Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 78.41

Retrieve articles in all journals with MSC: 78.41

Additional Information

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

American Mathematical Society