A canonical form for lossless multiport transmission lines

The propagation of TEM waves on a reciprocal
n
-port lossless nonuniform transmission line, with absolutely continuous characteristic impedance and locally equal wavefront velocities in each port, is described in this note by a canonical system of wave equations. The essential feature of this canonical system is an
n \times n
local reflection coefficient which generalizes the notion of a reflection coefficient for a single-port line. The reflection coefficient characterizes the local scattering behavior at any point on the line, and is unique up to a constant orthogonal transformation.