Modeling and stability analysis of cascade buck converters with N power stages

This paper presents a method for stability analysis of N-cell cascade step-down buck converters, which is a kind of complex nonlinear system. A nonlinear model in the form of time-variant state equations is derived, and then the loop gain describing the overall system is introduced. With the help of them, we obtain the equations for phase cross over frequency and gain margin by small-signal perturbation technique, harmonic balance method, and inverse iteration method. Based on the equations, the overall cascade system stability can be analyzed regardless of the number of converters cascaded. Finally, the cascade buck converter with three power stages is used to demonstrate the effectiveness of the proposed stability analysis method.