Unified Discrete-Time Modeling of Buck Converter in Discontinuous Mode

A 1-D discrete-time model is used to analyze the buck converter in discontinuous conduction mode. Both the buck converter power stage and the buck converter under current mode control are analyzed in a unified way. The effects of adding current control or a compensating ramp can be clearly seen. Conditions for multiple or zero steady-state solutions are obtained. A different instability reported previously is explained by the saddle-node bifurcation. Adding the compensating ramp into the current loop may be ineffective, because the instability is due to the dynamics of capacitor voltage, not the inductor current, and the saddle-node bifurcation is different from the period-doubling bifurcation.