Prediction of subharmonic oscillation in switching regulators: from a slope to a ripple standpoint

New exact critical conditions for predicting subharmonic instability in switching regulators are approximated by simple design-oriented expressions valid under practical conditions. These simplified expressions contain the ripple and slope information of the feedback control signal. Depending on the converter topology, the controller used and values of parasitic parameters, either the slope or the ripple can be dominant in predicting instability. A discussion on the validity of this interpretation is illustrated through six different examples of switching regulators using the concept of the spectral radius and the relative degree of the system loop. Using this approach, the boundary between the desired stable region and the subharmonic instability can be easily obtained. The theoretical results are validated by means of numerical simulations.