Stochastic characterization of the phase noise spectrum of coupled-oscillator circuits

This paper presents the phase-noise analysis of nearest-neighbor coupled-oscillator circuits for beam steering applications. The analysis includes the effect of flicker noise sources for the first time to our knowledge. It is based on a semi-analytical formulation, which uses a perturbation model of the individual oscillator extracted from a harmonic balance (HB) simulation of the individual oscillator element in free-running conditions. The model can be extracted from a commercial HB using two auxiliary generators at dc and the first harmonic component. The operation range, stability and phase noise of the coupled system are analyzed separately from HB with the extended semi-analytical formulation. A full stochastic characterization of the phase-noise spectrum from the variance of the phase-deviation is presented, which enables an accurate prediction of the near-carrier noise. The method has been applied to a system of four oscillators, obtaining good agreement with the measurement results.