Bifurcations in current-programmed DC/DC buck switching regulators—conjecturing a universal bifurcation path

Abstract

SUMMARY 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 Cuk 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 dierent 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 rst on-set of ip-bifurcation is predicted. Computer simulations from the ‘exact’ model verify the results. The exhibition of quasi-periodic orbits is conrmed 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.