Construction-Constrained Bernstein Synthesis of Joint Pitch-Width RDL Spiral Inductors for High-Q mmWave FoWLP Applications

RESUMO

We present a construction-constrained Bernstein framework for joint pitch-width synthesis of planar spiral inductors. A positive cubic Bernstein profile is integrated to prescribe a monotonic radial trajectory, while an independent Bernstein profile controls the conductor width. The nonnegativity, partition-of-unity, and convex-hull properties of the Bernstein basis convert endpoint, winding-direction, and width requirements into algebraic constraints. Embedded in differential evolution (DE), these constraints reject inadmissible candidates before full-wave evaluation, focusing expensive solver calls on geometries that satisfy the construction rules. The method is demonstrated on a two-turn mmWave inductor implemented in the redistribution layer (RDL) of fan-out wafer-level packaging (FoWLP), with the quality factor selected as the optimization objective. Searching the constrained Bernstein design space with DE yields a simulated Q of 34.85 at 30 GHz, compared with 29.66 for a uniform Archimedean baseline under the same stack, footprint, and ports. This corresponds to a 17.5% improvement while reducing planar copper area by 1.53%. The optimized response maintains Q >= 30 from 16 to 49 GHz.