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Path-Based Delay Variation Models for Parallel-Prefix Adders
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DOI：10.1109/TETC.2023.3242555.png)
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State-of-the-art static timing analysis algorithms can evaluate worst-case delay in statistical terms. In this paper, a modeling framework is introduced for the evaluation of the maximum-delay Cumulative Density Func-tion (CDF) of an ensemble of parallel-prefix adder topologies. For moderate variations and close-to-nominal supply voltages, the maximum delay of parallel-prefix adders is practically determined by the maximum of a set of near-critical-delay paths around the nominal maximum-delay path. These paths end to the most significant and neigh-boring bit positions. Matrix-based path delay formulations are derived for the particular set of paths. The introduced matrix formulations are exploited to assess the maximum-delay CDF by means of a multivariate Gaussian CDF. To validate the accuracy of the introduced models, a quantita-tive comparison of the proposed probabilistic delay models against Spice-level Monte-Carlo simulations is offered for certain parallel-prefix adders. Threshold-voltage variations summarize several process-dependent variation-inducing mechanisms and are modeled as Gaussian variations, in-troduced to BSIM-4 transistor models for a 16-nm technol-ogy node. For the nominal voltage case and 10% threshold-voltage variations, the introduced models estimate the 0.95 timing yield point with a mean absolute error below 1% compared to Spice-level simulations for the 16 bit-length case. Furthermore, an extension of the proposed approach to account for multiple end points is investigated that reduces the error for the estimation of maximum delay, demonstrated for a unit delay model and certain bit-lengths of Kogge-Stone adder.
Keyword:
Parallel-prefix adders
critical path delay
threshold-voltage variations
statistical static timing analysis
timing yield
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5.4
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1.1K
被引数:
3.4K
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