Ripple Based Index for Predicting Fast-Scale Instability of DC-DC Converters in CCM and DCM

It is well known that switching power electronic converters are prone to much nonlinear behavior. Both fast scale instability which is known also as flip bifurcation and slow scale instability which is known by the name of Neimark-Sacker bifurcation are possible. Recent finding has shown that the fast scale instability which can not be detected by the traditional averaged model could be detected by a ripple based unified index. This paper goes one step more in demonstrating that this index gives accurate results in obtaining the boundary of stability of DC-DC converters. The well known DC-DC buck converter under PWM voltage mode control is used to illustrate the results. Both continuous conduction mode CCM and discontinuous conduction mode DCM will be considered. In the later case we will show that our new approach gives more accurate results than those obtained from an approximated one dimensional discrete time model.