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In the verification of VLSI circuit design, static timing analysis (STA) techniques allow a designer to calculate the timing of a circuit at different process corners, which only consider cases where all the supplies are low or high. This analysis may not be the true maximum delay of a circuit due to the neglect of mismatch between drivers and load. We propose a new methodology for timing analysis where we identify all the possible critical paths of a circuit using new timing models while integrating the aforementioned mismatch for the logic gates. Given then these critical paths we tie the supplies of the gates to physical power grids and re-analyze for the worst-case time delay. This re-analysis is posed as a sequence of optimization problems where the complete operation of the entire circuit is abstracted in terms of current constraints. We present our technique and report on the implementation results using benchmark circuits tied to a number of test-case power grids.