Construction of the nodal conductance matrix of a planar resistive grid and derivation of the analytical expressions of its eigenvalues and eigenvectors using the Kronecker Product and Sum

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dc.authorid0000-0001-8590-1518
dc.contributor.authorTavşanoğlu, Ahmet Vedaten_US
dc.date.accessioned2017-03-13T08:53:27Z
dc.date.available2017-03-13T08:53:27Z
dc.date.issued2016-07-09
dc.departmentIşık Üniversitesi, Mühendislik Fakültesi, Elektrik-Elektronik Mühendisliği Bölümüen_US
dc.departmentIşık University, Faculty of Engineering, Department of Electrical-Electronics Engineeringen_US
dc.description.abstractThis paper considers the task of constructing an (MxN+1)-node rectangular planar resistive grid as: first forming two (MxN+1)-node planar sub-grids; one made up of M of (N+1)-node horizontal, and the other of N of (M+1)-node vertical linear resistive grids, then joining their corresponding nodes. By doing so it is shown that the nodal conductance matrices GH and GV of the two sub-grids can be expressed as the Kronecker products GH = I-M circle times G(N), G(V) = G(M)circle times I-N, and G of the resultant planar grid as the Kronecker sum G = G(N circle plus) G(M), where G(M) and I-M are, respectively, the nodal conductance matrix of a linear resistive grid and the identity matrix, both of size M. Moreover, since the analytical expressions for the eigenvalues and eigenvectors of G(M) - which is a symmetric tridiagonal matrix- are well known, this approach enables the derivation of the analytical expressions of the eigenvalues and eigenvectors of G(H), G(V) and G in terms of those of G(M) and G(N), thereby drastically simplifying their computation and rendering the use of any matrix-inversion-based method unnecessary in the solution of nodal equations of very large grids.en_US
dc.description.versionPublisher's Versionen_US
dc.identifier.citationTavşanoğlu, A. V. (2016). Construction of the nodal conductance matrix of a planar resistive grid and derivation of the analytical expressions of its eigenvalues and eigenvectors using the kronecker product and sum. Paper presented at the 2016 IEEE International Symposium on Circuits and Systems (ISCAS), 145-148. doi:10.1109/ISCAS.2016.7527191en_US
dc.identifier.doi10.1109/ISCAS.2016.7527191
dc.identifier.endpage148
dc.identifier.isbn9781479953417
dc.identifier.isbn9781479953400
dc.identifier.isbn9781479953424
dc.identifier.issn0271-4302
dc.identifier.issn2379-447X
dc.identifier.scopus2-s2.0-84983468206
dc.identifier.scopusqualityN/A
dc.identifier.startpage145
dc.identifier.urihttps://hdl.handle.net/11729/1189
dc.identifier.urihttp://dx.doi.org/10.1109/ISCAS.2016.7527191
dc.identifier.wosWOS:000390094700037
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.indekslendigikaynakConference Proceedings Citation Index – Science (CPCI-S)en_US
dc.institutionauthorTavşanoğlu, Ahmet Vedaten_US
dc.institutionauthorid0000-0001-8590-1518
dc.language.isoenen_US
dc.peerreviewedYesen_US
dc.publicationstatusPublisheden_US
dc.publisherIEEEen_US
dc.relation.ispartof2016 IEEE International Symposium on Circuits and Systems (ISCAS)en_US
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectCircuit theoryen_US
dc.subjectNodal conductance matrixen_US
dc.subjectResistive griden_US
dc.subjectKronecker producten_US
dc.subjectResistorsen_US
dc.subjectMathematical modelen_US
dc.subjectManganeseen_US
dc.subjectSymmetric matricesen_US
dc.subjectMatricesen_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.subjectTransmission line matrix methodsen_US
dc.subjectMatrix inversionen_US
dc.subjectNetwork analysisen_US
dc.subjectNodal equationsen_US
dc.subjectMatrix-inversion-based methoden_US
dc.subjectSymmetric tridiagonal matrixen_US
dc.subjectIdentity matrixen_US
dc.subjectLinear resistive griden_US
dc.subjectRectangular planar resistive griden_US
dc.subjectKronecker product and sumen_US
dc.subjectEigenvalues and eigenvectorsen_US
dc.subjectComputation theoryen_US
dc.subjectReconfigurable hardwareen_US
dc.subjectAnalytical expressionsen_US
dc.subjectConductance matrixen_US
dc.subjectIdentity matricesen_US
dc.subjectMatrix inversionsen_US
dc.titleConstruction of the nodal conductance matrix of a planar resistive grid and derivation of the analytical expressions of its eigenvalues and eigenvectors using the Kronecker Product and Sumen_US
dc.typeConference Objecten_US
dspace.entity.typePublication

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