Analyzing oscillators using multitime PDEs

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

Volumn 50, Issue 7, 2003, Pages 894-903

  Narayan, Onuttom ^a   Roychowdhury, Jaijeet ^b  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Frequency modulation (FM); Multitime partial differential equation (MPDE)

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CURRENT VOLTAGE CHARACTERISTICS; FREQUENCY MODULATION; NUMERICAL METHODS; OSCILLATORS (ELECTRONIC); PARTIAL DIFFERENTIAL EQUATIONS;

MULTITIME PARTIAL DIFFERENTIAL EQUATION; SOFTWARE PACKAGE SPICE; WARPED TIME;

ELECTRIC NETWORK ANALYSIS;

EID: 0042674189     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2003.813976     Document Type: Article

References (38)

1. H. G. Brachtendorf, G. Welsch, R. Laur, and A. B. Gerstner, "Numerical steady state analysis of electronic circuits driven by multi-tone signals," in Electrical Engineering. New York: Springer-Verlag, 1996, vol. 79, pp. 103-112.
2. J. Roychowdhury, "Analyzing circuits with widely-separated time scales using numerical PDE methods," IEEE Trans. Circuits. Syst., vol. 48, pp. 578-594, May 2001.
3. H. W. Broer, G. B. Huitema, and M. B. Sevryuk, Quasi-Periodic Motions in Families of Dynamical Systems: Order Amidst Chaos. New York: Springer-Verlag, 1996.
4. A. E. Siegman, Lasers. New York: University Science Books, 1986.
5. Y. Saad, Iterative Methods for Sparse Linear Systems PWS, MA, 1996.
6. R. W. Freund, "Reduced-Order modeling techniques based on krylov subspaces and their use in circuit Simulation," Bell Laboratories, Murray Hill, NJ, Tech. Rep. 11 273-980 217-02TM, 1998.
7. M. Rösch and K. J. Antreich, "Schnell stationäre simulation nichtlinearer schaltungen im frequenzbereich," (AEU) Elektr. Ubertragung, vol. 46, no. 3, pp. 168-176, 1992.
8. P. Feldmann, R. C. Melville, and D. Long, "Efficient frequency domain analysis of large nonlinear analog circuits," in Proc. IEEE Custom Integrated Circuits Conf., May, 5-8 1996, pp. 461-464.
9. G. D. Vendelin, Design of Amplifiers and Oscillators by the S-Parameter Method. New York: Wiley, 1982.
10. B. Parzen, Design of Crystal and Other Harmonic Oscillators. New York: Wiley, 1983.
11. U. Rhode and, Microwave and Wireless Synthesizers: Theory and Design. New York: Wiley, 1997.
12. I. M. Gottlieb, Practical Oscillator Handbook. New York: Oxford, 1997.
13. M. Farkas, Periodic Motions. New York: Springer-Verlag, 1994.
14. C. Hayashi, Nonlinear Oscillations in Physical Systems. New York: McGraw-Hill, 1964.
15. H. Haaken, Advanced Synergetics. New York: Springer-Verlag, 1987.
16. J. A. Murdock, Perturbations: Theory and Methods. New York: Wiley, 1991.
17. A. Nayfeh and D. Mook, Nonlinear Oscillations. New York: Wiley, 1979.
18. B. van der Pol, "On oscillation hysteresis in a simple triode generator," Phil. Mag., vol. 43, pp. 700-719, 1922.
19. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag, 1989.
20. A. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics. New York: Wiley, 1995.
21. E. N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci, vol. 20, pp. 130-141, 1963.
22. L. O. Chua, "The genesis of Chua's circuit," (AEU) Arch. Elektr. Ubertragung, vol. 46, pp. 248-291, 1992.
23. J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics. New York: Springer-Verlag, 1981.
24. R. Mickens, Oscillations in Planar Dynamic Systems. Singapore: World Scientific, 1995.
25. L. W. Nagel, "SPICE2: A Computer Program to Simulate Semiconductor Circuits," Ph.D. dissertation, Elec. Res. Lab., EECS Dept., Univ. of California, Berkeley, CA, 1975,.
26. T. L. Quarles, SPICE 3C.1 User's Guide. Berkeley, CA: Univ. of California, Apr. 1989, p. 94 720.
27. T. J. Aprille and T. N. Trick, "Steady-state analysis of nonlinear circuits with periodic inputs," Proc. IEEE, vol. 60, pp. 108-114, Jan. 1972.
28. S. Skelboe, "Computation of the periodic steady-state response of nonlinear networks by extrapolation methods," IEEE Trans. Circuits. Syst., vol. CAS-27, pp. 161-175, Mar. 1980.
29. R. Telichevesky, K. Kundert, and J. White, "Efficient steady-state analysis based on matrix-free Krylov subspace methods," in Proc. IEEE Decision and Control, vol. 1, 1995, pp. 480-484.
30. M. S. Nakha and J. Vlach, "A piecewise harmonic balance technique for determination of periodic responses of nonlinear systems," IEEE Trans. Circuits. Syst., vol. CAS-23, p. 85, Jan. 1976.
31. S. A. Haas, Nonlinear Microwave Circuits. Norwood, MA: Artech House, 1988.
32. V. Rizzoli and A. Neri, "State of the art and present trends in nonlinear microwave CAD techniques," IEEE Trans. Microwave Theory Tech., vol. 36, pp. 343-365, Feb. 1988.
33. K. S. Kundert, J. K. White, and A. Sangiovanni-Vincentelli, Stead-State Methods for Simulating Analog and Microwave Circuits. Norwell, MA: Kluwer, 1990.
34. R. J. Gilmore and M. B. Steer, "Nonlinear circuit analysis using the method of harmonic balance - A review of the art. Part I. Introductory concepts," Int. J. Microwave Millimeter Wave CAE, vol. 1, no. 1, 1991.
35. M. Rösch, "Schnell Simulation des stationären Verhaltens nichtlinearer Schaltungen," Ph.D. dissertation, Technischen Univ. München, Munich, Germany, 1992.
36. H. G. Brachtendorf and R. Laur, "Transient simulation of oscillators," Bell Labs, Murray Hill, NJ, Tech. Rep. ITD-98-34 096K, 1998.
37. L. O. Chua and P.-M. Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1975.
38. E. L. Allgower and K. Georg, Numerical Continuation Methods. New York: Springer-Verlag, 1990.