Fast Analysis of On-Chip Power Grid Circuits by Extended Truncated Balanced Realization Method
In this paper, we present a novel analysis approach for large on-chip power grid circuit analysis. The new approach, called ETBR for extended truncated balanced realization, is based on model order reduction techniques to reduce the circuit matrices before the simulation. Different from the (improved) extended Krylov subspace methods EKS/IEKS [2],[3], ETBR performs fast truncated balanced realization on response Gramian to reduce the original system. ETBR also avoids the adverse explicit moment representation of the input signals. Instead, it uses spectrum representation in frequency domain for input signals by fast Fourier transformation. The proposed method is very amenable for threading-based parallel computing, as the response Gramian is computed in a Monte-Carlo-like sampling style and each sampling can be computed in parallel. This contrasts with all the Krylov subspace based methods like the EKS method. where moments have to be computed in a sequential order. ETBR is also more flexible for different types of input sources and can better capture the high frequency contents than EKS, and this leads to more accurate results especially for fast changing input signals. Experimental results on a number of large networks (up to one million nodes) show that, given the same order of the reduced model, ETBR is indeed more accurate than the EKS method especially for input sources rich in high-frequency components. If parallel computing is explored, ETBR can be an order of magnitude faster than the EKS/IEKS method.
truncated balanced realization model order reduction power grid analysis