Special Nonlinear Effects of the Harmonic 3rd Overtone Thickness-Shear Mode on its Fundamental Mode in F-3F Modal Interactions and Drive Level Dependency

Previous papers and experiments have well documented the drive level dependency in a single mode. The parameters governing drive level dependency in quartz resonators however are still not well understood. We show in this paper the nonlinear interactions of the 3
^rd
overtone of thickness shear (f
₃
) mode and the fundamental thickness shear mode (f
₁
) on the drive level dependency of a quartz resonator. We have developed a finite element program/model for nonlinear frequency responses of f-2f-3f modal interactions and drive level dependency in quartz resonators. Our model results compared well with the measured results in quartz 33-MHz fundamental mode AT-cut and SC-cut resonators for which the fundamental mode and third overtone mode frequencies were closely matched by design. The fundamental mode interacted nonlinearly with the third overtone mode. An interesting effect was observed that the frequency shift (drive level dependency) was greater for when the 3
^rd
harmonic 3f frequency was higher than the 3
^rd
overtone f3 frequency, especially for the AT-cut resonators.