Automated Design of Multi-Layer Planar Transformers: An EDA Tool Based on a Constraint-Preserving Genetic Algorithm

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Abstract
Inhomogeneous magnetic field distributions in high-frequency planar transformers frequently cause severe localized thermal hotspots and elevated leakage inductance. Traditional interleaved winding designs rely heavily on empirical trial-and-error, which becomes computationally prohibitive for multi-layer parallel structures due to the factorial “curse of dimensionality.” To address this bottleneck, this paper proposes a universal, data-driven optimization methodology. First, a quantitative one-dimensional prefix-sum model is established to correlate winding arrangements with spatial magnetomotive force (MMF) distributions, effectively simplifying the electromagnetic evaluation. Subsequently, a customized Genetic Algorithm (GA) framework, featuring physical-constraint-preserving operators such as Order Crossover (OX), is introduced to efficiently navigate the high-dimensional discrete search space. Using an extreme 26-layer complex parallel winding configuration (Np:Ns = 9:2) as a primary case study, the proposed GA method effectively bypasses over 1.5 million permutations, converging to the global optimum within 100 generations. The optimized structure achieves profound peak-shaving, drastically reducing both the peak MMF and total uncoupled magnetic energy area. This methodology provides a systematic, computationally lightweight EDA solution that fundamentally replaces empirical trial-and-error in the design of high-frequency magnetic components.

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