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Compact and stable modeling of partial inductance and reluctance matrices

Published: 18 January 2005 Publication History

Abstract

The sparsification of the reluctance matrix L-1 (where L denotes the usual inductance matrix L) has been widely used in several recent investigations to make the problem of simulation of interconnects tractable. Although these sparsification techniques work well in practice, the stability of these approximations has not been established, i.e., the sparsified reluctance and inductance matrices are not guaranteed to be positive-definite. In this work, we propose a band matching method that enjoys two advantages: First, we exploit the elegant structure of the inverse of banded matrices so as to construct an approximate inductance matrix L whose band entries match the band entries of original L, and whose inverse is a banded matrix. This approach yields a compact representation of both inductance and reluctance matrices. Second, we establish that the compact approximant L is guaranteed to be positive-definite. Simulation results show that our approach enjoys an approximation accuracy that is comparable to that of existing methods.

References

[1]
W. W. Barrett and P. J. Feinsilver. Inverses of banded matrices. Linear Algebra and its Applications, 41:111-130, 1981.
[2]
M. Beattie and L. Pileggi. Efficient inductance extraction via windowing. In Proc. Design Automation and Test in Europe Conf., pages 430-436, 2001.
[3]
M. Beattie and L. Pileggi. Modeling magnetic coupling foron-chip inter-connect. In Proc. Design Automation Conf, pages 335-340, 2001.
[4]
T. H. Chen, C. Luk, H. Kim, and C. C.-P. Chen. INDUCTWISE: Inductance-wise interconnect simulator and extractor. In Proc. Int. Conf. on Computer Aided Design, pages 215-220, 2002.

Cited By

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  • (2014)Selective Inversion of Inductance Matrix for Large-Scale Sparse RLC SimulationProceedings of the 51st Annual Design Automation Conference10.1145/2593069.2593213(1-6)Online publication date: 1-Jun-2014
  • (2006)Stable and compact inductance modeling of 3-D interconnect structuresProceedings of the 2006 IEEE/ACM international conference on Computer-aided design10.1145/1233501.1233503(1-6)Online publication date: 5-Nov-2006
  • (2006)Stable and Compact Inductance Modeling of 3-D Interconnect Structures2006 IEEE/ACM International Conference on Computer Aided Design10.1109/ICCAD.2006.320097(1-6)Online publication date: Nov-2006

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cover image ACM Conferences
ASP-DAC '05: Proceedings of the 2005 Asia and South Pacific Design Automation Conference
January 2005
1495 pages
ISBN:0780387376
DOI:10.1145/1120725
  • General Chair:
  • Ting-Ao Tang
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 18 January 2005

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Cited By

View all
  • (2014)Selective Inversion of Inductance Matrix for Large-Scale Sparse RLC SimulationProceedings of the 51st Annual Design Automation Conference10.1145/2593069.2593213(1-6)Online publication date: 1-Jun-2014
  • (2006)Stable and compact inductance modeling of 3-D interconnect structuresProceedings of the 2006 IEEE/ACM international conference on Computer-aided design10.1145/1233501.1233503(1-6)Online publication date: 5-Nov-2006
  • (2006)Stable and Compact Inductance Modeling of 3-D Interconnect Structures2006 IEEE/ACM International Conference on Computer Aided Design10.1109/ICCAD.2006.320097(1-6)Online publication date: Nov-2006

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