Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The use of the perturbation method for determining the pumping frequencies of parametric amplifiers


Author: Carl A. Ludeke
Journal: Quart. Appl. Math. 23 (1965), 1-17
MSC: Primary 78.41
DOI: https://doi.org/10.1090/qam/176748
MathSciNet review: 176748
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Abstract: This paper demonstrates that an old but very powerful and very general mathematical technique, the perturbation method, may be used to investigate such a modern application as parametric amplification. All possible pumping frequencies are predicted without recourse to any specialized procedures.


References [Enhancements On Off] (What's this?)

  • [1] ``Les méthodes nouvelles de la mécanique céleste,'' by H. Poincaré, Gauthier--Villars. Paris, Vol. 1, 1892, Chapters III and IV
  • [2] ``Differential Gleichungen der StÖvungstheorie,'' by Arid. Lindstedt, Mémories de l'Académie Impériale des Sciences de St. Petersbourg, Vol. XXXI, No. 4, 1883
  • [3] ``Theory of Parametric Amplification Using Nonlinear Reactances,'' by S. Bloom and K. K. N. Chang, RCA Review, Vol. XVIII, Dec. 1957, No. 4
  • [4] ``Introduction to Non-Linear Mechanics,'' by N. Kryloff and N. Bogoliuboff, Kieff, (Russian), 1937
  • [5] ``Asymptotic Methods in the Theory of Nonlinear Oscillations,'' Moscow, (Russian), 1958
  • [6] Nicolas Minorsky, Nonlinear oscillations, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1962. MR 0137891
  • [7] ``Sub-Harmonic Pumping of Amplifiers,'' by K. E. Mortenson, General Electric Research Laboratory Report No. 60--RL--2516E, September 1960
  • [8] If the reader is interested in other cases, including stability and bandwidth, he may refer to-- ``Theory of Parametric Amplification, ``by C. A. Ludeke, General Electric FPD Technical Information Series Report No. R61FPD531 December, 1961 For bandwidth see Part II, Page 10 For stability see Part III, Page 21

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Additional Information

DOI: https://doi.org/10.1090/qam/176748
Article copyright: © Copyright 1965 American Mathematical Society


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