General non linear perturbation model for flicker noise in LC oscillator

We present a circuit based LC oscillator phase noise model for flicker noise using non linear perturbation techniques. Closed form equations for obtaining phase and amplitude spectra have been developed which then lead to the final expression of voltage noise density across the oscillator terminal. Since flicker noise occurs at very low frequencies, we propose that any perturbation in oscillation due to this noise is equivalent to perturbation in the dc bias of the devices present in the oscillator and develop the closed form analytic expressions on the basis of this assumption. A trap level model of flicker noise is used for that analysis. Expressions are obtained for a single trap, which are then scaled up for all traps. Doing so enables us to work around the problem of "blow up" of flicker noise at low frequencies. The derivations take into account the correlation existing between amplitude and phase deviations due to noise which has previously not been documented and new parameters are introduced which account for this correlation. The noise spectrum shows a 1/f³ distribution as has been shown in other literature. The proposed model is applied on a practical differential oscillator for comparison. We introduce a novel method of analysis by splitting the noise contribution of the various transistors into modes. The modes that contribute the most to flicker noise are picked. Further the tail noise contribution is analyzed and shown to be mostly upconverted noise. The proposed model which is compared with simulation results and agreement of within 1.5 dB with simulation results was obtained