Generating Stable and Sparse Reluctance/Inductance Matrix under Insufficient Discretization

Yuichi TANJI  Takayuki WATANABE  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E93-C   No.3   pp.379-387
Publication Date: 2010/03/01
Online ISSN: 1745-1353
DOI: 10.1587/transele.E93.C.379
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on Circuits and Design Techniques for Advanced Large Scale Integration)
Category: 
Keyword: 
inductance,  reluctance,  sparse,  signal/power integrity,  

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Summary: 
This paper presents generating stable and sparse reluctance/inductance matrix from the inductance matrix which is extracted under insufficient discretization. To generate the sparse reluctance matrix with guaranteed stability, the original matrix has to be (strictly) diagonally dominant M matrix. Hence, the repeated inductance extractions with a smaller grid size are necessary in order to obtain the well-defined matrix. Alternatively, this paper provides some ideas for generating the sparse reluctance matrix, even if the extracted reluctance matrix is not diagonally dominant M matrix. These ease the extraction tasks greatly. Furthermore, the sparse inductance matrix is also generated by using double inverse methods. Since reluctance components are not still supported in SPICE-like simulators, generating the sparse inductance matrix is more useful than the sparse reluctance one.