Novel Closed-Form 2-D Green's Function of Shielded Layered Media And Its Use in Transmission Lines Inductance Extraction

2022 IEEE 31st Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS) Pub Date : 2022-10-09 DOI:10.1109/EPEPS53828.2022.9947164

Shucheng Zheng, V. Okhmatovski

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Abstract

New closed-form expression for quasi-static 2-D Green's function of fully-shielded layered medium is proposed. Along the vertical direction of the medium stratification the spectrum of the Green's function can be obtained through the 1-D ordinary differential equation and expressed as pole-residual form. This rational function representation of the spectrum allows to evaluate space domain Green's function in layered medium shielded from top and bottom with horizontal ground planes in a closed-form. This closed-form expression allows to analytically add up contributions from infinite number of source images with respect to the vertical side walls of the rectangular enclosure, hence, producing the new closed-form expression for the 2-D Green's function of rectangular enclosure vertically filled with multilayered medium. Availability of such Green's functions enable construction of integral equation based magneto-quasi-static and electro-quasi-static 2-D extractors. Such 2-D magneto-quasi-static extractor based on solution of Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for multi-conductor transmission lines (MTLs) situated in shielded layered media is demonstrated.

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屏蔽层状介质的新型封闭二维格林函数及其在传输线电感提取中的应用

提出了全屏蔽层状介质准静态二维格林函数的新的封闭表达式。沿介质分层的垂直方向，格林函数的谱可以通过一维常微分方程得到，并表示为极点残差形式。这种谱的有理函数表示允许在封闭形式的水平地平面上下屏蔽的层状介质中评估空间域格林函数。这种封闭形式的表达式允许将无限数量的源图像相对于矩形围护体的垂直侧壁的贡献解析相加，从而产生垂直填充多层介质的矩形围护体的二维格林函数的新的封闭形式表达式。这些格林函数的可用性使得基于积分方程的磁准静态和电准静态二维提取器的构建成为可能。针对屏蔽层状介质中的多导体传输线，给出了基于表面-体积-表面电场积分方程(SVS-EFIE)求解的二维磁准静态提取器。

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2022 IEEE 31st Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS)

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