1/f frequency fluctuations and nonlinearity of quartz resonators and quartz crystal oscillators

Levels of flicker fluctuations of VHF quartz crystal resonators parameters have been obtained from experimental data. For the same resonators nonlinear model characteristics have been measured. It turned out that resonators with unusual nonlinearity characteristics had very high levels of parameters fluctuations. The data reported in this paper are the result both in-bridge and in-oscillator measurements for 5th overtone AT-cut quartz crystal resonators operating at 140 MHz. The in-oscillator phase noise measurement results for 92 resonators are presented as functions of their unloaded Q-factors and series resistance R_s. The results show that on the average phase noise goes down when Q and 1/R_s go up. But a scattering of the phase noise levels for resonators with the same Q and R_s is more than average lowering. An approach to these results explanation and quartz resonator noise model development is suggested