Analytical Equations for Nonlinear Phase Errors and Jitter in Ring Oscillators
Srivastava, S.
Roychowdhury, J.
Minnesota Univ., Minneapolis;
This paper appears in: Circuits and Systems I: Regular Papers, IEEE Transactions on
Publication Date: Oct. 2007
Volume: 54,
Issue: 10
On page(s): 2321-2329
ISSN: 1549-8328
INSPEC Accession Number: 9630068
Digital Object Identifier: 10.1109/TCSI.2007.905637
Current Version Published: 2007-10-15
Abstract
In this paper, we present a simple analytical equation for capturing phase errors in 3-stage ring oscillators. The model, based on a simple but useful idealization of the ring oscillator, is provably exact for small noise perturbations. Despite its simplicity and purely analytical form, our model correctly captures the time- dependent sensitivity of oscillator phase to external perturbations. It is thus well suited for estimating both qualitative and quantitative features of ring oscillator phase response to internal noises, as well as to power, ground and substrate interference. The nonlinear nature of the model makes it suitable for predicting injection locking as well. Comparisons of the new model with existing phase models are provided, and its application for correct prediction of thermal jitter demonstrated. Requiring knowledge only of the amplitude and frequency of the oscillator, the model is ideally suited for early design exploration at the system and circuit levels.
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