A General Approach to Sampled-Data Modeling for Ripple-Based Control—Part I: Peak/Valley Current Mode and Peak/Valley Voltage Mode

Abstract

This article is aiming to unify the modeling methods for various ripple-based control schemes. It is divided into two parts, and the first part presents a sampled-data modeling method for the peak/valley current mode (PCM/VCM) control and the peak/valley voltage mode (PVM/VVM) control. It is pointed out that due to the high bandwidth of the dc–dc converter under PCM/VCM or PVM/VVM control, the sideband effect cannot be ignored in the modeling process. Meanwhile, with the small-signal assumption, the feedback perturbation signal has a discontinuity of the first kind at each sampling instant, so the perturbation value at this instant should be obtained according to the Dirichlet conditions, which is equal to half of the sum of the limit values on the left and right sides of the signal. Then, by using Shannon's sampling theorem, the transfer functions of the modulator and the loop gain are derived, and they are used to analyze the influence of the sideband components on the converter stability. Finally, the experimental results from a PCM controlled buck converter validate the proposed modeling technique.