Nonlinear analysis of the Colpitts oscillator and applications to design

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 46, Issue 9, 1999, Pages 1118-1130

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

^a IEEE

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY COLLEGE DUBLIN   (Ireland)

^d EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; CIRCUIT OSCILLATIONS; NONLINEAR NETWORK ANALYSIS; NONLINEAR NETWORK SYNTHESIS;

COLPITTS OSCILLATORS;

OSCILLATORS (ELECTRONIC);

EID: 0033328895     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.788813     Document Type: Article

References (24)

1. A. I. Mees and L. Chua, The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems, IEEE Trans. Circuits Syst., vol. 26, pp. 235-254, Apr. 1979.
2. M. Basso, R. Genesio, and A. Tesi, A frequency method for predicting limit cycle bifurcations, Nonlinear Dynamics, vol. 13, pp. 339-360, 1997.
3. R. Genesio and A. Tesi, A harmonic balance approach for chaos prediction: Chua's circuit, Int. J. Bifurcation Chaos, vol. 2, no. 1, pp. 61-79, 1992.
4. M. Gilli and G. M. Maggio, Predicting chaos through an harmonic balance technique: An application to the Time-Delayed Chua's Circuit, IEEE Trans. Circuits Syst. I. vol. 43, pp. 872-874, Oct. 1996.
5. L. O. Chua, The genesis of Chua's circuit, Archiv Fuer Elektronik und Uebertragungstechnik, vol. 46, no. 4, pp. 250-257, 1992.
6. E. Freire, E. Ponce, and F. Torres, Hopf bifurcations in piecewise linear planar dynamical systems, in Proc. NDES'96, Seville, Spain, June 1996, pp. 129-134.
7. H. Kawakami and R. Lozi, Structure and Bifurcations of Dynamical Systems. Singapore: World Scientific, 1992.
8. M. P. Kennedy, Chaos in the Colpitts oscillator, IEEE Trans. Circuits Syst. I, vol. 41, pp. 771-774, Nov. 1994.
9. C. Wegener, G. M. Maggio, and M. P. Kennedy, An approximate one-dimensional model for the chaotic Colpitts oscillator, in Proc. NDES'96, Seville, Spain, June 1996, pp. 275-278.
10. G. M. Maggio, C. Kennedy, and M. P. Kennedy, Experimental manifestations of chaos in the Colpitts oscillator, in Proc. ISSC'97, Derry, Ireland, June 1997, pp. 235-242.
11. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering. New York: Addison-Wesley, 1994.
12. W. Jansen, CANDYS/QA: Algorithms, Programs, and User's Manual, Univ. Potsdam, Dec. 1995.
13. J. Millman and A. Grabel, Microelectronics, 2nd ed. Singapore: McGraw-Hill, 1988.
14. G. M. Maggio and M. P. Kennedy, On the relationship between continuous-time and discrete-time models of the Colpitts oscillator, in Proc. NDES'97, Moscow, Russia, 1997, pp. 240-245.
15. E. Doedel, H.B. Keller, and J.P. Kernévez, Numerical analysis and control of bifurcation problems (I) bifurcation in finite dimension, Int. J. Bifurcation Chaos, vol. 1, no. 3, pp. 493-520, 1991.
16. A. R. Champneys and Y. A. Kuznetsov, Numerical detection and continuation of codimension-2 homoclinic bifurcations, Int. J. Bifurcation Chaos, vol. 4, no. 4, pp. 785-822, 1994.
17. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory. New York: Springer-Verlag, 1995.
18. E. Doedel and J. Kernévez, AUTO: Software for continuation problems in ordinary differential equations with applications, Applied Math., 1986.
19. Y. A. Kuznetsov and V. V. Levitin, CONTENT: A multiplatform environment for continuation and bifurcation analysis of dynamical systems, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands, 1997.
20. P. Glendinning and C. Sparrow, Local and global behavior near homoclinic orbits, J. Stat. Phys., vol. 35, nos. 5/6, pp. 645-696, 1984.
21. P. Gaspard, R. Kapral, and G. Nicolis Bifurcation phenomena near homoclinic systems: A two parameter analysis, J. Stat. Phys., vol. 35, pp. 697-727, 1984.
22. J. P. Carcasses, Determination of different configurations of fold and flip bifurcation curves of a one or two-dimensional map, Int. J. Bifurcation Chaos, vol. 3, no. 4, pp. 869-902, 1993.
23. A. P. Kuznetsov, S. P. Kuznetsov, I. R. Sataev, and L. O. Chua, Two-parameter study of transition to chaos in Chua's circuit: Renormalization group, universality and scaling, Int. J. Bifurcation Chaos, vol. 3, no. 4, pp. 943-962, 1993.
24. S. E. Newhouse, The abundance of wild hyperbolic sets and nonsmooth sets for diffeomorphisms, Publ. Math., IHES 50, pp. 101-151, 1979.