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This paper examines high-frequency losses of thick rectangular and round wire windings due to the fringing fields of an air-gap. It derives formulas for the losses and validates them numerically using the 2-D finite-element method (FEM). It also provides a procedure for including the effect of self and proximity fields in the loss calculations, using the principle of superposition and a one-dimensional model of self and proximity fields. The paper validates the latter procedure numerically, using a 2-D finite element model.