Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator

Resonators driven into self-oscillation via active feedback often form the basis of clocks and other sensitive measurement instrumentation. The phase stability of such an oscillator is ultimately limited by the noise associated with the resonator's intrinsic losses. However, it is often the case that amplifier noise is the dominant cause of the oscillator's phase diffusion. Here it is shown that when the resonator possesses a suitable nonlinearity, the phase diffusion due to amplifier noise can be suppressed, allowing one to achieve a long-term phase stability comparable to the ultimate noise limit.