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Published March 2003 | public
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Virtual damping and Einstein relation in oscillators


This paper presents a new physical theory of oscillator phase noise. Built around the concept of phase diffusion, this work bridges the fundamental physics of noise and existing oscillator phase-noise theories. The virtual damping of an ensemble of oscillators is introduced as a measure of phase noise. The explanation of linewidth compression through virtual damping provides a unified view of resonators and oscillators. The direct correspondence between phase noise and the Einstein relation is demonstrated, which reveals the underlying physics of phase noise. The validity of the new approach is confirmed by consistent experimental agreement.

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"© 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." Manuscript received July 16, 2002; revised October 5, 2002. This work was supported by the Office of Naval Research under Grant N00014-01-1-0764, the National Science Foundation under Grant EC4-0083220, the Lee Center for Advanced Networking, and an IBM Graduate Fellowship. The authors would like to thank C. White of Caltech for his sharp insights and exciting discussions. The authors also thank B. Analui, H. Hashemi, A. Komijani, and H. Wu of Caltech for their valuable comments. A special debt of gratitude is due to Prof. Rutledge, Prof. Tai, Prof. Vaidyanathan, and Prof. Cross of Caltech, who gave the authors much helpful feedback. The authors would also like to thank the anonymous reviewers for their valuable suggestions.


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August 22, 2023
August 22, 2023