SUMMARY The first period‐doubling bifurcation of a dc–dc buck converter controlled by a zero‐average dynamic strategy is studied in detail. Owing to the saturation of the duty cycle, this bifurcation is followed by a border‐collision bifurcation, which is the main mechanism to introduce instability and chaos in the circuit. The multiparameter analysis presented here leads to a complete knowledge of the relatioship between these two bifurcations. The results are obtained by using a frequency‐domain approach for the study of period‐two oscillations in maps. Copyright © 2010 John Wiley & Sons, Ltd.