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In this paper, an unconditionally stable finite-difference time-domain algorithm is presented for analysis of lossy nonuniform multiconductor transmission line (MTL). The results of the proposed algorithm are confirmed by those of the Leap-Frog algorithm. The unconditionally stable algorithm alone cannot decrease the time consumption, especially when the MTL is excited by modulated signals. The complex phasor transformation approach is used to separate the modulating signal from the carrier signal when an MTL is excited by a modulated signal. A new set of equations is generated using this approach. The new equations are based on the modulating signal, and the carrier signal is eliminated in these equations. The derived equations are solved by Leap-Frog algorithm, and the results confirm the accuracy of these equations. Finally, the proposed equations are solved by the unconditionally stable algorithm at several temporal step sizes. The results indicate that this method has much lower CPU time compared with the conventional method and also has a very good accuracy.