Sampled-Data Modeling and Stability Analysis of Digitally Controlled Buck Converter With Trailing-Edge and Leading-Edge Modulations

For a digitally controlled dc-dc converter with leading-edge modulation or trailing-edge modulation, due to the delay and different sampled points, its nonlinear behavior and the magnitude-phase response in high frequency and low frequency cannot be accurately depicted by the averaged modeling method, but can be predicted by the sampled-data modeling method. However, the conventional sampled-data model is usually more complicated and less intuitive, which is not conducive to the presentation of physical meaning and the design of the controller for the converter. Based on the reasonable approximation of the sampled-data model, this article proposes a second-order global equivalent circuit for the buck converter with different modulations. Meanwhile, the small-signal model in the z-domain based on the equivalent circuit is derived. Using the proposed equivalent circuit, the detailed operating waveform of the switching circuit of dynamic and stable state can be predicted without considering the ripple ratio of the state variables and the stability boundaries of various parameters of the system can be accurately analyzed, including the parasitic parameters. Furthermore, based on the stability analysis of the controller parameters, a proportional-integral-derivative controller is designed to verify the stability difference between the two modulation modes when the load steps. Finally, a prototype of the buck converter was constructed to verify the effectiveness of the model and theoretical analysis.