Generating Current Constraints to Guarantee RLC Power Grid Safety

Abstract

A critical task during early chip design is the efficient verification of the chip power distribution network. Vectorless verification, developed since the mid-2000s as an alternative to traditional simulation-based methods, requires the user to specify current constraints (budgets) for the underlying circuitry and checks if the corresponding voltage variations on all grid nodes are within a user-specified margin. This framework is extremely powerful, as it allows for efficient and early verification, but specifying/obtaining current constraints remains a burdensome task for users and a hurdle to adoption of this framework by the industry. Recently, the inverse problem has been introduced: Generate circuit current constraints that, if satisfied by the underlying logic circuitry, would guarantee grid safety from excessive voltage variations. This approach has many potential applications, including various grid quality metrics, as well as voltage drop-aware placement and floorplanning. So far, this framework has been developed assuming only resistive and capacitive (RC) elements in the power grid model. Inductive effects are becoming a significant component of the power supply noise and can no longer be ignored. In this article, we extend the constraints generation approach to allow for inductance. We give a rigorous problem definition and develop some key theoretical results related to maximality of the current space defined by the constraints. Based on this, we then develop three constraints generation algorithms that target the peak total chip power that is allowed by the grid, the uniformity of current distribution across the die area, and a combination of both metrics.