Based upon an algorithm described in a separate paper , multiple transmission lines with skin effect losses and dispersive characteristics were analyzed by the potential theory method, and the scattering matrix [S(ω)] and characteristic impedance matrix [Zo(ω)] of the transmission lines were obtained. The [S(ω)] and [Zo(ω)] were then transformed by the inverse FFT into the time domain. The scattering matrix representation is multiplicative in nature, which leads to the time domain formulation as a set of convolution integrals. Instead of attempting to solve a set of coupled convolution integral equations by the multivariate Newton-Raphson method, which may occasionally be unstable, we generated a set of object functions and applied a multivariable optimization technique to attain the solutions. The new method, which is quite general, reduces to the special cases derived in many previous publications.