It is known that the dynamics and phase noise of resonator-based self-sustained nonlinear oscillators is affected by the presence of a nonlinear resonator. In fact, it has been shown that resonator nonlinearity can enhance the oscillator phase noise under certain conditions. This paper offers a new formulation and analytical approach to describe the effect of resonator nonlinearity on the phase noise of self-sustained oscillators. The analysis applies properties of stochastic Ito integrals to oscillator's averaged stochastic nonlinear differential equations with periodic steady state solutions. The results offer insight into designing low phase-noise oscillators with nonlinear resonators. We show that for a given nonlinear oscillator topology, there is an optimum power incident on the resonator that minimizes the phase noise. As a proof of concept, the analysis is applied to a 1.5-GHz CMOS oscillator that uses a nonlinear film bulk acoustic resonator (FBAR). A nonlinear model including memory effects for the FBAR is proposed and used in the formulation. At the optimum design point, the oscillator shows measured phase noise of -110 dBc/Hz at 1 kHz, -125 dBc/Hz at 10 kHz, -145 dBc/Hz at 100 kHz, and -160 dBc/Hz at 10-MHz offset frequencies while consuming 40 mW of dc power. This results in 10 fs of timing jitter.