Simultaneous, multi-frequency, multi-beam antennas employing synchronous oscillator arrays

J. Cothern, T. Heath, G. Hopkins, R. Kerr, D. Lie, J. Lopez, B. Meadows

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The theoretical foundations of coupled, nonlinear oscillator arrays as applied to beam forming have, almost exclusively, presumed the unit cells are well described by a Van der Pol oscillator model. In the past, a "weak" association was made between the spectral output of the differential-pair oscillator and that of an ideal Van der Pol oscillator. By applying the Method of Multiple Scales to the Van der Pol dynamical equations, one finds that only odd order harmonics are present. Moreover, one can determine the key Van der Pol parameters (i.e., the amplitude parameter, p, and nonlinearity parameter, μ) through the power contained in the first and third harmonics.

Original languageEnglish
Title of host publicationApplications of Nonlinear Dynamics
Subtitle of host publicationModel and Design of Complex Systems
Number of pages7
StatePublished - 2009

Publication series

NameUnderstanding Complex Systems
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840


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