A generalized multifrequency small-signal model for high-bandwidth buck converters under constant-frequency voltage-mode control

This article studies the modeling of high-bandwidth buck converters under constant-frequency voltage-mode control, where the traditional small-signal averaged model fails due to two major factors in the pulsewidth modulation (PWM), i.e., the large harmonics of modulation waveform and the considerable sideband components. Several modified small-signal models have been proposed to improve the predictions of the frequency domain characteristics. However, these models are less generalized or with high complexity, and may hardly be used in the closed-loop design of real applications. To handle this issue, this article proposes a generalized multifrequency small-signal model (G-MFSSM) for high-bandwidth buck converters, which makes further progress in accuracy while maintaining simplicity in deriving the analytical transfer functions for a closed-loop design. The generalized average model is adopted to precisely describe the first-order harmonic of the modulation waveform, from which a correction factor is extracted to evaluate the influence of the ripple. Furthermore, two dominant sideband components are selected optimally for extremely accurate loop gain predictions. Finally, a closed-loop design procedure is presented for wide-input, high-bandwidth buck converters based on the proposed G-MFSSM. The validity of the proposed G-MFSSM is verified by simulations and experiments.