Abstract-A companion analysis of clock jitter and phase noise of single-ended and differential ring oscillators is presented. The impulse sensitivity functions are used to derive expressions for the jitter and phase noise of ring oscillators. The effect of the number of stages, power dissipation, frequency of oscillation, and shortchannel effects on the jitter and phase noise of ring oscillators is analyzed. Jitter and phase noise due to substrate and supply noise is discussed, and the effect of symmetry on the upconversion of 1/f noise is demonstrated. Several new design insights are given for low jitter/phase-noise design. Good agreement between theory and measurements is observed.

An analysis of the phase noise in differential and singleended ring oscillators using a time-variant model is presented. An expression for the RMS value of the impulse sensitivity function (ISF) is derived. A closed-form equation for phase noise of ring oscillators is calculated and a lower limit on the phase noise of ring oscillators is shown. Phase noise measurements of oscillators running up to 5.5GHz are shown to be in good agreement with the theory. IntroductionDue to their integrated nature, ring oscillators have recently become an important building block in many digital and communication systems [1]. They can also be used for some low-tier RF products. Recently, there has been some work on modeling the phase noise in ring oscillators.[2] and [3] develop models for clock jitter based on time domain treatments of MOS and bipolar differential ring oscillators, respectively. Reference [4] proposes a frequency domain approach to find the phase noise based on an LTI model for differential ring oscillators with a small number of stages. In this work we present a general framework to calculate the phase noise of ring oscillators by applying a time-variant phase noise model [5] to ring oscillators. Based on this derivation we obtain a lower limit on the phase noise of ring oscillators in long and short channel regimes. Good agreement is observed between the predictions and measurement results of the phase noise of ring oscillators running up to 5.5GHz.

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