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Verifying global start-up for a Möbius ring-oscillator

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Abstract

This paper presents the formal verification of start-up for a differential ring-oscillator circuit used in industrial designs. We present an efficient algorithm for finding DC equilibria to establish a condition that ensure the oscillator is free from lock-up. Further, we present a formal verification solution for the problem. Using dynamical systems theory, we show that any oscillator must have a non-empty set of states from which it fails to start properly. However, it is possible to show that these failures only occur with zero probability. To do so, this paper generalizes the “cone argument” initially presented in (Mitchell and Greenstreet, in Proceedings of the third workshop on designing correct circuits, 1996) and proves the soundness of this generalization. This paper also shows how concepts from analog design such as differential operation can be soundly incorporated into the verification to produce simpler models and reduce the complexity of the verification task.

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Acknowledgements

Throughout this work we have benefited from interactions with many excellent colleagues. We would like to express our particular gratitude to Michael Friedlander, Kevin Jones, Victor Konrad, Ian Mitchell, John Poulton, and Mohamed Zaki for helpful conversations and inspiration in the course of this research. Mitchell

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Correspondence to Chao Yan.

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This work was supported in part by grants from Intel, Oracle, and the Natural Sciences and Engineering Research Council of Canada.

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Yan, C., Greenstreet, M.R. & Yang, S. Verifying global start-up for a Möbius ring-oscillator. Form Methods Syst Des 45, 246–272 (2014). https://doi.org/10.1007/s10703-013-0204-6

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  • DOI: https://doi.org/10.1007/s10703-013-0204-6

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