A Comparative Study of Boundary Control With First- and Second-Order Switching Surfaces for Buck Converters Operating in DCM

A performance comparison of boundary control with the first-(sigma¹) and second-order(sigma²) switching surfaces for buck converters operating in discontinuous conduction mode (DCM) is presented in this paper. Performance attributes under investigation include 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 sigma¹. Conversely, the operating point remains unchanged in converters with sigma². As well as in continuous conduction mode (CCM), sigma² can make the converter revert to the steady-state in two switching actions in DCM and gives better static and dynamic responses than in both CCM and DCM. Most importantly, its control law and settings are applicable for both modes. Experimental results of a prototype are found to be in good agreement with theoretical predictions.