A general method to predict the amplitude of oscillation in nearly sinusoidal oscillators

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 51, Issue 8, 2004, Pages 1586-1595

  Maggio, Gian Mario ^a,b   De Feo, Oscar ^c   Kennedy, Michael P ^a  

^a IEEE   (Ireland)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); CIRCUIT OSCILLATIONS; COMPUTER SIMULATION; MATHEMATICAL MODELS; STATE SPACE METHODS;

CENTER MANIFOLD THEOREM; COLPITTS OSCILLATOR; HOPF BIFURCATION; HOPF NORMAL FORM THEOREM; OSCILLATION AMPLITUDE;

OSCILLATORS (ELECTRONIC);

EID: 4344660183     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2004.832793     Document Type: Article

References (22)

1. S. Sedra and K. Smith, Microelectronic Circuits, 4th ed. New York: Oxford Univ. Press, 1998.
2. A. A. Andronov, S. E. Khaikin, and A. A. Vitt, Theory of Oscillators. New York: Dover, 1987.
3. J. E. Marsden and M. McCracken, The Hopf Bifurcation and its Applications. Berlin, Germany: Springer-Verlag, 1976, vol. 10.
4. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983.
5. C. Keidies, "Classification of nonlinear dynamic networks and its usage in oscillator design," Ph.D. dissertation (in German), Wuppertal Univ., Wuppertal, Germany, 1996.
6. W. Mathis, "Nonlinear electronic circuits - An overview," in Proc. MIXDES 2000, Gdynia, Poland, 2000, pp. 15-17.
7. L. O. Chua and Y. S. Tang, "Nonlinear oscillation via Volterra series," IEEE Trans. Circuits Syst., vol. CAS-29, pp. 150-168, 1982.
8. W. Mathis and B. Voigt, "Applications of lie series averaging in nonlinear oscillation," in Proc. ISCAS'97, Philadelphia, PA, May 1987, pp. 911-914.
9. C. Keidies and W. Mathis, "Application of normal forms to the analysis of nonlinear circuits," in Proc. NOLTA'93, Honolulu, HI, Dec. 1993, pp. 853-858.
10. K. K. Clarke and D. Hess, Communication Circuits: Analysis and Design. Reading, MA: Addison-Wesley, 1971.
11. M. Basso, R. Genesio, and A. Tesi, "A frequency method for predicting limit cycle bifurcations," Nonlinear Dynamics, vol. 13, pp. 339-360, 1997.
12. Q. Huang, "Exact calculation of oscillation amplitude and predicting power consumption for CMOS Colpitts oscillators," in Proc. ISCAS'97, Hong Kong, June 1997, pp. 1401-1404.
13. A. Buonomo and C. Di Bello, "Asymptotic formulas in nearly sinusoidal nonlinear oscillators," IEEE Trans. Circuits Syst. I, vol. 43, pp. 953-963, Dec. 1996.
14. A. I. Lur'e, Some Nonlinear Problems in the Theory of Automatic Control. London, U.K.: H. M. Stationery, 1957.
15. A. I. Mees and L. O. Chua, "The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems," IEEE Trans. Circuits Syst., vol. CAS-26, pp. 235-254, Apr. 1979.
16. Y. Kuznetsov, "Numerical normalization techniques for all codim 2 bifurcations of equilibria in odes," SIAM J. Numer. Anal., vol. 36, pp. 1104-1124, 1999.
17. G. M. Maggio, O. D. Feo, and M. P. Kennedy, "An explicit expression for the amplitude of oscillation in the Colpitts oscillator," in Proc. ECCTD'99, Stresa, Italy, 1999, pp. 869-872.
18. C. Keidies and W. Mathis, "Application of center manifolds to oscillator analysis," in Proc. ECCTD'95, Istanbul, Turkey, 1995, pp. 95-98.
19. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation. Cambridge, U.K.: Cambridge Univ. Press, 1991.
20. G. M. Maggio, O. De Feo, and M. P. Kennedy, "Nonlinear analysis of the Colpitts oscillator and applications to design," IEEE Trans. Circuits Syst. I, vol. 46, pp. 1118-30, Sept. 1999.
21. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2nd ed. New York: Springer-Verlag, 1995.
22. O. De Feo, G. M. Maggio, and M. P. Kennedy, "The Colpitts oscillator: Families of periodic solutions and their bifurcations," Int. J. Bifurc. Chaos, vol. 10, pp. 935-58, 2000.