The inductance matrix of a multiconductor transmission line inmultiple magnetic media |
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Authors: | Mautz J.R. Harrington R.F. Hsu C.G. |
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Affiliation: | Dept. of Electr. & Comput. Eng., Syracuse Univ., NY; |
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Abstract: | A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of Nc conducting cylinders in inhomogeneous media consisting of Nd homogeneous regions with permeabilities μi and permittivities ϵ i, the inductance matrix [L] for the line is obtained by solving the magnetostatic problem of Nc conductors in Nd regions with permeabilities μ i. The capacitance matrix [C] for the line is obtained by solving the electrostatic problem of Nc conductors in Nd regions with permittivities ϵ i. It is shown that [L]=μ0ϵ0[C'] -1, where [C'] is the capacitance matrix of an auxiliary electrostatic problem of Nc conductors in Nd regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. ϵ' i/ϵ0=μ0/μi |
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