A Stochastic Model of "Sleeping Sickness" of Crystal Oscillators

A stochastic model of a crystal oscillator is discussed at low drive levels, where a crystal resonator exhibits the effect termed "sleeping sickness". In the model, resonator losses are supposed to be nonlinear, R₁(I_r) = R₁₀(1 + gamma_R/I_r ⁿ), where I_r is a peak amplitude of the piezoelectric current, gamma_R is a drive level dependence (DLD) coefficient, and n is a degree of nonlinearity. We show that a nonlinear crystal resonator with sleeping sickness does not fall to an "absolute sleep" in the oscillator, when a feedback becomes insufficient after a long storage. It rather generates the noise-induced oscillations at the noise level