This paper offers a derivation of phase noise in oscillators resulting in a closed-form analytic formula that is both general and convenient to use. This model provides a transparent connection between oscillator phase noise and the fundamental device physics and noise processes. The derivation accommodates noise and nonlinearity in both the resonator and feedback circuit, and includes the effects of environmental disturbances. The analysis clearly shows the mechanism by which both resonator noise and electronics noise manifest as phase noise, and directly links the manifestation of phase noise to specific sources of noise, nonlinearity, and external disturbances. This model sets a new precedent, in that detailed knowledge of component-level performance can be used to predict oscillator phase noise without the use of empirical fitting parameters.
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