Construction-Constrained Bernstein Synthesis of Joint Pitch-Width RDL Spiral Inductors for High-Q mmWave FoWLP Applications
Abstract
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.
Related
- A Comprehensive Survey of Crystal Structural Prototypes: Construction, Classification, and Applications
- EPC-RawDC: Equivariant Physics Constrained 3D Diffusion with Raw Data Consistency for CBCT to CT Image Synthesis
- Design and synthesis of laser inscribed flexible Bragg gratings containing silicon oxynitride-doped silicon thin film for authentication applications with the insights from X-Ray Absorption Spectroscopy and Quantum Mechanical Calculations
- A Conditional Quantum Kac-Bernstein Theorem
- Quantum Bernstein--Kolmogorov--Arnold approximation
BibTeX
@misc{chen2026constructionconstrained,
title = {{Construction-Constrained Bernstein Synthesis of Joint Pitch-Width RDL Spiral Inductors for High-Q mmWave FoWLP Applications}},
author = {Shuhang Chen and Xinmeng Wang and Yuchong Sun and Qi Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06087},
eprint = {2609.06087},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06087},
}
RIS
TY - UNPB
TI - Construction-Constrained Bernstein Synthesis of Joint Pitch-Width RDL Spiral Inductors for High-Q mmWave FoWLP Applications
AU - Shuhang Chen
AU - Xinmeng Wang
AU - Yuchong Sun
AU - Qi Zhu
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.06087
UR - https://arxiv.org/abs/2609.06087
AB - 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.
ER -