This paper proposes a precise analysis and modeling technique for a coupled inductor based boost converter with a symmetrical winding and identical inductance structure. Previous studies have tended to simplify the analysis by restricting the coupling coefficient(0.8＜ k≤1) to a specific range or by using current conversion methods based on the turns ratio. Consequently, there have been limitations in precisely examining the impact of the coupling coefficient(k) and the actual secondary current on system dynamics and control stability. To address these issues, this study performs precise modeling that simultaneously considers the coupling coefficient(0＜k＜1) and secondary current by reflecting the practical electrical characteristics of the coupled inductor.1-5.The proposed method derives state-space equations for each operating mode based on voltage and current differential equations and transforms them into a small-signal model using the state-space averaging method. In particular, by applying the identical inductance condition(L₁ =L₂ ), the design variables are optimized to the inductance(L) and coupling coefficient(k), thereby reducing analytical complexity and enhancing practical utility. The validity of the proposed model was verified through double-loop controller design using MATLAB SISOTOOL and PSIM simulations. The results demonstrated a high correlation between the theoretical step response and the switching non-linear simulation waveforms, proving the precision of the proposed design parameters and the effectiveness of the system stability control.
Kim et al. (Tue,) studied this question.
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