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

摘要

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 (t₀) 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 Y₀ for time t₀, resolving the matrix Y₀ to determine a DC operating point, updating the RC equivalent circuits and the corresponding plurality of linear equations at a second time step t₁=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 Y₁ for time t₁, inverting the matrix Y₁ to form inverted matrix Y₁⁻¹, resolving the inverted matrix Y₁⁻¹, 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.