Fringing Field Formulas and Winding Loss Due to an Air Gap

The paper describes a simple treatment for the fringing fields of an air gap in the core of a magnetic component such as an inductor or a transformer. It verifies the derived analytical formulas for the fields by using numerical (finite-element) calculations. It then applies these formulas to the calculation of high-frequency eddy-current losses for two types of winding arrangements, both of which employ thin rectangular conductors. The rectangular conductors are commonly used in flex circuit windings, printed circuit windings, and thin-film windings. The two types of winding configurations are flat and barrel wound. Each behaves in a different way as a function of the position of the conductor.