Model of flicker noise effects on phase noise in oscillators

Abstract

Phase noise models that describe the near-carrier spectrum in an accurate but insightful way are needed, to better optimize the oscillator design. In this paper we present a model to describe the effect of flicker noise sources on the phase noise of an oscillator, that can be applied both to linear oscillators and to nonlinear structures like relaxation and ring oscillators, so extending previous works that considered only the effect of the flicker noise superimposed to the control voltage of a VCO. In the phase noise of an oscillator we can separate the effect of high frequency noise sources, that can be described by a short-time-constant system, and the effect of low frequency noises (mostly flicker sources), described by a system with time constants much slower than the oscillation period. Flicker noise has been considered to cause a change in the circuit bias point; this bias point change can be mapped in a shift of the oscillation frequency by exploiting Barkhausen conditions (for linear oscillators) or obtaining this link by simulations. The power spectral density of the oscillator can then be obtained as the probability distribution of the oscillation frequency, starting from the flicker noise probability distribution. If the effect of high frequency noise sources is also taken into account, the overall oscillator spectrum can be obtained as a convolution of the spectrum due to flicker sources with the Lorentzian-shaped spectrum due to white noise sources, in analogy with the description of inhomogeneous broadening of laser linewidth.