High-frequency, high-power-density planar transformers represent a key development direction for magnetic components in power converters, with winding loss optimization being a critical design issue. Under low-voltage, high-current operating conditions, the optimization potential of conventional parameters—such as operating frequency, copper thickness, and insulation thickness—is severely constrained by circuit topology and fabrication process limitations. As the number of paralleled PCB layer increases, the possible interlayer connection arrangements grow exponentially. Existing methods largely rely on enumerating and comparing predefined structures, lacking a systematic optimization approach and making it difficult to balance computational efficiency with global optimality. To address this problem, this paper proposes a systematic optimization method for the connection arrangement of parallel windings in planar transformers based on an impedance matrix and mathematical programming. First, an impedance-matrix-based loss model is established that uses the connection arrangement as an explicit variable, reducing the per-evaluation time to approximately 1% and eliminating the cumbersome need to rebuild the model for each candidate as in conventional approaches. The connection arrangement optimization problem is then transformed into a standard mathematical programming problem, enabling fast global solution for the optimal connections. The validity of the proposed model and optimization method is verified through impedance measurements and comparative simulations. This work provides a systematic solution for the interlayer connection design of high-frequency, high-current planar transformers.
jingyi et al. (Sun,) studied this question.