Solution of the transmission-line equations under the weak-coupling assumption

The transmission-line equations for a three-conductor lossless line in a nonhomogeneous medium are solved in symbolic form (as opposed to a numerical solution) in the time domain under the assumption of weak coupling. The result provides insight into crosstalk between the lines. Numerical solutions of this problem exist but do not illustrate the factors that influence the crosstalk waveforms. The symbolic solution given in this paper makes those factors clear. The validity of the weak-coupling assumption is also investigated.