Discontinuous Map Analysis of a DC-DC Converter Governed by Pulse Skipping Modulation

Abstract

This paper reports the bifurcation phenomena in a dc-dc converter governed by a pulse skipping modulation (PSM) scheme, which is normally used to improve efficiency under light load condition. It is shown that the discrete-time model of the system takes the form of a discontinuous map, where the discrete-time state space is piecewise smooth, divided into five regions, each with a different functional form and separated by four borderlines. One additional borderline is considered to identify an infeasible region during a PSM operation. For a restricted operating region, we show that the system is described by a one-dimensional discontinuous map; otherwise it is a combination 1-D and 2-D forms. We derive the conditions for the existence and stability of different periodic orbits. We observe a period-adding cascade in which the periodicity varies non-monotonically exhibiting abrupt changes in the spectral composition for a smooth parameter variation. The proposed method may be useful for modeling and analysis of other dc-dc converter topologies governed by a PSM operation.