Analytical treatment of circulant nonuniform multiconductor transmission lines

The authors analytically study a certain class of nonuniform multiconductor transmission lines (NMTL). This class is described by circulant impedance and admittance matrices. Due to the properties of circulant matrices (which form a special set of normal matrices) it is shown that the NMTL equations can be simultaneously diagonalized with the aid of the position-independent so-called Fourier matrix. Thereby, the NMTL equations decouple completely and the resulting equations for the modal components of the voltages and currents may be solved with techniques and methods already known from the analyses of single nonuniform transmission lines. Application examples covering the high-frequency propagation on NMTL and an exact solution (in the frequency domain) a coupled transmission line model for a unit cell of a periodic array of wave launchers are presented. The methods are also applied to a diverging pair of conductors above a perfectly conducting plane. Special interest, however, is focused on C_N and C_Nc symmetry of the NMTL configurations