[Objective] To address the issue of significantly increased AC winding losses in planar transformers caused by the flat winding structure exacerbating proximity and skin effects

this study proposes a topology optimization method for windings based on variable-width design

aiming to improve current distribution uniformity and reduce losses. [Methods] A multi-physics coupling model of winding AC effects was established

and eletromagnetic field theory was employed to analyze current density distribution patterns. A gradient variable-width parametric model was developed for circular windings to validate the regulatory mechanism of width variation on loss reduction. Building on circular winding optimization

nonlinear variable-width design criteria for rectangular windings were formulated

and two differentiated width adjustment schemes were developed. The electromagnetic performance of these schemes was evaluated using 3D finite element simulations. [Results] Experimental data demonstrated that the optimized rectangular variable-width windings achieved a 7.789% reduction in AC Ohmic losses while maintaining equivalent conductive area. Additionally

the maximum magnetic flux density in the winding region decreased by 3.766%

and current density distribution uniformity improved by 21.6%. The leakage inductance of the optimized variable-width winding was

on average

49.1% higher than that of the equal-width winding. This indicated that the variable-width design indirectly increases the leakage inductance by altering the winding width and the number of turns per unit length. [Conclusion] The optimization design of variable-width circular windings is applied to rectangular windings. By actively controlling the electromagnetic field boundary conditions of the conductor cross-section

the phenomenon of eddy current accumulation under high-frequency conditions is effectively suppressed. This work prorides a quantifiable design paradigm for multi-objective collaborative optimization of planar transformer windings.