A linear fractional transform (LFT) based model for interconnect parametric uncertainty

ABSTRACT

As we scale toward nanometer technologies, the increase in interconnect parameter variations will bring significant performance variability. New design methodologies will emerge to facilitate construction of reliable systems from unreliable nanometer scale components. Such methodologies require new performance models which accurately capture the manufacturing realities. In this paper, we present a Linear Fractional Transform (LFT) based model for interconnect Parametric Uncertainty. This new model formulates the interconnect parameter uncertainty as a repeated scalar uncertainty structure. With the help of generalized Balanced Truncation Realization (BTR) based on Linear Matrix Inequalities (LMI's), the new model reduces the order of the original interconnect network while preserves the stability. This paper also shows that the LFT based model even guarantees passivity if the BTR reduction is based on solutions to a pair of Linear Matrix Inequalities (LMI's) which generalizes Lur'e equations.

REFERENCES

• 1: Ying Liu , Lawrence T. Pileggi , Andrzej J. Strojwas, Model order-reduction of RC(L) interconnect including variational analysis, Proceedings of the 36th ACM/IEEE conference on Design automation, p.201-206, June 21-25, 1999, New Orleans, Louisiana, United States [doi>10.1145/309847.309914]
• 2: K.J.Kerns, and A.T. Yang, "Stable and Efficient Reduction of Large Multiport RC Networks by Pole analysis via Congruence Transformations", IEEE Trans. CAD, Vol. 16, pp. 734--744, 1997.
• 3: A. Odabasioglu, M. Celik, L. Pileggi, "PRIMA: Passive Reduced-Order Interconnect Macromodeling Algorithm", IEEE Trans. CAD, vol. 17, No. 8, pp. 645--654, Aug. 1998.
• 4: C. Beck, J. Doyle, and K. Glover, "Model Reduction of Multidimensional and Uncertain Systems", IEEE Trans. Automatic Control, vol. 41, No. 10, pp. 1466--1477, October, 1996.
• 5: C. Beck, J. Doyle, "A Necessary and Sufficient Minimality Condition for Uncertain Systems", IEEE Trans. Automatic Control, vol. 44, No. 10, pp. 1802--1813, Oct. 1999.
• 6: Time-Domain Simulation of Variational Interconnect Models, Proceedings of the 3rd International Symposium on Quality Electronic Design, p.419, March 18-21, 2002
• 7: J. Phillips, L. Daniel, L. Silveira, "Guaranteed Passive Balancing Transformations for Model Order Reduction", IEEE Trans. CAD, Vol. 22, No. 8, pp. 1--15, Aug. 2003.
• 8: P. Heydari, and M. Pedram, "Model Reduction of Variable-Geometry Interconnects Using Variational Spectrally-Weighted Balanced Truncation", Design Automation Conference 2001.
• 9: G. Golub, and C. Loan, "Matrix Computation", pp. 390--405, Johns Hopkins Univeristy Press, 1996.

INDEX TERMS

Primary Classification:
  K. Computing Milieux
  K.2 HISTORY OF COMPUTING

General Terms:
Algorithms, Design, Theory

Keywords:
linear fractional transform, parametric uncertainty