Discrete-Time Poles and Dynamics of Discontinuous Mode Boost and Buck Converters Under Various Control Schemes

TL;DR

This paper presents a systematic analysis of the discrete-time poles and dynamics of nonlinear switching DC-DC boost and buck converters under various control schemes, revealing a single-pole model with phase responses beyond -90 degrees.

Contribution

It introduces a simple one-dimensional discrete-time model capturing the dynamics of boost and buck converters in discontinuous mode across multiple control schemes, highlighting the effects of control and load on system poles.

Findings

Single pole in discrete-time model with no zero.

Phase response can exceed -90 degrees.

Adding ramp slope affects control gain and susceptibility.

Abstract

Nonlinear systems, such as switching DC-DC boost or buck converters, have rich dynamics. A simple one-dimensional discrete-time model is used to analyze the boost or buck converter in discontinuous conduction mode. Seven different control schemes (open-loop power stage, voltage mode control, current mode control, constant power load, constant current load, constant-on-time control, and boundary conduction mode) are analyzed systematically. The linearized dynamics is obtained simply by taking partial derivatives with respect to dynamic variables. In the discrete-time model, there is only a single pole and no zero. The single closed-loop pole is a linear combination of three terms: the open-loop pole, a term due to the control scheme, and a term due to the non-resistive load. Even with a single pole, the phase response of the discrete-time model can go beyond -90 degrees as in the two-pole average models. In the boost converter with a resistive load under current mode control, adding the compensating ramp has no effect on the pole location. Increasing the ramp slope decreases the DC gain of control-to-output transfer function and increases the audio-susceptibility. Similar analysis is applied to the buck converter with a non-resistive load or variable switching frequency. The derived dynamics agrees closely with the exact switching model and the past research results.