The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling because it can capture the frequency-dependent variation of skin depth with only a surface-based discretization of the structure. Conventional BEM formulations rely on the mutual coupling of electric and magnetic fields and can become inaccurate or unstable at low frequencies. We develop a new full-wave BEM formulation based on potentials that can accurately model lossy conductors from exactly DC to very high frequencies. A new set of simple boundary conditions is proposed along with a modified Lorenz gauge to ensure that the proposed formulation has a stable condition number down to DC. Moreover, coupling the potential-based integral equations to a circuit model allows the straightforward extraction of network parameters. Realistic numerical examples at both the chip and package level demonstrate the accuracy and stability of the proposed method from DC to high frequencies, beyond the capabilities of state-of-the-art BEM formulations based on fields.

中文翻译：

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使用基于电位的边界元公式对从直流到高频的有损互连进行电磁建模


低频和高频物理场的精确电磁建模对于电气互连的信号和电源完整性分析至关重要。边界元法 (BEM) 对于有损导体建模很有吸引力，因为它只需对结构进行基于表面的离散化即可捕获趋肤深度的频率相关变化。传统的 BEM 公式依赖于电场和磁场的相互耦合，在低频下可能会变得不准确或不稳定。我们开发了一种基于电势的新全波 BEM 公式，可以准确地模拟从直流到极高频率的有损导体。提出了一组新的简单边界条件以及修改后的洛伦兹规范，以确保所提出的公式具有低至 DC 的稳定条件数。此外，将基于势的积分方程耦合到电路模型可以直接提取网络参数。芯片和封装级别的真实数值示例证明了所提出的方法从直流到高频的准确性和稳定性，超出了基于场的最先进的 BEM 公式的能力。