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In this paper the extraction of the generalized scattering matrix using the finite-volume time-domain (FVTD) method is presented. The extraction scheme takes advantage of the flux-splitting formulation that is inherent to the FVTD algorithm. Thus the incident and reflected waves in a transmission line are immediately known at every time step. A new way to determine the power waves is shown as well as the implementation of the ports and the mode separation in a multimode environment. The ability of the proposed scheme to extract the scattering parameters correctly is illustrated in an example that compares the simulated return loss of a balun to measurements.