Ripple-based Period-2 bifurcation border detection in switching power regulators

This paper extends the validity of a ripple-based index able to predict the frontier of fast-scale instability bifurcation in switching power converters, for the whole design-space and for different conduction modes. Hitherto a first validation of the index, based on the approximated ripple level in the PWM modulator, was carried out for a basic proportional voltage feedback PWM buck converter and for L, C, f
s
, K
p
parameters. This article carries out a complete design-space analysis and the stability boundary dependence on converter parameters is found. Besides, the circuit-based approach has been validated through a comparison between the proposed index and the classical analytical methods based in the linearization of the discrete-time nonlinear map. The paper also validated the proposed index with a numeric recursive simulation based on use the exact analytic ripple expression obtained by Laplace transform. These simulations also give a new perspective of the period-doubling phenomena as a simple negative feedback in the system due the ripple.