Calculation of Transformer Leakage Inductance by Simplified Flux Path Geometries

Series inductance is a critical energy storage element in isolated power converters. Many have explored methods of estimating the total leakage inductance of transformers as an integrated series inductance without external inductors. However, this poses challenges with medium frequency converters and magnetic ribbon-based cores, e.g., metal amorphous nanocrystalline. The material's relatively high conductivity allows eddy currents to develop when magnetic flux intersects wide surfaces. These eddy currents result in significant additional losses that increase with increasing power flow. This paper presents a simplified and accurate method of estimating leakage flux while identifying separate leakage flux paths that correlate with the magnetic material surfaces. This enables an understanding the proportion of leakage flux that will contribute to extra losses. The methods presented are applicable to both leakage and fringing (around heterogeneous material interfaces) fluxes. This paper includes detailed FEA studies and 3D flux vector measurements matching the presented analytical models.