Close-in phase noise in electrical oscillators

Understanding the properties of close-in phase noise is crucial for analyzing the effects of low-frequency, colored noise on the frequency stability of electrical oscillators. This paper shows these properties are distinctly different from those of far-out phase noise, which are commonly studied in the literature. Unlike far-out phase noise, the spectrum of close-in phase noise caused by several uncorrelated noise sources is not the same as the sum of the phase noise spectra caused by individual sources. Furthermore, in the absence of colored noise, this spectrum is not necessarily Lorentzian as generally believed. We show that the phase noise spectrum of a periodic signal with zero cycle-to-cycle jitter is always Lorentzian and demonstrate the appearance of 1/f 4 phase noise due to a Lorentzian noise source. We also study two methods for suppressing the effects of low-frequency, colored noise on phase noise: signal symmetrization and noise-source switching. We show that the suppression of 1/f 3 phase noise in single-ended ring oscillators is due to switching and not because of symmetrization. Symmetrization is effective only for the noise sources which are constantly on, such as the tail current source in differential ring oscillators. These findings provide effective guidelines for designing low-phase-noise oscillators.