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This paper presents a new model for the apparent characteristic impedance of finned waveguide and finlines from the standpoint of per-unit-length capacitance of the fins, obtained by conformal mapping, and of the waveguide, obtained from cutoff wavelengths, without going into the controversy of definition. The model strongly supports the power-voltage definition. Closed-form synthesis equations have also been derived which are within 1.5 percent of the analysis equations. The model will be useful in computer-aided design of millimeter-wave finned waveguide and finlines.