Theoretical Analysis and Optimization of Coupled Inductor for Boost-Extender Topology

A coupling coefficient optimization procedure for a boost-extender topology converter with coupled inductors is presented. The method focuses on minimizing inductor current ripple to reduce losses and improve magnetic core utilization, enabling a potential increase in converter power density. The major innovation of this study is the theoretical formulation of the coupling coefficient and leakage inductance in the UU/UI cores. The study includes a theoretical loss analysis covering two dominant loss mechanisms of the topology. A magnetic core structure enabling current ripple cancelation is presented and analyzed using a reluctance model. To address the analytically intractable field distribution at the core center tap, an empirical leakage model is introduced. The model is validated through ANSYS Maxwell simulations 2023.R1 and corroborated by experimental measurements. The results demonstrate that appropriate coupling coefficient selection significantly suppresses current ripple and enables a more efficient and compact converter design. Simulation and experimental results on experimental prototype of 100 W running at 100 kHz and attaining voltage gain of 20 V to 200 V confirm the accuracy of the models and the effectiveness of the optimization procedures.