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Probabilistic properties of dynamic modulation characteristics of quartz oscillators

V. N. Roman’ko, Yu. S. Shmalii


A probabilistic analysis of the dynamic modulation characteristics (DMCs) of quartz self-excited oscillators (QSOs) in the vicinity of anharmonic resonances of a resonator is made. It is shown that the probability density functions of the phase and frequency DMCs obey the generalized Rice law. The expected values and variances of the DMCs were investigated in a fluctuating field of parameters of signals of a generalized scheme of QSOs. Results enabling making a conclusion about the necessary level of the amplitude of the modulating signal for which the DMCs acquire stabilizing properties providing minimum instability of the frequency of the output oscillations of the reference QSOs using the modulation method of frequency stabilization are obtained.

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