A Design-Oriented Combined Approach for Bifurcation Prediction in Switched-Mode Power Converters

In this brief, two different approaches are combined for studying the stability of a buck switching power dc–dc converter and for predicting its bifurcations. Instability indexes derived from both approaches are combined to get a complete design-oriented perspective of bifurcation analysis in terms of practical circuit parameter and to show the effect of each parameter on the system behavior. The first approach is based on the conventional Routh–Hurwitz criterion applied to the averaged converter dynamics, and it is suitable for detecting low-frequency oscillations but is unsuitable for predicting fast-scale period-doubling instabilities. Complementarily, the second approach considers the ripple component before the pulsewidth modulator to quantitatively predict the occurrence of subharmonic oscillations. The usefulness of the combined approach is shown by analytically deriving inequalities that compress the complete design space into simple instability indexes, which, used complementarily, allow a division of the design space into the different instability regions (both period-doubling or fast-scale instability, and Hopf or slow-scale instability). Comparison of the design-oriented complete map obtained combining both methods and their related stability indexes with the results obtained both from time-domain numerical simulations of the exact switched state equations, as well as the stability border obtained from discrete recurrent maps, corroborates the approach.