Bifurcations due to transition from continuous conduction mode to discontinuous conduction mode in the boost converter

We investigate the bifurcations that occur when a power-electronic converter moves from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) due to on-load parameter fluctuations. We derive the discrete map and show that the map is piecewise smooth, with the special property that on one side of the borderline, the determinant is less than -1, and on the other side the determinant is zero. We develop the theory of border collision bifurcations for this special condition, and explain the bifurcations observed at the CCM-DCM transition in the current mode controlled boost converter in the light of this theory.