Small-Signal Models With Extended Frequency Range for DC–DC Converters With Large Modulation Ripple Amplitude

Abstract

Application of pulse width modulation (PWM) is known to produce sideband effects. The accuracy of the models of dc–dc converters can be improved if essential information of the sideband effects of PWM can be incorporated. In this paper, the aliasing effect of the sideband components on the closed-loop control is analyzed, and an effective representation of the transfer function of the pulse-width modulator is derived. Applying this transfer function to the dc–dc converter, an extended-frequency-range small-signal model is obtained, which can be conveniently used for deriving the loop gain of a PWM-controlled dc–dc converter. Furthermore, for wideband control applications, the large switching ripple in the modulation signal necessitates adjustment of the representation of the gain of the pulse-width modulator, which is dependent on the controller. Despite being highly accurate for stability assessment, the extended-frequency-range model is relatively complex after incorporating the effects of the sideband components and the large switching ripple. An approximate approach is introduced to simplify the loop gain expression and to provide physical insights into the effects of the sideband components and large modulation ripple amplitude. Experimental verification of the extended-frequency-range model is provided for a buck converter and a boost converter.