System, method and apparatus for sensitivity based fast power grid simulation with variable time step

Abstract

A system and method of analyzing a power grid in an integrated circuit includes inputting a circuit design to a test bench, inputting a plurality of initial values for the circuit design in to the test bench, setting a current time t to 0 value for an initial time (t) of the operation of the circuit design, representing each capacitor in an RC circuit corresponding to the power grid circuit design by the each capacitor's respective time variant equivalent companion model, describing each one of the plurality of RC equivalent circuits mathematically as one of a corresponding plurality of linear equations, storing the plurality of linear equations in a matrix Yfor time t, resolving the matrix Yto determine a DC operating point, updating the RC equivalent circuits and the corresponding plurality of linear equations at a second time step t=t+h where h is a time step value equal to the current time t and a next simulated operation time, storing the updated plurality of linear equations in a matrix Yfor time t, inverting the matrix Yto form inverted matrix Y, resolving the inverted matrix Y, calculating a new time step and setting the current time t to t+h, comparing the new time step h to a plurality of time steps in a time step database, selecting one of the plurality of time steps substantially equal to the new time step and recalling a solution corresponding to the selected time step.