An integral equation associated with the inverse problem for nonuniform transmission lines with terminal discontinuities

The frequency-domain inverse problem for nonuniform transmission lines is considered; that is, the problem of determining the characteristic impedance
Z_{0}(x)
of a lossless nonuniform line from spectral admittance data. The theory presented is related to the inverse scattering theory of Marchenko and accounts for possible discontinuities at the input and output of the line. The principal result is the derivation of a linear integral equation, the solution of which leads to a reconstruction of
Z_{0}(x)
. The kernel function in the integral equation is determined from spectral measurements of the input conductance of the line. The derivation is based on an integral representation of the solutions of the transmission line equations and the asymptotic properties of these solutions. A particular solution of the inverse problem is presented as an illustrative example.