Fast analysis of structured power grid by triangularization based structure preserving model order reduction

In this paper, a triangularization based structure preserving (TBS) model order reduction is proposed to verify power integrity of on-chip structured power grid. The power grid is represented by interconnected basic blocks according to current density, and basic blocks are further clustered into compact blocks, each with a unique pole distribution. Then, the system is transformed into a triangular system, where compact blocks are in its diagonal and the system poles are determined only by the diagonal blocks. Finally, projection matrices are constructed and applied for compact blocks separately. The resulting macromodel has more matched poles and is more accurate than the one using flat projection. It is also sparse and enables a two-level analysis for simulation time reduction. Compared to existing approaches, TBS in experiments achieves up to 133/spl times/ and 109/spl times/ speedup in macromodel building and simulation respectively, and reduces waveform error by 33/spl times/.