Leakage inductance design of toroidal transformers by sector winding

Toroidal transformers are commonly used in power electronics applications when the volume or weight of a component is at a premium. There are many applications that require toroidal transformers with a specific leakage inductance value. A transformer with a large (or tuned) leakage inductance can be used to eliminate a (series) filter inductor. In this paper, a procedure to control the leakage inductance of toroidal transformers by leaving unwound sectors in the winding is presented. Also, a simple formula is obtained in this paper that can be used to design transformers with a specific leakage inductance value. The leakage inductance formula is expressed as a function of the number of turns, the geometrical dimensions of the toroidal transformer, such as core internal diameter, external diameter, and height, and the angle of the unwound sector. The formula proposed in this paper has been obtained and validated from laboratory experiments and hundreds of three-dimensional finite element simulations. The techniques described in this paper will find applications in the design of transformers that in addition of providing voltage boosting need to double as filters.