Surface charge measurement/calculations for the prediction of spurious modes and frequency jumps in AT-cut quartz resonators

The 2-dimensional FEM analysis using the 3rd-order Mindlin´s plate equations was employed for the prediction of the spurious modes and frequency jumps in the frequency temperature behavior of AT-cut quartz resonators. The surface charge over the electrode was employed as a means for predicting the strength of coupling of the spurious modes with the fundamental thickness shear mode (main mode). The magnitudes of frequency jumps are also qualitatively related to the magnitude of surface charges of the spurious modes when compared to the surface charge of the main mode. FEM results were verified by comparison with the experimental data of an electroded resonator and bi-convex resonators. The measurements of charge distribution for a few spurious vibration modes were in good agreement with the calculated results in a flat resonator. A 14 MHz bi-convex model was analyzed. Spurious modes were shown with their surface charge in the frequency Spectrum. A large surface charge in spurious mode was shown to a large frequency jump