One-port noise model of a crystal oscillator

This paper presents a one-port noise model of a crystal oscillator combined with equivalent impedances of a resonator and linearized feedback amplifier. Based on the noise conversion technique, we translate the thermal additive and flicker noise of both the resonator and amplifier into the oscillator signal amplitude and phase. The generic transformation coefficients for the noise are derived, and the power spectral density (psd) function of the oscillator signal phase is analyzed in detail. The remarkable property of the model is demonstrated by determining the separate contribution of each noise source to the oscillator performance. Some important rules for shaping the phase psd are noted. The consistency with Leeson's model also is reported.