2-D Winding Losses Calculation for Round Conductor Coil

Winding loss calculation is essential for inductor and transformer design. In this article, a revised 1-D Ferreira's formula is proposed, which considers the interaction between conductors. Then, a 2-D loss calculation approach is proposed based on the analytical solution of round conductors under a uniform external field. An equivalent external magnetic field is calculated to estimate the winding losses, considering the impact of eddy current. The proposed approach is compared with the 2-D FEM with three types of windings and shows good accuracy with less than 10% error. 3-D FEMs and samples are built based on two simulated windings to validate the loss calculation.