Analysis of nonlinear termination networks for coupled lossy and dispersive transmission lines

Based on an algorithm developed by the authors, multiple transmission lines with skin effect losses and dispersive characteristics are analyzed by the volume equivalent principle, and the scattering matrix [Sω] and characteristic impedance matrix [Z_0ω] of the transmission lines are obtained. The [Sω] and [Z_0(w)] are then transformed by the inverse fast Fourier transform (FFT) into the time domain. The scattering matrix representation is multiplicative in nature, which leads to a time-domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariable Newton-Raphson method, which may occasionally be unstable, the authors generate a set of object functions and apply a multivariable optimization technique, referred to as the modified Levenberg-Marquardt algorithm, to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications