STATIC AND DYNAMIC BEHAVIOR OF QUARTZ RESONATORS

The frequency-temperature (f-T) behavior of a crystal resonator depends upon temperature, and its spatial and temporal gradients. For quasi-isothermal changes the static f-T curve can be used to determine frequency shifts that occur, e.g., in oven-controlled units. The frequency then depends upon the parameters of the static f-T curve, the temperature range over which the oven cycles, and upon the oven setting point. The maximum frequency excursion has been computed for the Atand Sccuts of quartz in terms of these parameters as a function of the orientation angle. When thermal-transient-compensated cuts are not utilized, oven cyclings or other temperature perturbations introduce an additional nonnegligible component of the frequency shift. This effect is quantified by means of a simple mathematical model. The model is capable of predicting the thermal transient effects for AT cuts appearing in the literature. Simulations, using the model, disclose that sinusoidal temperature variations with periods of hours can readily lead to frequency instabilities much larger than would be expected using the static f-T curve for the AT cut. This effect should be greatly diminished in the vicinity of the SC cut. © 1979, IEEE. All rights reserved.