The Amplitude-Frequency Effect in Quartz Resonators

Measurements of the amplitude-frequency effect have been carried out on X-, Y-, AT-, and BT-cut quartz resonators. Unacceptably large frequency shifts of several hundred Hz are observed under high drive levels. The effect is largely due to the thermal stresses caused by localized heating. As the central portion of resonator beneath the electrode expands, it is clamped by a cooler ring of quartz around it. A number of thermal and mechanical experiments were performed to confirm the origin of the amplitude-frequency effect, and several ways of minimizing the drift in frequency with drive level are suggested.