The inverse scattering problem for L C R G transmission lines

The inverse scattering problem for one-dimensional nonuniform transmission lines with inductance L(z), capacitance C(z), series resistance R(z) and shunt conductance G(z) per unit length (z∈R) is considered. It is reduced to the inverse scattering problem for the Zakharov–Shabat system. It is found that one can construct from the data the following functions of the travel time x: q̃±(x)=[(1/4)(d/dx)(ln(L/C))±(1/2)(R/L−G/C)] ×exp(∓∫x∞(R/L+G/C)dy).