Tavşanoğlu, Ahmet Vedat2017-03-132017-03-132016-07-09Tavşanoğlu, 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.2016.75271919781479953417978147995340097814799534240271-43022379-447Xhttps://hdl.handle.net/11729/1189http://dx.doi.org/10.1109/ISCAS.2016.7527191This 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.eninfo:eu-repo/semantics/closedAccessCircuit theoryNodal conductance matrixResistive gridKronecker productResistorsMathematical modelManganeseSymmetric matricesMatricesEigenvalues and eigenfunctionsTransmission line matrix methodsMatrix inversionNetwork analysisNodal equationsMatrix-inversion-based methodSymmetric tridiagonal matrixIdentity matrixLinear resistive gridRectangular planar resistive gridKronecker product and sumEigenvalues and eigenvectorsComputation theoryReconfigurable hardwareAnalytical expressionsConductance matrixIdentity matricesMatrix inversionsConference Object145148N/AWOS:0003900947000372-s2.0-8498346820610.1109/ISCAS.2016.7527191N/A