Integrated Circuit Timing Analysis Using Statistical Sampling
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Solution Overview
Problem
Current static timing analysis (STA) techniques are overly pessimistic due to worst-case timing assumptions, making it difficult to meet timing constraints as clock frequencies increase, and are computationally costly when using statistical methods to account for variations in integrated circuit manufacturing processes, especially when variations are correlated.
Innovation Solution
A system that generates samples of an integrated circuit based on probability distributions for its parameters, calculates output performance metrics, and creates distributions of these metrics to accurately model variations, allowing for more precise timing and power analysis without the need for mixing data from multiple samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If worst-case timing assumptions are used in static timing analysis, then timing safety is improved, but timing analysis accuracy deteriorates
Solution Approach 1:
The patent transforms the deterministic worst-case parameters into statistical parameters with probability distributions. Instead of using fixed worst-case values for gate delays and path timings, the invention models these as random variables with defined distributions (e.g., normal, uniform, or triangular distributions), allowing timing analysis to reflect the actual statistical behavior of the circuit rather than overly conservative worst-case scenarios.
2Measurement precision
If statistical techniques are used to calculate timing with variations, then timing analysis accuracy is improved, but computational cost increases
Solution Approach 1:
The patent segments the circuit into independent paths and models the timing variations along each path separately. By dividing the overall timing analysis into discrete path segments and using statistical composition rules to combine their distributions, the invention reduces the computational complexity compared to analyzing the entire circuit as a single statistical system, while still capturing the essential variation effects.
Solution Approach 2:
The patent uses analytical distribution functions to represent timing variations, which can be manipulated mathematically without requiring extensive Monte Carlo simulations. This analytical approach creates a simplified statistical model that replicates the essential behavior of the circuit variations at lower computational cost.
3Measurement precision
If correlated variations are handled using traditional statistical methods, then measurement accuracy is improved, but analysis complexity increases
Solution Approach 1:
The patent introduces correlation coefficients as intermediary parameters that quantify the relationship between variations in different circuit elements. By using these correlation coefficients to adjust the statistical composition of path timings, the invention handles correlated variations in a systematic way that is more manageable than full-blown statistical analysis, reducing the complexity while maintaining accuracy.
Data Source
AI summary
A system that determines the performance of an integrated circuit (IC). During operation, the system receives probability distributions for parameters for the IC. Next, the system generates samples of the IC, wherein generating a given sample involves using the probability distribution to assign values to the parameters for components within the IC. The system then calculates output performance metrics for the samples based on the assigned values of the parameters, and uses the calculated output performance metrics to generate a distribution of output performance metrics for the samples.