Suppression of lower harmonic responses on overtone AT-cut quartz crystal resonators

This paper proposes a method to suppress harmonic responses lower than a specified overtone mode in an overtone quartz crystal resonator, by providing a subelectrode in addition to the main electrode. An analysis is performed assuming isotropic elasticity. It is pointed out that energy trapping in the finite plate is well represented by considering the phase shift of the vibration displacement in the main electrode region. The vibration displacement at the plate edge is calculated, and the equivalent series resistance is estimated. It is found that the vibration displacement of the fundamental mode can be increased more than that of the third overtone mode, by appropriately setting the energy trapping factor. It is also shown that the above tendency is enhanced when the subelectrode is made thicker than the main electrode. An experiment was performed for the 93-MHz third overtone quartz crystal resonator, and it is shown that the oscillator operates without a coil. (C) 1999 Scripta Technica.