__Keywords:__resonator lithium tantalate shear vibrations phase wave velocity

M. V. Dolzhin, I. N. Borodin

It is known that spectrum of thickness vibrations of X-cut modes of lithium tantalate has many spurious modes. This presentation considers different cuts besides X-cut with 1D vibration theory of plates. It is shown that the wave velocity of X-cut of the operating vibration mode has the maximum value as compared to other angles of cuts.
The basic X-cut of lithium tantalate has a significant gap between series and parallel resonances and a lot of spurious resonances are included in this gap. We consider spectrum of different single-rotated cuts of lithium tantalate using 1D thickness vibration theory. For this purpose we write the stress-equation of motion of thickness modes. These equations describe the propagation of plane waves in elastic anisotropic medium [1]. They have three eigenvalues which correspond to A-, B- and C-modes.
Assume that spurious modes of X-cut spectrum are anharmonic thickness modes. From the experience data it is known that X-cut is exited at B-mode. Then there are many anharmonic resonances of C-mode in the vicinity of B-mode that have an effect on spectrum of B-mode. If the wave velocity of B-mode is enough as compared with the wave velocity of C-mode then magnitudes of spurious frequencies of C-mode will be low. This situation occurs in BT-cut quartz. It is possible to state a problem as to find a cut angle that has the most different value between wave velocities of B- and C-modes. This work shows that X-cut is the best choice in this condition.
In this work it is also described an example of single-rotated yzb/-45. It is characterized by the maximum distance between C- and B-modes. However, this cut has no implementation because it has lost the important preference of X-cuts i.e. there is no large frequency space between series and parallel resonances.
From experimental data and this work it has been known that X-cut has the most valuable vibration on B-mode. Measurements show that it has the minimal equivalent resistance as compared with the vibrations of other cuts and modes. It is shown that X-cut has the maximum difference between C- and B- modes therefore it has the maximum suppression of spurious thickness shear modes.

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