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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Dosyalar
Tarih
2016-07-09
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Yayıncı
IEEE
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This 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.
Açıklama
Anahtar Kelimeler
Circuit theory, Nodal conductance matrix, Resistive grid, Kronecker product, Resistors, Mathematical model, Manganese, Symmetric matrices, Matrices, Eigenvalues and eigenfunctions, Transmission line matrix methods, Matrix inversion, Network analysis, Nodal equations, Matrix-inversion-based method, Symmetric tridiagonal matrix, Identity matrix, Linear resistive grid, Rectangular planar resistive grid, Kronecker product and sum, Eigenvalues and eigenvectors, Computation theory, Reconfigurable hardware, Analytical expressions, Conductance matrix, Identity matrices, Matrix inversions
Kaynak
2016 IEEE International Symposium on Circuits and Systems (ISCAS)
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Sayı
Künye
Tavşanoğlu, 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.2016.7527191
