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The paper focuses on revealing the salient structural aspects of a new transmission-line model with a view to exploiting them for gains in efficiency and accuracy. The new transmission-line model has as its basis the Telegraphers Equations but the manner of solution is what distinguishes the new approach from existing transmission-line simulation techniques. The technique is based on identifying natural modes of oscillation on the transmission line. The result is a model structure which can be tailored to the accuracy requirements of a simulation and which is amenable to tuning to fit measured admittance data.