Generalized Moment Timing Analysis for Circuit Variation
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Solution Overview
Problem
Current statistical timing analysis methods, such as parametric on-chip variation (POCV), rely on Gaussian distribution assumptions that fail to accurately capture the shapes of gate delay distributions, leading to inaccuracies and pessimistic performance penalties in circuit designs due to their inability to account for skewness and kurtosis.
Innovation Solution
A generalized moment-based variation aware timing analysis method that uses higher-order statistical moments, including skewness and kurtosis, to accurately represent gate delay distributions, allowing for more accurate propagation of timing variations through moment matching techniques like Asymptotic Waveform Evaluation (AWE), which converts these moments into time-domain parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Gaussian distribution assumption is used in POCV approach, then computational simplicity is maintained, but accuracy of gate delay distribution representation deteriorates
Solution Approach 1:
The patent changes the statistical parameters used to represent gate delay distributions from simple Gaussian parameters (mean and standard deviation only) to higher-order statistical moments including skewness and kurtosis. This allows the model to capture the true shape of delay distributions while maintaining computational efficiency through moment-based calculations.
Solution Approach 2:
The patent combines multiple statistical moments (mean, standard deviation, skewness, kurtosis) into a composite statistical model that accurately represents gate delay distributions. This composite approach integrates various distribution characteristics into a unified framework that is both accurate and computationally tractable.
2Ease of operation
If Gaussian distribution is assumed for gate delays, then mathematical tractability is improved, but ability to capture skewness and kurtosis deteriorates
Solution Approach 1:
The patent extends the statistical parameter set beyond Gaussian assumptions to include higher-order moments (skewness and kurtosis). This enables the model to mathematically represent non-Gaussian delay distributions while maintaining analytical tractability through moment-based propagation methods.
Solution Approach 2:
The patent introduces dynamic statistical parameters that can adapt to different gate and circuit characteristics. By using higher-order moments that can vary across different parts of the circuit, the model dynamically captures the true distribution shape rather than forcing a static Gaussian assumption.
3Productivity
If crude approximation is applied to maximum operation to maintain Gaussian assumption, then computational efficiency is maintained, but pessimism in timing analysis increases
Solution Approach 1:
The patent changes the statistical representation from Gaussian parameters to higher-order moments, which enables accurate modeling of the maximum operation without crude approximations. The moment-based approach naturally handles the statistical properties of maximum operations, reducing pessimism while maintaining computational efficiency.
Data Source
AI summary
A method and apparatus of a device that performs a generalized moment based variation aware timing analysis on a circuit design is described. The device receives a signal path that traverses a plurality of gates. For each of the plurality of gates, the device retrieves a statistical distribution that represents delay variation at the gate. The statistical distribution for each gate is measured by a number of statistical moments that include higher order statistical moments besides the mean and the standard deviation of the distribution. The device computes statistical moments to represent the timing variation on the signal path by propagating statistical distributions of the gates on the signal path. The device reconstructs a statistical distribution function for timing variation on the signal path based on the computed statistical moments.