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This paper presents an efficient passive time-domain macromodeling algorithm for distributed lossy transmission lines based on the generalized method of characteristics (MoC). A new theorem is described that specifies sufficient conditions to guarantee the passivity of the MoC by construction. A key feature of the proposed methodology is that the curve fitting to realize the MoC depends only on the per-unit-length (p.u.l.) parameters and not on the discretization of the macromodel. Thus, with the knowledge of the rational functions derived from the p.u.l. parameters, the MoC can be formulated in a closed-form manner for any line length while ensuring passivity.