Stability Analysis With Considering the Transition Interval for PWM DC-DC Converters Based on Describing Function Method

The nonlinearity of the switching process in DC-DC converters can result in the inaccuracy and invalidation of traditional stability criterion based on linear modeling, which is very harmful in practice, especially for the DC-DC converters with high stability requirements. In this paper, the describing function method is adopted for the modeling of switching process, namely, pulse width modulation (PWM), in DC- DC converters, and the describing function of the PWM is derived in detail. Considering the nonlinear items in the obtained describing function of PWM, the selection of the parameters in these nonlinear items are first provided and proved in this paper. With the obtained describing function, the stability of the PWM DC-DC converter can be analyzed exactly. Taken a PWM boost converter as an example, the nonlinear model based on describing function and the linear model are established, respectively; furthermore, the stability analysis based on these two kinds of models are carried out. Comparing with the traditional linear stability criterion, the simulation and experimental results validate the effectiveness and accuracy of the stability analysis based on describing function method. Furthermore, the transition interval of the PWM DC-DC converter from a stable region to an unstable region can be determined exactly by the proposed stability analysis method, which is helpful to determine the stability margin in real engineering applications. Therefore, this paper provides a practical stability analysis method for PWM DC-DC converters.