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Effective Resistance of Finite Two-Dimensional Grids Based on Infinity Mirror Technique
IEEE Transactions on Circuits and Systems I: Regular Papers ( IF 5.1 ) Pub Date : 2020-09-01 , DOI: 10.1109/tcsi.2020.2985652
Rassul Bairamkulov , Eby G. Friedman

Conventional numerical circuit analysis tools typically scale superlinearly with the number of nodes. With the rapid increase in nodes in modern VLSI systems, alternative methods are required. The effective resistance is an important characteristic of electrical systems, which is used to simplify the circuit analysis process. An infinite resistive rectangular mesh is commonly assumed in the analysis of grid structures to determine the effective resistance of a grid. The assumption of infinity provides a useful approximation when a large grid is analyzed far from the boundaries. If however the grid is analyzed in close proximity to a boundary or if the grid dimensions are small, the assumption of infinity may lead to significant error. To address this issue, the infinity mirror technique is proposed to determine the effective resistance of a two-dimensional structure, where one or both dimensions are finite. The method exhibits good agreement with nodal analysis, achieving an error below 1% in case studies. The proposed expressions enhance the speed of static grid analysis by several orders of magnitude by replacing computationally expensive nodal analysis with an equivalent reduced grid analysis. A 1,400 fold speedup is achieved in the analysis of 100 nodes within a $10^{3}\times 10^{4}$ grid.

中文翻译:

基于无限镜技术的二维有限网格有效电阻

传统的数值电路分析工具通常随着节点的数量超线性地扩展。随着现代 VLSI 系统中节点的快速增加,需要替代方法。有效电阻是电气系统的一个重要特性,用于简化电路分析过程。在分析网格结构以确定网格的有效电阻时,通常假设无限电阻矩形网格。当分析远离边界的大网格时,无穷大假设提供了一种有用的近似值。然而,如果网格在边界附近进行分析或者如果网格尺寸很小,无穷大的假设可能会导致重大错误。为了解决这个问题,提出了无限镜技术来确定二维结构的有效电阻,其中一维或两维是有限的。该方法与节点分析表现出良好的一致性,在案例研究中实现了低于 1% 的误差。所提出的表达式通过用等效的简化网格分析代替计算上昂贵的节点分析,将静态网格分析的速度提高了几个数量级。在 $10^{3}\times 10^{4}$ 网格内的 100 个节点的分析中实现了 1,400 倍的加速。所提出的表达式通过用等效的简化网格分析代替计算上昂贵的节点分析,将静态网格分析的速度提高了几个数量级。在 $10^{3}\times 10^{4}$ 网格内的 100 个节点的分析中实现了 1,400 倍的加速。所提出的表达式通过用等效的简化网格分析代替计算上昂贵的节点分析,将静态网格分析的速度提高了几个数量级。在 $10^{3}\times 10^{4}$ 网格内的 100 个节点的分析中实现了 1,400 倍的加速。
更新日期:2020-09-01
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