Distribution of the Surface Current Density in the Plate of a Quartz Resonator

The basis of most thermostated quartz oscillators is quartz resonators of two-turn cuts TD, SC, and AT. Resonators based on crystalline elements of these cuts, compared to resonators based on the most popular AT cut, have the main advantage – less influence of climatic and mechanical influences on the frequency, which explains their widespread use. At the same time, double-turn cut resonators have one significant drawback - insufficient mono-frequency, associated with a higher quality factor and low dynamic resistance of the side oscillation (mode B) compared to the main oscillation (mode C). Since the frequency of the secondary oscillation is only ~10% higher than the frequency of the main one, the oscillator circuit has to be complicated by introducing additional selective elements into it, mainly resonant circuits based on inductors. The purpose of the work is a theoretical study of the physical properties of the quartz element of the resonator, namely the calculation of the surface current density on the surface of the crystal element in different modes of oscillation. It has been established that the distributions of current densities over the surface of the piezoelectric element of the side mode B and the working mode C differ from each other and are asymmetrical relative to the center of the piezoelectric element.