Voltage-Aware Static Timing Analysis

Abstract—Static timing analysis (STA) techniques allow a designer to check the timing of a circuit at different process corners, which typically include corner values of the supply voltages as well. Traditionally, however, this analysis only considers cases where the supplies are either all low or all high. As will be demonstrated, this may not yield the true maximum delay of a circuit because it neglects the possible mismatch between the supplies of successive gates on a path. A new methodology for timing analysis is proposed, where, in a first step, the critical paths of a circuit are identified under an assumption that all the supply nodes are independent of one another, thus allowing for mismatch between the supplies. Then, given these critical paths, the authors incorporate into the analysis the relationships between the supply node voltages by considering the power grid that they are tied to, and refine the worst case time delay values on a per-critical-path basis. This refinement is posed as a sequence of optimization problems where the operation of the circuit is abstracted in terms of current constraints. The authors present their technique and report on the implementation results using benchmark circuits tied to a number of test-case power grids. Index Terms—Power grid, rail voltage variations, static timing analysis, verification tools. I