Analytical treatment of uniform multiconductor transmission lines

The authors study a certain class of solutions of the multiconductor-transmission-line (MTL) equations. This class is basically defined by two reasonable but otherwise arbitrary demands: the commutativity between the propagation matrix and the characteristic impedance matrix, and the assumption that the matrices of interest are real matrices times complex-valued functions (e.g., functions of the constitutive parameters of the medium). On the basis of the above requirements, it can be shown that all matrices that are relevant for the MTL equations and for their solutions can be simultaneously diagonalized with only one set of eigenvectors (e.g., the eigenvectors of the per-unit-length inductance matrix). Of course, the sets of eigenvalues corresponding to different matrices are different. The authors investigate the MTL equations and their solutions for different environments and different properties, including lossy lines and lossy media. Mechanisms that can cause splitting of natural frequencies are considered.