**Piotr Dworakowski 1,\*, Andrzej Wilk 2, Michal Michna 2, Bruno Lefebvre 1, Fabien Sixdenier <sup>3</sup> and Michel Mermet-Guyennet <sup>1</sup>**


Received: 4 February 2020; Accepted: 11 March 2020; Published: 14 March 2020

**Abstract:** The magnetizing inductance of the medium frequency transformer (MFT) impacts the performance of the isolated dc-dc power converters. The ferrite material is considered for high power transformers but it requires an assembly of type "I" cores resulting in a multi air gap structure of the magnetic core. The authors claim that the multiple air gaps are randomly distributed and that the average air gap length is unpredictable at the industrial design stage. As a consequence, the required effective magnetic permeability and the magnetizing inductance are difficult to achieve within reasonable error margins. This article presents the measurements of the equivalent *B*(*H*) and the equivalent magnetic permeability of two three-phase MFT prototypes. The measured equivalent *B*(*H*) is used in an FEM simulation and compared against a no load test of a 100 kW isolated dc-dc converter showing a good fit within a 10% error. Further analysis leads to the demonstration that the equivalent magnetic permeability and the average air gap length are nonlinear functions of the number of air gaps. The proposed exponential scaling function enables rapid estimation of the magnetizing inductance based on the ferrite material datasheet only.

**Keywords:** average air gap length; dc-dc power converters; gapped magnetic core; magnetic permeability; magnetizing inductance; medium frequency transformer
