An Analytical Approach of Discrete-Time Modeling of Fixed and Variable Frequency Digital Modulation

This paper proposes an analytical approach of discrete-time (DT) large-signal and small-signal modeling of digitally controlled DC-DC converters operated under different fixed-frequency and variable-frequency modulation techniques using uniform and event-based sampling. The proposed framework (i) provides a mathematical basis for existing approximate DT small-signal modeling and (ii) further improves accuracy, (iii) allows natural extensions to a wider class of fixed and variable frequency digital modulators, sampling techniques and converter topologies, and finally provides (iv) DT large-signal models for nonlinear analysis and high performance digital controller design. Boost converter design cases studies are considered, and the usefulness of variable frequency modulation is demonstrated using simulation and experimental results over its fixed-frequency counterpart. The proposed approach provides a basis to develop, analyze, and design of future high performance digital control.