A Comparative Study of the Boundary Control of Buck Converters Using First- and Second-Order Switching Surfaces -Part II: Discontinuous Conduction Mode

This paper extends the scope of the part-I companion paper on comparing the performance characteristics of buck converters with the first- (sigma
¹
) and second-order (gamma
²
) switching surfaces. Major emphasis is given to converters operating in discontinuous conduction mode (DCM). Similar to the companion paper, performance attributes under investigation in this paper includes the average output voltage, output ripple voltage, switching frequency, parametric sensitivities to the component values, and large-signal characteristics. Due to the presence of the output hysteresis band, an additional switching boundary formed by the zero-inductor-current trajectory is created. This phenomenon causes a shift of the operating point in converters with sigma
¹
. Conversely, the operating point remains unchanged in converters with sigma
²
. As well as in continuous conduction mode (CCM), sigma can make the converter revert to the steady state in two switching cycles in DCM and gives better static and dynamic responses than sigma in both CCM and DCM. Most importantly, its control law and settings are the same in both modes. Experimental results of a prototype are found to be in good agreement with theoretical predictions