A stochastic approach to power grid analysis

Power supply integrity analysis is critical in modern high perfor-mance designs. In this paper, we propose a stochastic approach to obtain statistical information about the collective IR and LdI/dt drop in a power supply network. The currents drawn from the power grid by the blocks in a design are modelled as stochastic processes and their statistical information is extracted, including correlation infor-mation between blocks in both space and time. We then propose a method to propagate the statistical parameters of the block currents through the linear model of the power grid to obtain the mean and standard deviation of the voltage drops at any node in the grid. We show that the run time is linear with the length of the current wave-forms allowing for extensive vectors, up to millions of cycles, to be analyzed. We implemented the approach on a number of grids, including a grid from an industrial microprocessor and demonstrate its accuracy and efficiency. The proposed statistical analysis can be use to determine which portions of the grid are most likely to fail as well as to provide information for other analyses, such as statistical timing analysis.