局部松弛电路理论及其在电热分析中的应用

Localized relaxation theory of circuits and its applications in electro-thermal analyses

在复杂度日益增高的高性能集成电路设计中,高效的性能分析是一项重要的设计内容,其中由电源线/地线网络(P/G)分析与芯片热分析构成的电热分析则是目前研究的热点问题.针对电热分析方程所具有的大规模稀疏(电导或热导)系数矩阵,根据该系数矩阵所具有的对称正定严格对角占优等特性,本文从理论上证明了电热分析具有局部性,在相同的截断误差限松弛结束条件下,局部松弛和全局松弛具有相同的松弛精度.基于局部松弛理论,本文提出了一个高效实用的局部过松弛(SOR)算法(LSOR2),并在文章最后将其用于如下的3个具体的电热分析问题研究:(1)P/G网中的过压降点电压变化统计分析;(2)3D热分析中的过热点温度变化统计分析;(3)单开路故障下的P/G网快速分析.实验数据表明:与全局SOR算法相比,在保证精度的前提下,LSOR2算法可以将电热分析的求解速度提高1-2个数量级.

In the high-performance IC design with increasing design complexity,it is a very important design content to efficiently analyze IC parameters.Thus,the electro-thermal（ET） analyses including power/ground（P/G） analysis and thermal analysis are hot topics in today＇s IC research.Since ET analysis equation has a sparse,positive definite and strictly diagonally dominant coefficient-matrix,we prove that the ET analysis has the advantage of locality.Owing to this advantage,localized relaxation method is formally proposed,which has the same accuracy as the global relaxation done with the constraint of the same truncation error limitation.Based on the localized relaxation theory,an efficient and practical localized successive over-relaxation algorithm（LSOR2） is introduced and applied to solve the following three ET analysis problems：（1） Single-node statistical voltage analysis for over-IR-drop nodes in P/G networks;（2） single-node statistical temperature analysis for hot spots in 3D thermal analysis;（3） fast single open-defect analysis for P/G networks.A large amount of experimental data demonstrates that compared with the global successive over-relaxation（SOR） algorithm,LSOR2 can speed up 1-2 orders of magnitudes with the same accuracy in ET analyses.