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Proceedings Paper

Theory Of Phase-Locked Regenerative Oscillators With Nonlinear Frequency-Shift Effects
Author(s): J. E. Walsh; R. C. Davidson; D. J. Sullivan
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Paper Abstract

Nonlinear frequency-shift effects in a regenerative oscillator driven by an external locking signal can be modeled in canonical fashion by inclusion in the Van der Pol equation of an additional cubic restoring force term. This can be seen from an analysis based on the complex Poynting's theorem and from the presence of an additional frequency shift term in the first-order phase evolution equation. This Van der Pol/Duffing equation was proposed by Lashinsky as a model of the generic regenerative oscillator. Both Van der Pol and Duffing nonlinearities are important in conventional high-power sources. In the case of microwave sources the linear and nonlinear behavior of the system is governed primarily by the interaction term which appears in the complex Poynting's theorem. This term is itself complex and in the small-signal limit the real and imaginary components are related by the Kramers-Kriinig relations. Extension into the large-signal regime thus naturally results in the appearance of both Van der Pol and Duffing contributions to the nonlinear coupled-mode equations. Approximate analytic and numerical studies of the Van der Pol/Duffing equation, with emphasis on phase-locking behavior, will be presented. Finally the connection between the general theory and intense microwave source behavior will be illustrated by an analysis of the elementary monotron.

Paper Details

Date Published: 25 July 1989
PDF: 9 pages
Proc. SPIE 1061, Microwave and Particle Beam Sources and Directed Energy Concepts, (25 July 1989); doi: 10.1117/12.951794
Show Author Affiliations
J. E. Walsh, Dartmouth College (United States)
R. C. Davidson, Plasma Fusion Center, M.I.T. (United States)
D. J. Sullivan, Mission Research Corp. (United States)


Published in SPIE Proceedings Vol. 1061:
Microwave and Particle Beam Sources and Directed Energy Concepts
Howard E. Brandt, Editor(s)

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