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In this paper, the time domain circuit finite difference method is studied. This method can be used to analyze the transient transmission characteristics of the equivalent circuit constructed by the distributed circuit parameters, which are extracted from the non-uniform transmission lines. The stability of the method is studied. The method is then used to analyze the reflected and transmitted pulse waveforms of the equivalent circuit. By comparing the waveforms obtained by this method with those obtained by FDTD, the applicability of this method can be studied.