Abstract
A physically justifiable mathematical model is proposed for a class of current-controlled, negative resistance oscillators having terminal characteristics which are poorly represented by the van der Pol, Scott, and Ceschia-Zecchin equations. Such resonators are typified by the monolithic emitter-coupled astable multivibrator (ECAM). A unique, three-parameter equation, based on the inverse hyperbolic tangent, is matched to the ECAM voltage-current curve. Using the method of Kryloff and Bogoliuboff, the transient and steady-state behavior of the ECAM is derived for oscillation with single-mode and double-mode LCR networks under quasi-linear conditions. An expression for the time of amplitude build-up and decay is derived. A phase plane is constructed for the double-mode case, yielding a system apparently free of simultaneous modes. The validity of the model is experimentally verified for quartz-controlled ECAM devices. The analysis results are extendable ton resonant modes and may be generalized to voltage-controlled devices.
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References
T. Endo and T. Ohta, “Multimode oscillations in a coupled oscillator system with fifth-power nonlinear characteristics,”IEEE Trans. Circuits Syst., Vol. CAS-27, pp. 277–283, April 1980.
T. Endo and T. Ohta, “Multimode oscillations in a coupled oscillator system, a case of fifth-power nonlinear character,”Trans. Inst. Electron. andCommun. Eng. Jpn., Sect. E. Vol. E 61, pp. 828–829, October 1978.
S. P. Datardina and D. A. Linkens, “Multimode oscillations in mutually coupled van der Pol type oscillators with fifth-power nonlinear characteristics,”IEEE Trans. Circuits Syst., Vol. CAS-25, pp. 308–315, May 1978.
T. Endo and S. Mori, “Mode analysis of a ring of a large number of mutually coupled van der Pol oscillators,”IEEE Trans. Circuits Syst., Vol. CAS-25, pp. 7–18, January 1978.
T. Endo and S. Mori, “Mode analysis of a multimode ladder oscillator,”IEEE Trans. Circuits, Syst., Vol. CAS-23, pp. 100–113, February 1976.
R. R. Cordell and W. G. Garrett, “A highly stable VCO for application in monolithic phase-locked loops,”IEEE J. of Solid State Circuits, Vol. SC-10, pp. 480–485, December 1975.
E. N. Murthi, “A monolithic phase-locked loop with post detection processor,”IEEE J. of Solid State Circuits, Vol. SC-14, pp. 155–161, February 1979.
N. Kryloff and N. Bogoliuboff,Introduction to Nonlinear Mechanics (translation by S. Lefschetz), Princeton University Press, Princeton, New Jersey, 1943.
N. Minorsky,Introduction to Non-Linear Mechanics, J. W. Edwards, Ann Arbor, Michigan, 1947.
W. A. Edson, “Frequency memory in multimode oscillators,”IRE Trans. Circuit Theory, Vol CT-2, pp. 58–66, March 1955.
J. S. Schaffner, “Simultaneous oscillations in oscillators,”IRE Trans Circuit Theory, Vol. CT-1, pp. 2–8, June 1954.
M. E. Frerking, “Spurious oscillations in crystal oscillators,”Proc. Nat. Symp. on Frequency Control., pp. 501–516, 1966.
R. E. Fontana, “Internal resonance in circuits containing nonlinear resistance,”Proc IRE, Vol. 39, pp. 945–951,August 1951.
W. A. Edson, “Multiple resonance effects in oscillators,”Proc. Nat. Elec. Conf., Vol. 9, pp. 171–177, 1953.
E. M. Dewan, “Harmonic entrainment of van der Pol oscillations: phase-locking and asynchronous quenching,”IEEE Trans. Automatic Control, Vol. AC-17, pp. 655–663, October 1972.
Y. Ueda and N. Akamatsu, “Chaotically transitional phenomena in the forced negative-resistance oscillator,”IEEE Trans. Circuits and Systems, Vol. CAS-28, pp. 217–224, March 1981.
B. van der Pol, “On oscillation hysteresis in a triode generator with two degrees of freedom,”Phil. Mag., Vol. 43, pp. 701–719, April 1922.
M. L. Cartwright, “Forced oscillations in nearly sinusoidal systems,”J. IEE (London), Vol. 95, pp. 88–96, 1948.
N. Kryloff and N. Bogoliuboff, “Sur le phénomène de l'entraÎnment en radiotechnique,”Comptes Rendus, Vol. 194, pp. 1064–1066, March 21, 1932.
M. I. Disman and W. A. Edson, “Simultaneous asynchronous oscillations in class-C oscillators,”Proc. IRE, Vol. 46, pp. 895–903, May 1958.
P. R. Scott, “Large amplitude operation of the nonlinear oscillator,”Proc. IEEE, Vol. 56, pp. 2182–2183, December 1968.
M. Murata, M. Ohta, and T. Namekawa, “Analysis of an oscillator consisting of digital integrated circutis,”IEEE J. Solid State Circuits, Vol. SC-5, pp. 165–168, August 1970.
R. J. Mulholland, P. M. Honnell, and K. J. Borgwald, “Bounds for a twoparameter nonlinear oscillator,”IEEE Trans. Circuits and Systems, Vol. CAS-21, pp. 96–99, January 1974.
M. Ceschia and G. Zecchin, “Asymptotic amplitude from a two-parameter strongly nonlinear oscillator, ”IEEE Trans. Circuits and Systems, Vol. CAS-28, pp. 448–455, May 1981.
M. Ceschia and G. Zecchin, “Asymptotic amplitudes for a three-parameter oscillator,”IEEE Trans. Circuits and Systems, Vol. CAS-28, pp. 456–459, May 1981.
F. C. Fitchen,Electronic Integrated Circuits and Systems, Van Nostrand, New York, 1970, p. 128.
J. A. Connelly,Analog Integrated Circuits, Wiley, New York, 1975, pp. 58–87.
P. R. Gray and R. G. Meyer,Analysis and Design of Analog Integrated Circuits, Wiley, New York, 1977, p. 160.
W. J. Cunningham,Introduction to Nonlinear Analysis, McGraw-Hill, New York, 1958.
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Walker, S.S., Connelly, J.A. A new negative resistance oscillator model. Circuits Systems and Signal Process 2, 213–238 (1983). https://doi.org/10.1007/BF01599160
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DOI: https://doi.org/10.1007/BF01599160