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Solutions for a three‐dimensional non‐linear stabilized oscillator
Author(s) -
Daboul J.,
Kaplan B. Z.
Publication year - 1986
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490140402
Subject(s) - limit (mathematics) , class (philosophy) , mathematics , linear system , control theory (sociology) , phase (matter) , limit cycle , voltage controlled oscillator , voltage , mathematical analysis , computer science , physics , quantum mechanics , control (management) , artificial intelligence
A system of coupled non‐linear equations, describing a three‐phase stabilized oscillator, is analysed by introducing ‘cyclotomic’ co‐ordinates. We show that this system, under certain conditions, approaches asymptotically non‐conservative linear systems; and yet it does have stabilized solutions (limit cycles). The non‐linear system is solved analytically for an important class of stabilizing functions. We show that the frequency ω of our oscillator responds instantaneously to changes of certain parameters. This result has useful applications in building quickly responding novel electronic voltage‐controlled oscillators.