Fractional‐Order Modeling and Gain Curve Analysis of Full‐Bridge CLLC Resonant Converter

Based on fractional calculus theory and the fact that inductors and capacitors inherently exhibit fractional‐order characteristics, this paper extends the traditional first harmonic approximation (FHA) method from the integer‐order domain to the fractional‐order domain to model and analyze the fractional‐order CLLC (FO‐CLLC) resonant converter. Compared to the conventional integer‐order model, this FO‐CLLC modeling and analysis method provides more accurate predictive analysis for the converter's gain model, purely resistive boundary and resonant frequency when considering the fractional‐order characteristics of the resonant tank. In addition, these operational characteristics of FO‐CLLC converter are all confirmed and verified with high accuracy in simulation results. Moreover, the design methodology for FO‐CLLC resonant converters is also discussed. Finally, hardware fractional‐order inductors (FOIs) and fractional‐order capacitors (FOCs) are constructed, and an experimental hardware prototype of FO‐CLLC is built to further validate the effectiveness of theoretical analysis.