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Equipotential shells for efficient inductance extraction
To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstab...
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Published in: | IEEE transactions on computer-aided design of integrated circuits and systems 2001-01, Vol.20 (1), p.70-79 |
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creator | Beattie, M. Krauter, B. Alatan, L. Pileggi, L. |
description | To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. To demonstrate the overall efficacy for on-chip extraction, ellipsoid shells, which are a special case of the general equipotential shell approach, are presented and demonstrated for both on-chip and system-level extraction examples. |
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It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. 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(IEEE) 2001</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c367t-6071675617abec2e316c67cff60d6f8c4f38ef3510e745fddedac1061694d2733</citedby><cites>FETCH-LOGICAL-c367t-6071675617abec2e316c67cff60d6f8c4f38ef3510e745fddedac1061694d2733</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/905676$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,54796</link.rule.ids></links><search><creatorcontrib>Beattie, M.</creatorcontrib><creatorcontrib>Krauter, B.</creatorcontrib><creatorcontrib>Alatan, L.</creatorcontrib><creatorcontrib>Pileggi, L.</creatorcontrib><title>Equipotential shells for efficient inductance extraction</title><title>IEEE transactions on computer-aided design of integrated circuits and systems</title><addtitle>TCAD</addtitle><description>To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. To demonstrate the overall efficacy for on-chip extraction, ellipsoid shells, which are a special case of the general equipotential shell approach, are presented and demonstrated for both on-chip and system-level extraction examples.</description><subject>Approximation</subject><subject>Capacitance</subject><subject>Coupling circuits</subject><subject>Couplings</subject><subject>Effectiveness</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Ellipsoids</subject><subject>Equipotentials</subject><subject>Extraction</subject><subject>Inductance</subject><subject>Integrated circuit interconnections</subject><subject>Integrated circuit modeling</subject><subject>Mutual coupling</subject><subject>Shells</subject><subject>Sparse matrices</subject><subject>Symmetric matrices</subject><subject>System-on-a-chip</subject><issn>0278-0070</issn><issn>1937-4151</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNqF0TtPwzAQAGALgUR5DKxMEQOIIcUXO-d4RFV5SJVYYLaMcxau2qS1Ewn-PYFUDAwwnXT36R46xs6ATwG4vpFiqnmJCvfYBLRQuYQS9tmEF6rKOVf8kB2ltOQcZFnoCavm2z5s2o6aLthVlt5otUqZb2NG3gcXhnwWmrp3nW0cZfTeReu60DYn7MDbVaLTXTxmL3fz59lDvni6f5zdLnInUHU5cgWoSgRlX8kVJAAdKuc98hp95aQXFXlRAiclS1_XVFsHHAG1rAslxDG7GvtuYrvtKXVmHZIbtrQNtX0yGiRKLDQf5OWfsqhKRAD4H6Iexn93vPgFl20fm-FcU1VSgRQFDuh6RC62KUXyZhPD2sYPA9x8_cRIYcafDPZ8tIGIftyu-AlYwYUW</recordid><startdate>200101</startdate><enddate>200101</enddate><creator>Beattie, M.</creator><creator>Krauter, B.</creator><creator>Alatan, L.</creator><creator>Pileggi, L.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7U5</scope><scope>7TB</scope><scope>FR3</scope><scope>F28</scope></search><sort><creationdate>200101</creationdate><title>Equipotential shells for efficient inductance extraction</title><author>Beattie, M. ; Krauter, B. ; Alatan, L. ; Pileggi, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c367t-6071675617abec2e316c67cff60d6f8c4f38ef3510e745fddedac1061694d2733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>Approximation</topic><topic>Capacitance</topic><topic>Coupling circuits</topic><topic>Couplings</topic><topic>Effectiveness</topic><topic>Eigenvalues and eigenfunctions</topic><topic>Ellipsoids</topic><topic>Equipotentials</topic><topic>Extraction</topic><topic>Inductance</topic><topic>Integrated circuit interconnections</topic><topic>Integrated circuit modeling</topic><topic>Mutual coupling</topic><topic>Shells</topic><topic>Sparse matrices</topic><topic>Symmetric matrices</topic><topic>System-on-a-chip</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Beattie, M.</creatorcontrib><creatorcontrib>Krauter, B.</creatorcontrib><creatorcontrib>Alatan, L.</creatorcontrib><creatorcontrib>Pileggi, L.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library Online</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Engineering Research Database</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><jtitle>IEEE transactions on computer-aided design of integrated circuits and systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Beattie, M.</au><au>Krauter, B.</au><au>Alatan, L.</au><au>Pileggi, L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Equipotential shells for efficient inductance extraction</atitle><jtitle>IEEE transactions on computer-aided design of integrated circuits and systems</jtitle><stitle>TCAD</stitle><date>2001-01</date><risdate>2001</risdate><volume>20</volume><issue>1</issue><spage>70</spage><epage>79</epage><pages>70-79</pages><issn>0278-0070</issn><eissn>1937-4151</eissn><coden>ITCSDI</coden><abstract>To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. 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source | IEEE Electronic Library (IEL) Journals |
subjects | Approximation Capacitance Coupling circuits Couplings Effectiveness Eigenvalues and eigenfunctions Ellipsoids Equipotentials Extraction Inductance Integrated circuit interconnections Integrated circuit modeling Mutual coupling Shells Sparse matrices Symmetric matrices System-on-a-chip |
title | Equipotential shells for efficient inductance extraction |
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