A Unified Rule-Based Small-Signal Modelling Technique for Two-Switch, Non-Isolated DC–DC Converters in CCM

Abstract

The inherent non-linear behavior of switch-mode power supplies complicates the task of computing their linear models, which are essential for a model-oriented control design of DC–DC converters. In a model-oriented control design approach, the accuracy of the plant model directly influences the performance of the control system as the plant parameters tend to be linked to the controllers’ gains. Moreover, the extractions of linear dynamic models of high-order non-linear plants such as DC–DC converters are laborious and mathematically intractable. Therefore, in this paper, a generalized expression that represents either the audio-susceptibility or the control-to-output voltage transfer function for voltage-mode control is proposed. The proposed generalization reduces the task of computing the small-signal model of a given converter to simple calculations of coefficients of generalized transfer function/expression. It is shown that the coefficients of the generalized model can be deduced by inspection, directly from the circuit diagram, allowing the whole model to be computed by inspection. Additionally, the proposed modelling technique will be shown to have secondary use of verifying accuracy even when conventional modelling techniques such as state-space averaging or circuit averaging are used.

Keywords

• DC–DC converter
• small-signal modelling
• converter dynamics
• unified analysis
• controller design
• generalized model