Unified discrete‐map modelling and dynamical behaviour analysis of current mode controlled tri‐state dc–dc converters

Abstract

Through analysing the operating principle of current mode controlled (CMC) tri-state dc-dc converters, the inductor current borders are obtained and a unified discrete-map model of CMC tri-state dc-dc converters with ramp compensation is established. According to this model, the dynamical behaviour of the tri-state dc-dc converters is analysed by utilising bifurcation diagram. In addition, the boundary equation of tri-state dc-dc converters from stable pseudo-continuous conduction mode (PCCM) period-1 state to unstable state is derived. The expressions of the minimum slope of ramp compensation for the converter shifting from unstable state to stable PCCM period-1 state are also obtained. Meanwhile, the operating regions are divided effectively by the boundary equation. The research results indicate that border collision bifurcation could occur when the circuit parameters vary, including a bifurcation from one periodic orbit to another periodic orbit, such as period-1 to period-2 or period-2 to period-4 and so on, or a bifurcation from a period orbit to chaotic orbit. By using ramp compensation, the stable working range of the CMC tri-state dc-dc converter could be broadened. Finally, an experimental circuit is built and the experiment results verify the theoretical analysis.