Study on the origin of 1/f noise in quartz resonators

Intrinsic frequency fluctuations with a 1/f power spectral density limit the short-term stability in quartz crystal ultra-stable oscillators. The physical origin of this 1/f noise remains not clearly explained. In this paper, a review of an experimental study on numerous ultra-stable quartz crystal resonators is presented. A comparison with past measurements is given. A theoretical approach, based on the fluctuation-dissipation theorem, is used in order to put numerical constraints on a model of 1/f noise caused by an internal (or structural) dissipation proportional to the amplitude and not to the speed, in the limit of low frequencies. The order of the magnitude of the noise is then discussed using a candidate physical process. Comparisons between theoretical and experimental results show that internal damping of thickness fluctuations by any internal friction force proportional to strain and independent of frequency may not be the dominant noise mechanism for the best SC-cut quartz resonators. Finally, we conclude on the work that could be done to solve the remaining open problems.