Kong
AU - Patel, Mihir S.
AU - Tanaka, Masako
PY - 2006
Y1 - 2006
N2 - A new method which accurately predicts the frequency-temperature (f-T) behavior of quartz resonators affected by transient and steady state temperature changes is presented. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the f- T curves of quartz resonators under thermal stresses. In our previous paper [1], we had proposed a method which employed a superposition of two f-T curves: one due to a stress-free, homogeneous thermal strain field, and the other due to the nonhomogeneous thermal stresses. The assumptions underlying the two f-T curves were not satisfactorily consistent. This paper presents a consistent and superior method for the problem: the constitutive equations for the Lagrangean, incremental displacements (small vibrational displacements) incorporate the temperature derivatives of the material constants. The incremental equations of small vibrations superposed on initial thermal stresses and strains are solved, and there was no need for the superposition of two f-T curves. Numerical results are compared with experimental results for a 50MHz AT-cut quartz resonator mounted on a glass package. Good comparison between the experimental results and numerical results from our new method is shown. The difference between the thermal expansion coefficients of glass and quartz give rise to the thermal stresses that have an adverse effect on the f-T curves of AT-cut resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package.
AB - A new method which accurately predicts the frequency-temperature (f-T) behavior of quartz resonators affected by transient and steady state temperature changes is presented. Most practical resonators are subjected to thermal stresses. Conventional finite element analytical tools such as ANSYS cannot provide a sufficiently accurate model for the f- T curves of quartz resonators under thermal stresses. In our previous paper [1], we had proposed a method which employed a superposition of two f-T curves: one due to a stress-free, homogeneous thermal strain field, and the other due to the nonhomogeneous thermal stresses. The assumptions underlying the two f-T curves were not satisfactorily consistent. This paper presents a consistent and superior method for the problem: the constitutive equations for the Lagrangean, incremental displacements (small vibrational displacements) incorporate the temperature derivatives of the material constants. The incremental equations of small vibrations superposed on initial thermal stresses and strains are solved, and there was no need for the superposition of two f-T curves. Numerical results are compared with experimental results for a 50MHz AT-cut quartz resonator mounted on a glass package. Good comparison between the experimental results and numerical results from our new method is shown. The difference between the thermal expansion coefficients of glass and quartz give rise to the thermal stresses that have an adverse effect on the f-T curves of AT-cut resonators. Different optimal crystal cut angles of quartz, and resonator geometry were found to achieve stable frequency-temperature behavior of the resonator in a glass package.
UR - http://www.scopus.com/inward/record.url?scp=63149111949&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=63149111949&partnerID=8YFLogxK
U2 - 10.1109/ULTSYM.2006.150
DO - 10.1109/ULTSYM.2006.150
M3 - Conference contribution
SN - 1424402018
SN - 9781424402014
T3 - Proceedings - IEEE Ultrasonics Symposium
SP - 568
EP - 571
BT - 2006 IEEE International Ultrasonics Symposium, IUS
ER -