On the form of feedback function that can lead to chaos in discontinuous-mode DC/DC converters

In this paper we study the conditions for the DC/DC boost and buck switching regulators operating in discontinuous conduction mode to possibly undergo a period-doubling route to chaos. The essential mathematical tool is the Schwarzian derivative. The result helps determine the form of feedback control scheme for which a period-doubling route to chaos may exist. Results from the calculations reveal that these two types of converter share the same set of conditions. Specifically, any monotonically decreasing control function with a sufficiently large small-signal gain may give rise to a period-doubling cascade in both the boost and the buck DC/DC switching regulators. The analysis in principle can be applied to other types of converters operating in discontinuous conduction mode