An optimization approach to the frequency-domain inverse problem for a nonuniform LCRG transmission line

The inverse problem for a nonuniform LCRG transmission line is considered in the frequency domain. Imbedding equations for the reflection and transmission coefficients are derived through the concept of wave-splitting. An optimization approach is applied to reconstruct the line parameters as functions of the position using band-limited reflection and/or transmission data. Exact and explicit expressions for the gradients are derived, and the reconstruction algorithm (based upon a conjugate gradient method) is tested with both clean and noisy data, The problem of the nonuniqueness is also discussed.