The Amplitude-Frequency Effect in SC-Cut Resonators

The effect of excitation level on the performance of quartz crystal resonators has been of interest for many years. A consequence of the nonlinearity of quartz is a distortion of the impedance vs. frequency function. The resonant frequency is, therefore, a function of the drive level. Above a certain drive level there are instabilities which cause discontinuities in the observed resonance curves. The subject of amplitude-frequency behavior is of current interest due to the increasing importance of low phase noise oscillators. In this paper experimental results on the amplitude-frequency effect for SC-cut resonators of various contours, frequencies, and overtones will be reported. The results will be compared with those obtained from AT-cut resonators of the same overtones and frequencies. The measurements were performed on high-precision ultrahigh vacuum and high temperature processed ceramic flatpack enclosed devices. As a review and starting point, the basic form of nonlinear resonance will be derived using a polynomial expansion of the motional capacitance in the equivalent circuit of the resonator. SC-cut, AT-cut, nonlinearity. INTRODUCTION