Dynamics of the mean signal amplitude of a crystal oscillator with a nonlinear resonator and low drives

Yuriy S. Shmaliy; Juan Rosales

doi:10.1117/12.583402

24 September 2004 Dynamics of the mean signal amplitude of a crystal oscillator with a nonlinear resonator and low drives

Yuriy S. Shmaliy, Juan Rosales

Author Affiliations +

Proceedings Volume 5582, Advanced Optoelectronics and Lasers; (2004) https://doi.org/10.1117/12.583402
Event: 2003 Chapter books, 2003, Bellingham, WA, United States

Abstract

Dynamics of the mean amplitude of oscillations of a crystal oscillator with a linear feedback is outlined for low drives when the losses (friction) of a resonator become large and nonlinear after a long storage. The drive-level-dependence (DLD) of the crystal resonator losses is assumed to change inversely to the piezoelectric current. A stochastic differential equation for the mean amplitude is derived and solved in a sense of Ito. The development and attenuation processes are learned and it is shown that attenuation finishes at some non-zero level associated with the effect termed "sleeping sickness." The critical value of the friction is calculated and the conditions are discussed to avoid attenuation. Based upon, we show in that (1) if the value of the DLD coefficient of the resonator losses ranges below the critical point, the effect occurs primarilly in a delay of self-excitation; (2) contrary, noise drives the crystal oscillator.

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Yuriy S. Shmaliy and Juan Rosales "Dynamics of the mean signal amplitude of a crystal oscillator with a nonlinear resonator and low drives", Proc. SPIE 5582, Advanced Optoelectronics and Lasers, (24 September 2004); https://doi.org/10.1117/12.583402

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