Accurate analytical model of winding losses in round Litz wire windings

An accurate analytical model of losses in round Litz wire windings is presented. The model is based on the exact analytical equations for round conductors, and it closely includes the distribution of the leakage field across the winding space. A closed-form formula of the ac resistance of round Litz wire windings is developed from the model. An analytic solution of the optimal value of the ac resistance is derived. The expression of the strand dimension corresponding to the optimal value of the ac resistance is also determined.