A physics based close form inductance model for three-dimensional (3-D) solenoid inductors with ground shileding is proposed in this letter. The expressions are derived in full consideration of partial self inductance and mutual inductance. The proposed model is extracted based on the process parameters and design parameters without any optimization. The 3-D inductor samples are fabricated on glass substrate by Through Glass Via (TGV) process. The accuracy of the proposed model is validated by comparing the results from the 3-D full-wave electromagnetic solver High Frequency Simulator Structure (HFSS) and measurement.

中文翻译：

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基于物理的三维螺线管电感器可扩展电感模型

在这封信中，提出了具有接地屏蔽的三维（3-D）螺线管电感器的基于物理的闭合形式电感模型。这些表达式是在充分考虑了部分自感和互感的基础上得出的。基于过程参数和设计参数提取提出的模型，而无需进行任何优化。通过玻璃通孔（TGV）工艺在玻璃基板上制造3-D电感器样品。通过比较3-D全波电磁求解器高频模拟器结构（HFSS）和测量结果，验证了所提出模型的准确性。