Winding loss from an air-gap

A simple treatment is provided for the fringing fields of an air-gap in the core of a magnetic component such as an inductor or a transformer. Approximate analytical formulas for the fields show good agreement with finite-element calculations. These formulas are then applied to the calculations of high-frequency eddy current losses for two types of windings, which employ conductors with rectangular cross section. The rectangular conductors are commonly used in flex circuit windings. The two types of windings are flat and barrel wound. Distinctively different behavior is found for the two types of windings as a function of the position of the conductor. The applications to the circular conductors such as a wire are also discussed.