Multifrequency Small-Signal Model for Buck and Multiphase Buck Converters

To investigate the high-frequency behaviors of buck and multiphase buck converters, this paper develops a modeling method based on the harmonic-balance approach. Because the nonlinear pulse-width modulator generates sideband components, the sideband effect occurs in a closed-loop converter. Taking this effect into account, the multifrequency small-signal model is proposed, which is applicable beyond half of the switching frequency. In a voltage-mode-controlled buck converter, the introduced model predicts the measured phase delay of the loop gain, while the conventional average model fails to explain this phenomenon. Furthermore, this model is extended to the case of the multiphase buck converter. The influence from the interleaving technique is discussed and the frequency-domain characteristics are clearly explained. Simulation and experimental results are provided to verify the achievements of the proposed model