片上电源分配网络的最大电压降：正方形、三角形和六边形电源焊盘排列的分析
The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements
摘要：
在片上配电网络中出现的电压降的数学模型用于比较在向芯片供电的焊盘的不同几何布置的情况下的最大电压降。这些包括目前占主导地位的正方形或曼哈顿电源焊盘布置，以及等边三角形和六边形布置。与文献中的研究结果一致，并与物理和SPICE模型，等边电源焊盘的安排，独立的底层电源网格配置，被发现最大电压降最小化。这个标题发现是相对简单的电压降公式的结果，具有明确的误差范围，这些公式是使用复杂的分析技术，特别是椭圆函数建立的。
英文摘要：
A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with findings in the literature and with physical and SPICE models, the equilateral power pad arrangement, independent of the underlying power mesh configuration, is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.
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