24 September 2004 A generalized asymptotical model of a single-mode noisy crystal oscillator with a nonlinear resonator
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Proceedings Volume 5582, Advanced Optoelectronics and Lasers; (2004) https://doi.org/10.1117/12.583403
Event: 2003 Chapter books, 2003, Bellingham, WA, United States
Abstract
We present the generalized asymptotical model of a single-mode crystal oscillator with a nonlinear resonator. The motional and static equivalent parameters associated with the fundamental mode of a crystal resonator are assumed to be drive level dependent (DLD) and flicker noisy. A thermal noise of the resonator losses is also taken into account. A concept of the feedback amplifier is discussed resulting in a series branch of the equivalent resistance and inductance (both flicker-noisy and negative) along with the thermal additive noise source. The generic differential equation of the second order is derived, in which the auxiliary sub-functions are introduced being responsible for the equilibrium, anisochronisms, thermal noise (additive and multiplicative) effect, and colored (flicker) noise effect. We show that such a model covers all three special ranges of the piezoelectric current, namely those with low, normal, and high drives.
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Yuriy S. Shmaliy, Yuriy S. Shmaliy, } "A generalized asymptotical model of a single-mode noisy crystal oscillator with a nonlinear resonator", Proc. SPIE 5582, Advanced Optoelectronics and Lasers, (24 September 2004); doi: 10.1117/12.583403; https://doi.org/10.1117/12.583403
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