Generalized noisy model of a single-mode crystal oscillator with a nonlinear resonator

Fluctuations in crystal oscillators have been under peer investigation during several decades owing to a number of reasons. In electronics, optoelectronics, and radio electronics systems, the oscillator phase noise influences selectivity of the channels and purity of the signals. In the precise positioning and measuring systems, it is ordinarily the prime limiter of accuracy. During decades, the crystal oscillator theory has passed over three principle stages depending upon improvement of the resonator model. In addition to the classical imagination, it had been noticed a multi-modal nature of crystal resonators. Accordingly, the single-mode net was complicated by the anharmonic series branches. Investigations of the anisochronisms have forced to think that the resonator motional capacity, inductance and losses are drive level dependent (DLD). Finally, the noise studies in the time and frequency domains have required complicating the model by the noise sources and thinking that the resonator motional parameters are flicker-noisy. Generalizing the above-given observation, we combine the model of a single mode crystal oscillator by the piezoelectric resonator and feedback amplifier