In this paper, an efficient approach is proposed for the problem of transient simulation of lossy transmission lines. The complexity of the conventional convolution approach for lossy transmission lines is reduced from O(N^2) to O(Nlog^2N) by utilizing a multilevel FFT convolution method, where N is the total number of time points. Numerical convolution formula that exploits both the analytical forms of the lossy transmission line impulse responses and adaptive time steps are developed for the multilevel FFT convolution method. A new breakpoint control scheme is also proposed to adaptively control the time step. Experimental results show the proposed approach is over 100 times faster than berkeley SPICE3 [1, 4] while remains the same accuracy.
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