Variable Time Step Power Grid Simulation
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Solution Overview
Problem
The increasing complexity of integrated circuits with millions of devices leads to excessively long simulation and analysis times for power grid performance, significantly increasing design cycle times, as current methods require repeated simulations for each design modification.
Innovation Solution
A method that discretizes time-dependent electrical elements into RC equivalent circuits, solving linear equations using matrices Y0 and Y1, inverting Y1 to determine node voltages, and selectively reusing solutions based on time step differences to reduce the frequency of matrix inversions, thereby accelerating the power grid analysis process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional power grid simulation methods are used to analyze integrated circuits with millions of devices, then accurate power grid performance analysis is achieved, but the simulation time becomes excessively long (several days)
Solution Approach 1:
The patent divides the power grid analysis into discrete time steps, segmenting the continuous simulation process into manageable intervals. By representing capacitors with time-variant equivalent companion models at each time step, the method breaks down the complex simulation into sequential, computationally efficient stages while maintaining accuracy through proper time-step resolution.
Solution Approach 2:
The patent performs preliminary matrix inversion and solution computation at each time step, storing the inverted matrix Y1^-1 and corresponding solutions for reuse. This preliminary action allows subsequent time steps to leverage previously computed results, avoiding redundant calculations and significantly reducing overall simulation time while preserving measurement precision.
2Measurement precision
If repeated simulations are performed for each design modification, then accurate power grid analysis is maintained, but the design cycle time significantly increases
Solution Approach 1:
The patent utilizes time step as a variable parameter that can be adjusted based on design modifications. By comparing new time steps against stored solutions in a time step database and selecting substantially equal time steps, the method adapts to design changes efficiently. This parameter-based approach maintains analysis accuracy while dramatically reducing redundant simulations and accelerating the design cycle.
Solution Approach 2:
The patent creates and stores copies of inverted matrices and solutions in a time step database for future reuse. When design modifications occur, the system searches the database for matching or substantially equal time steps and recalls pre-computed solutions, avoiding redundant calculations. This copying strategy preserves accuracy by using validated solutions while significantly improving design iteration speed.
3Measurement precision
If matrix inversion is performed at every time step, then accurate node voltage determination is achieved, but computational complexity and processing time increase
Solution Approach 1:
The patent performs matrix inversion as a preliminary action at each time step, computing and storing the inverted matrix Y1^-1 along with corresponding solutions. This preliminary inversion allows subsequent operations to use the pre-computed inverse directly, avoiding repeated inversion operations. The approach maintains node voltage accuracy while significantly reducing computational complexity by eliminating redundant matrix inversions.
Solution Approach 2:
The patent strategically discards redundant matrix inversion operations by recovering and reusing previously computed inverted matrices and solutions from the time step database. When a new time step matches or substantially equals a stored time step, the system recalls the existing solution instead of performing another inversion. This discarding-and-recovering strategy preserves measurement precision while dramatically reducing computational complexity and processing time.
Data Source
AI summary
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.