Power grid physics and implications for CAD

Much research has been done lately concerning analysis and optimization techniques for on-chip power grid networks. However, all of these approaches assume a particular model or behavior of the power delivery. In this paper, we describe the first detailed full-die dynamic model of an industrial microprocessor design, including package and non-uniform decap distribution. This model is justified from the ground up using a full-wave model and then increasingly larger but less detailed models with only the irrelevant elements removed. Using these models we show that there is little impact of on-die inductance in such a design, and that the package is critical to understanding resonant properties of the grid. We also show that transient effects are sensitive to non-uniform decap distribution and that locality is a tight function of frequency and of the package-die resonance, producing newly explained localized resonant effects. Specifically, all of these points have impact on what kind of analysis and optimization are required from CAD.