Accurate circuit based non linear perturbation model of phase noise in LC oscillators

We present a circuit based model of LC oscillator phase noise due to white noise using non linear perturbation techniques. Differential equations establishing the relation between device noise and amplitude and phase deviations have been rigorously developed which lead to closed form equations for obtaining the phase and the amplitude spectra. These relations are then used to obtain the final expression for voltage noise density across the oscillator terminals. We introduce new parameters which take into account the correlations existing between amplitude and phase deviations due to noise and give better agreement with simulation results. Further, the buffer noise in oscillators is examined. We mathematically demonstrate that the noise floor of an oscillation spectrum arises due the buffer present in an oscillator circuit. The oscillator noise spectrum is shown to have a Lorentzian distribution initially, which then flattens out due to the noise floor. As a result, two distinct corner frequencies arise. The proposed model is compared with simulation results for both a practical differential oscillator as well as a Van Der Pol oscillator. For the Van Der Pol oscillator the proposed model matches perfectly with the simulation results and for the differential oscillator a close agreement of within 1.5 dB is obtained