Nature of 1/f phase noise in quartz crystal resonators

It is shown that the universality and main characteristics of 1/ f noise can be understood on the basis of a dispersive wave approach. However, it is noted that 1/f noise in quartz crystals seems to come from nonlinear dispersion. A clear correlation between 1/f noise level and phonon-phonon interactions between 4 K and 50 K has been observed for 10-MHz resonators. This confirms previous correlations observed at room temperature between the noise and the quality factor of bulk and surface wave resonators. A drastic increase of noise is also observed at very low temperature in connection with a glassy-like loss mechanism. On the theoretical side, the wave amplitude is shown to increase at very low frequencies due to the dispersive lattice, leading to nonlinearities. It is shown that the experimental findings can be understood with the help of a one-dimensional nonlinear wave model of the double-well potential type