The inductance matrix of a multiconductor transmission line in multiple magnetic media

A simple relationship between the inductance matrix and the auxiliary capacitance matrix is given. For a multiconductor transmission line consisting of N/sub c/ conducting cylinders in inhomogeneous media consisting of N/sub d/ homogeneous regions with permeabilities mu /sub i/ and permittivities epsilon /sub i/, the inductance matrix (L) for the line is obtained by solving the magnetostatic problem of N/sub c/ conductors in N/sub d/ regions with permeabilities mu /sub i/. The capacitance matrix (C) for the line is obtained by solving the electrostatic problem of N/sub c/ conductors in N/sub d/ regions with permittivities epsilon /sub i/. It is shown that (L)= mu /sub 0/ epsilon /sub 0/(C/sup '/)/sup -1/, where (C/sup '/) is the capacitance matrix of an auxiliary electrostatic problem of N/sub c/ conductors in N/sub d/ regions with relative permittivities set equal to the reciprocals of the relative permeabilities of the magnetostatic problem, i.e. epsilon /sup '//sub i// epsilon /sub 0/= mu /sub 0// mu /sub i/.>