Accurate Small-Signal Modeling and Stability Analysis of Wide-Input Buck Converter Considering Modulation Waveform Ripples

Buck converters are widely used in consumer electronics, electric vehicles, and dc microgrids. Small-signal models are necessary tools to design high-quality controllers. However, most of them neglect modulation waveform ripples, which introduces significant errors under high-bandwidth controls. Recently, two models explain the influences of nondifferentiable modulation waveform ripples by their left-side derivatives at crossing points. However, this conclusion is built on the premise that infinite sideband components caused by switching have been considered, which largely complicates these models. The accurate small-signal model with finite sideband components is proposed for nondifferentiable modulation waveform ripples in this article. Based on it, the stable working region and control design of wide-input high-bandwidth Buck converters are talked about. Simulations and experiments validate the accuracy and effectiveness of the proposed model.

I. Introduction

Dc/dc converters feature with strong nonlinearity and time variance due to switching effects. The small-signal averaged model transforms them into linear and time-invariant systems to simplify control designs [1]. As shown in Fig. 1, this model is built on the following two basic assumptions from the perspective of the frequency domain [2]. 1)

The dc component of modulation waveforms (solid line on 0 of the horizontal axis) is treated as pulsewidth modulation (PWM) steady-state operating points, while modulation waveform ripples (MWRs) are ignored (other solid lines on horizontal axis).

2)

The output perturbation of PWM merely considers the fundamental frequency component (dashed lines on ±ω_p of the horizontal axis), while sideband components caused by switching (other dashed lines) are neglected.

Fig. 1.

Modulation waveform harmonics in steady state and sideband components under small-signal perturbation, where ω_s and ω_p represent the switching frequency and the small-signal perturbation frequency in angular form.