General Phase-Noise Analysis From the Variance of the Phase Deviation

For an accurate calculation of close-to-carrier phase noise, the nonlinearity of the perturbed oscillator with respect to the common phase deviation must be taken into account. Existing analysis methods are based on the decoupling of this variable from the perturbed oscillator system and the resulting spectrum can only exhibit slopes of - 30 or - 20 dB per decade at sufficiently large frequency offset from the carrier. However, other forms of variations are often observed in the measurement, due to the influence of close-in poles of the perturbed-oscillator system. These poles are mathematically eliminated in the decoupled analysis of the phase process. Here, a new analysis method is presented for a general calculation of phase noise, taking into account the nonlinearity in the phase deviation and enabling an accurate prediction of the phase-noise spectrum as the offset frequency increases. It considers the influence of the amplitude modulation on the variance of the phase deviation and, in this manner, can predict the effect on the phase-noise spectrum of close-in poles. The method is initially applied to a semi-analytical formulation, based on a reduced-order Jacobian matrix, which enables good insight into the possible effect of the close-in poles. Then, it is generalized to a perturbation analysis of the full harmonic-balance system. The method has been successfully applied to a bipolar-based oscillator at 1 GHz and to a finite-element-transistor-based oscillator at 5 GHz.