Magnetic vector potential based model for eddy-current loss calculation in round-wire planar windings

An analytical development of the magnetic vector potential is used to investigate the losses in round-wire planar windings. The current distribution in wires is affected by the skin effect and the field created by adjacent wires (proximity effect). This field depends on the current distribution in conductors, resulting in a closed-form problem. In this paper, we obtain the vector potential outside a conductor to estimate the effect of induced currents in the field shape over the neighboring conductors. We use the results to calculate the losses in planar windings such as those in domestic induction heaters. We obtain an equivalent resistance representing the losses in windings and compare it with measurements. This solution provides an accurate analytical approach to modeling the losses in close-packed windings