ABSTRACT
Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterisation. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact, nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterisation of timing jitter and spectral dispersion, for computing which we develop efficient numerical methods. We demonstrate our techniques on practical electrical oscillators, and obtain good matches with measurements even at frequencies close to the carrier, where previous techniques break down.
- 1.A. Demir. Floquet theory and phase noise in oscillators with differential-algebraic equations. Technical memorandum, Bell Laboratories, Murray Hill, January 1998.Google Scholar
- 2.M. Farkas. Periodic Motions. Springer-Verlag, 1994. Google ScholarDigital Library
- 3.J. Roychowdhury. Multi-time analysis of mode-locking and quasi-periodicity in forced oscillators. Technical memorandum, Bell Laboratories, Murray Hill, 1997.Google Scholar
- 4.D.B. Leeson. A simple model of feedback oscillator noise spectrum. Proceedings of the IEEE, 54(2):329, February 1966.Google ScholarCross Ref
- 5.W.P. Robins. Phase Noise in Signal Sources. Peter Peregrinus, 1991.Google Scholar
- 6.U.L. Rohde. Digital PLL Frequency Synthesizers: Theory and Design. Prentice-Hall, 1983.Google Scholar
- 7.J.R. Vig. Quartz Crystal Resonators and Oscillators for Frequency Control and Timing Applications. Army Research Laboratory, 1994.Google Scholar
- 8.B. Razavi. Analysis, modeling and simulation of phase noise in monothilic voltage-controlled oscillators. In Proc. IEEE Custom Integrated Circuits Conference, May 1995.Google ScholarCross Ref
- 9.E. Hafner. The effects of noise in oscillators. Proceedings of the IEEE, 54(2):179, February 1966.Google ScholarCross Ref
- 10.K. Kurokawa. Noise in synchronized oscillators. IEEE Transactions on Microwave Theory and Techniques,MTT- 16:234-240, 1968.Google ScholarCross Ref
- 11.V. Rizzoli, A. Costanzo, F. Mastri, and C. Cecchetti. Harmonic-balance optimization of microwave oscillators for electrical performance, steady-state stability, and near-carrier phase noise. In IEEE MTT-S International Microwave Symposium Digest, May 1994.Google Scholar
- 12.M. Okumura and H. Tanimoto. A time-domain method for numerical noise analysis of oscillators. In Proceedings of the ASP-DAC, January 1997.Google ScholarCross Ref
- 13.F. Kartner. Analysis of white and noise in oscillators. International Journal of Circuit Theory and Applications, 18:485519, 1990.Google Scholar
- 14.A. Hajimiri and T.H. Lee. A state-space approach to phase noise in oscillators. Technical memorandum, Lucent Technologies, July 1997.Google Scholar
- 15.A. Demir and J. Roychowdhury. On the validity of orthogonally decomposed perturbations in phase noise analysis. Technical memorandum, Bell Laboratories, Murray Hill, 1997.Google Scholar
- 16.R. Grimshaw. Nonlinear Ordinary Differential Equations. Blackwell Scientific, 1990.Google Scholar
- 17.L. Arnold. Stochastic Differential Equations: Theory and Applications. John Wiley & Sons, 1974.Google Scholar
- 18.C.W. Gardiner. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer-Verlag, 1983.Google Scholar
- 19.H. Risken. The Fokker-Planck Equation. Springer-Verlag, 1989.Google ScholarCross Ref
- 20.J.A. McNeill. Jitter in Ring Oscillators. PhD thesis, Boston University, 1994.Google Scholar
- 21.K.S. Kundert, J.K. White, and A. Sangiovanni-Vincentelli. Steady-State Methods for Simulating Analog and Microwave Circuits. Kluwer Academic Publishers, 1990.Google ScholarCross Ref
- 22.A. Dec, L. Toth, and K. Suyama. Noise analysis of a class of oscillators. To be published in IEEE Transactions on Circuits and Systems, 1997.Google Scholar
- 23.T.C. Weigandt, B. Kim, and P.R. Gray. Analysis of timing jitter in cmos ring-oscillators. In Proc. IEEE ISCAS, June 1994.Google ScholarCross Ref
Index Terms
Phase noise in oscillators: a unifying theory and numerical methods for characterisation
Recommendations
Phase noise in oscillators: DAEs and colored noise sources
ICCAD '98: Proceedings of the 1998 IEEE/ACM international conference on Computer-aided designNew Computational Results and Hardware Prototypes for Oscillator-based Ising Machines
DAC '19: Proceedings of the 56th Annual Design Automation Conference 2019In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes using CMOS ...
Gen-Adler: the Generalized Adler's equation for injection locking analysis in oscillators
ASP-DAC '09: Proceedings of the 2009 Asia and South Pacific Design Automation ConferenceInjection locking analysis based on classical Adler's equation is limited to LC oscillators as it is dependent on quality factor. In this paper, we present the Generalized Adler's equation applicable for injection locking analysis on oscillators ...
Comments