Alternate forms of the PWM switch model in discontinuous conduction mode [DC-DC converters]

A pulsewidth-modulated (PWM) DC-DC converter enters discontinuous conduction mode (DCM) as its inductor current attempts to reverse direction, but cannot do so because of switch implementation, and remains at zero in the last interval of each switching period. Three equivalent three-terminal nonlinear transformers are described as the models for the PWM switch in a DCM converter, each having one of the three terminals serving as the common terminal. Each model facilitates the analysis of those corresponding converters in which the PWM switch terminal corresponds to the common transformer terminal is DC-grounded. Examples are given to demonstrate how the models are used to derive the DCM criteria, and the ideal and nonideal voltage gains for the buck-boost, buck, and boost DC-DC converters. The results predicted by the models agree with those reported and verified in the literature