### Abstract

We show how advances in the handling of correlated interval representations of range uncertainty can be used to approximate the mass of a probability density function as it moves through numerical operations and, in particular, to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in resistanceinductance-capacitance (RLC) parameters as sets of correlated intervals and show how classical model-order reduction methods-asymptotic waveform evaluation and passive reducedorder interconnect macromodeling algorithm-can be retargeted to compute interval-valued, rather than scalar-valued, reductions. By applying a simple statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show that the technique can predict mean delay and standard deviation with errors between 5% and 10% for correlated RLC parameter variations up to 35%.

Original language | English (US) |
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Pages (from-to) | 1602-1613 |

Number of pages | 12 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | 26 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2007 |

### Keywords

- Affine arithmetic
- Design-for-manufacturing
- Interconnect simulation
- Numerical analysis
- Statistical modeling

### ASJC Scopus subject areas

- Software
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*,

*26*(9), 1602-1613. https://doi.org/10.1109/TCAD.2007.895577