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Bifurcations in current‐programmed DC/DC buck switching regulators—conjecturing a universal bifurcation path
Author(s) -
Chan William C. Y.,
Tse C. K.
Publication year - 1998
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/(sici)1097-007x(199803/04)26:2<127::aid-cta997>3.0.co;2-j
Subject(s) - bifurcation , control theory (sociology) , period doubling bifurcation , mathematics , sequence (biology) , lyapunov exponent , logistic map , converters , topology (electrical circuits) , computer science , mathematical analysis , nonlinear system , physics , voltage , control (management) , combinatorics , chaotic , quantum mechanics , artificial intelligence , biology , genetics
Abstract This paper studies the bifurcation paths exhibited by a DC/DC buck switching regulator under current‐programmed control. Previous studies with the boost converter and the Ćuk converter have shown that two distinct types of bifurcation paths, namely one that goes through a region of quasi‐periodic orbits and via period‐doubling , are possible. We conjecture that these two different types of bifurcation paths are part of another bifurcation in which the quasi‐periodic sequence transmutes into the period‐doubling sequence, and that such a bifurcation is characteristic of current‐programmed DC/DC converters. In this paper we demonstrate that such a universal phenomenon is manifested in the current‐programmed buck switching regulator. We shall derive the describing iterative map in closed form and use it to develop the main results via a series of computer experiments. The characteristic multipliers are calculated and the first on‐set of flip‐bifurcation is predicted. Computer simulations from the ‘exact’ model verify the results. The exhibition of quasi‐periodic orbits is confirmed by computation of the Lyapunov exponent. Finally, a series of return maps are generated to provide an alternative viewpoint to the reported bifurcations in terms of a transmutation from a tent‐like map to a logistic‐like map. © 1998 John Wiley & Sons, Ltd.