In the analysis of characteristic behaviors of a real transformer with coupling coefficient K is less than 1, this paper presents the more accurate and practical profits than the traditional analysis of the transformer treated as K∼1. This results from the use of the coupling coefficient type equivalent circuit of the transformer which includes K as positive parameter. Furthermore, a leakage transformer is analyzed in a unified method and the results of analysis are consistent with the practical measurements of the transformer. By using the above equivalent circuit, the characteristics referred to the load side are expressed as Thevenin voltage source and the leakage inductor (1-K2)L2. Therefore, these analysis about the output voltage and the damping factor in the transient state which are affected by the leakage inductor are confirmed to be an effective method.