Full Time-Varying Phase Noise Analysis for MOS Oscillators Based on Floquet and Sylvester Theorems

Abstract

In this paper a set of full time-varying analyzing methods of phase noise for oscillators based on Floquet and Sylvester theorems are established, it provides a good idea for designing oscillators with perfect phase noise performance. The periodic state solution space of a linear periodic time-varying system is constructed with Floquet and Sylvester theorems, and the phase noise perturbation vectors of an oscillator autonomous system are characterized on this space. The analytical expressions of the phase noise spectrums, both 1/(Δf)2 and Lorentzian forms, are obtained, and the contributions to the phase noise of each noise sources are determined. With a generator approach and some modification, the method could be extended to the flicker noise. For RF front-end oscillators composed of MOS active devices, planar inductors and MOS varactors, the time-varying model parameters of the small signal equivalent circuits are constructed according to the periodic varying working-points. By the means of automatic small-signal equivalent-circuit construction, state-variable selection and periodic time-varying state-matrix generation, the system perturbation vectors and phase noise power spectrums are efficiently calculated. For a 10 GHz MOS oscillator, the 1/(Δf)2 and Lorentzian spectrums are calculated. Comparing with the results of SpectreRF, it indicates the proposed methods are accurate and reliable, especially the Lorentzian spectrum close to the carrier is more reasonable than previous methods. Every noise source contributions to the phase noise are listed and the results are analyzed. At last the applications of the methods to designing low phase noise oscillators and to analyzing the phase noise of composite systems, as well as the difficulty of flicker noise analysis, are addressed.