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A new transient analysis method for the transmission line circuits is presented in this paper. Based on the semidiscretization of the telegraph equations, a discretized time domain companion models for the transmission lines which can be conveniently implemented in a general circuit simulator such as SPICE is derived. The computation required for the model is linear with time, equivalent to the recursive convolution-based method. The formulations for both single and coupled lossy transmission lines are given. Numerical experiments are carried out to demonstrate the validity of the method.