A general unified approach to modelling switching DC-to-DC converters in discontinuous conduction mode

Abstract

A method for modelling switching converters in the discontinuous conucction mode is developed, whose starting point is the unified state-space representation, and whose end results is a complete linear circuit model which correctly represents all essential features, namly, the input, output, and transfer properties (static dc as well as dynamic ac small signal). While the method is generally applicable to any switching converter operating in the discontinuous conduction mode, it is extensively illustrated for the three common power stages (buck, boost, and buck-boost). The results for these converters are then easily tabulated owing to the fixed equivalent circuit topology of their canonical circuit model. The outlined method lends itself easily to investigation of the discontinuous conduction mode in more complex structures (cascade connection of buck and boost converters, for example), in which more thean one inductor current may become discontinuous. As opposed to other modelling techniques, the new method considers the discontinuous conduction mode as a special case of the continuous conduction mode.