NONHOMOGENEOUS LONG TRANSMISSION LINE WITH AN INFINITE NUMBER OF PROPAGATING MODES.

The use of the theory of Riccati equations is exposed for a correct exclusion from the waveguide equations of the infinite number of reflected modes and of strongly attenuated modes, propagating in the forward direction. Correction factors which account for the effect of the excluded modes are derived for the modes remaining in the equation. The method is illustrated by examples of a periodically inhomogeneous line and of a line with random, stationary inhomogeneities. An algorithm for computation of correction factors to the coefficients of the long-line equations is indicated for the first example. For the second example authors establish the stationarity of matrix functions of infinite order for the coefficient of reflection and for the relative wake current of strongly attenuated modes, and compute the coefficients of the appropriate diffusion equation.