Analytical Calculation of Static Leakage Inductances of HF Transformers Using PEEC Formulas

When the total current going through a transformer window is equal to zero, only a negligible part of the magnetic energy reaches its core. This is shown by finite-element-method simulations carried out on several two-winding transformers having different shapes. Moreover, induction and energy-density values obtained by 3-D simulations and by 2-D approximations are very close to each other. These two key observations justify the use of formulas that give the induction created by straight rectangular cross-sectional wires, as used in the partial-element-equivalent-circuit method, to compute the window field and, thus, to value the leakage inductances. To refine this approach, weak magnetic-core effects are accounted for by introducing the magnetic images of currents that flow in the windings. A comparison between the calculated values and measured ones is provided.