Estimation of frequency-temperature characteristics of AT-cut quartz resonators with large mass-loading

This paper evaluates the effect of electrodes on the frequency-temperature (f-T) characteristics of a very thin plate. The calculated results show that the f-T behavior of the fundamental resonance greatly depends on the mass-loading effect R through the thermal coefficient of R and the mass-loading effect is sensitive to the thermal expansion coefficient α_E of the electrodes. Consequently, both the mass-loading effect and α_E can have a great influence upon the f-T behavior. It is also shown that the electrode size hardly affects the f-T behavior.