Efficient statistical analysis method of power/ground (P/G) network

In this paper, we propose an incremental statistical analysis method with complexity reduction as a pre-process for on-chip power/ground (P/G) networks. The new method exploits locality of P/G network analyses and aims at P/G networks with a large number of strongly connected subcircuits (called strong connects) such as trees and chains. The method consists of three steps. First it compresses P/G circuits by removing strong connects. As a result, current variations (CVs) of nodes in strong connects are transferred to some remaining nodes. Then based on the locality of power grid voltage responses to its current inputs, it efficiently calculates the correlative resistor (CR) matrix in a local way to directly compute the voltage variations by using small parts of the remaining circuit. Last it statistically recovers voltage variations of the suppressed nodes inside strong connects. This new method for statistically compressing and expanding strong connects in terms of current or voltage variations in a closed form is very efficient owning to its property of incremental analysis. Experimental results demonstrate that the method can efficiently compute low-bounds of voltage variations for P/G networks and it has two or three orders of magnitudes speedup over the traditional Monte-Carlo-based simulation method, with only 2.0% accuracy loss.