Fast algorithms for power grid analysis based on effective resistance

The size of on-chip power distribution networks is increasing with each technology generation. Accurate and computationally efficient analysis of these power distribution networks has therefore become increasingly challenging. High performance power distribution networks are generally implemented as a uniform mesh structure. The uniformity of these power distribution networks can be exploited for fast, accurate nodal analysis. A closed form expression is presented here for determining the voltage at any arbitrary node in a power distribution network. The error of the proposed method as compared with SPICE is less than 0.2%. Since no iterations are required, the proposed method significantly outperforms previously proposed power grid analysis techniques in terms of computational speed while exhibiting low error.