Stability of DC-DC converters: A ripple based index approach

In this paper we combine two different approaches for studying stability of DC-DC power electronic circuits. The first method is based on the Routh-Hurwitz criterion for stability of linear systems and it is suitable for detecting low frequency oscillations. The second approach uses the ripple injected in the modulator from the controller and it is suitable for predicting subharmonic oscillations. A DC-DC buck converter is used as an example to put in evidence the usefulness of the method. After showing that the system can undergo both period doubling and Neimark-Sacker bifurcation by numerical time domain simulations from the switching model, we give analytical closed form conditions for slow scale (low frequency) instability. The ripple at the PWM modulator is taken into account to predict the subharmonic oscillations.