Fourth-Order Quadratic Buck Converter Controller Design

Abstract

This paper aims to outline the process of dimensioning a controller tailored for a fourth-order step-down converter. In order to conduct a thorough small-signal analysis, it is imperative to find the state–space model in matrices form. Given its fourth-order nature, the control-to-output transfer function also aligns with this order, although its degree is ultimately reduced to a second-order using the tfest function. It is remarkable that the design of the type III error amplifier assumes a central position in the overall controller design process. The theoretical analysis was then subjected to rigorous validation via simulation, with particular attention paid to the step response in both input voltage and output resistance. This study developed from the desire to validate the efficacy of reducing the control-to-output transfer function degree using the tfest function, aiming to highlight a fourth-order converter to which controller design theory can be applied, related to that for a second-order converter.

Keywords

• controller design
• coupled inductors
• type III error amplifier
• static conversion ratio
• step-down converter