Statistical Circuit Timing Analysis via Moment Conjugation
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Solution Overview
Problem
Current graph-based timing analysis methods using the Parametric On-Chip Variation model often fail to accurately bound path-based timing analysis results, leading to missed critical paths and incorrect path ordering, which complicates the integrated circuit design process and makes it difficult to achieve deterministic timing sign-off.
Innovation Solution
The method employs moment conjugation and moment negation operations for statistical graph merging and path tracing, ensuring that statistical graph slack bounds path slack, and uses novel statistical min/max operations to maintain accurate critical path extraction and ordering, thereby ensuring that critical path slack matches graph slack.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing graph merging and path searching methods are used with the POCV model, then statistical timing analysis can be performed, but the GBA results cannot bound PBA results and correct path ordering cannot be ensured
Solution Approach 1:
The patent transforms statistical timing values into moment representations (mean, standard deviation, skewness, kurtosis) and applies moment conjugation and moment negation operations. This parameter transformation enables deterministic bounding relationships between GBA and PBA results while maintaining statistical accuracy, resolving the contradiction between reliability and complexity.
Solution Approach 2:
The patent introduces moment conjugation and moment negation operations as intermediary mathematical transformations between statistical timing values and bounding operations. These intermediary operations enable the derivation of deterministic bounds from statistical data, ensuring GBA results bound PBA results without requiring empirical margins.
2Reliability
If empirical margins are added during path reporting to ensure bounding, then GBA results can bound PBA results, but run time and memory consumption increase significantly
Solution Approach 1:
The patent changes the parameter representation from statistical distributions to moment-based deterministic values through conjugation and negation operations. This transformation enables exact bounding calculations without requiring conservative empirical margins, thereby maintaining reliability while eliminating the productivity penalty associated with excessive safety margins.
3Measurement precision
If statistical distributions are used to describe timing information, then variable impact on circuit timing is captured accurately, but existing merging and path searching methods fail to ensure correct ordering
Solution Approach 1:
The patent transforms statistical distribution parameters into moment representations and applies deterministic conjugation and negation operations. This parameter transformation maintains the accuracy of variable impact capture while enabling straightforward path extraction and ordering through deterministic mathematical operations, resolving the contradiction between measurement precision and ease of operation.
Data Source
AI summary
An arrival time propagation method and system for statistical circuit analysis that uses a conjugation operation and a negation operation to determine and adjust arrival times in a circuit model and to determine path ordering in a circuit.