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A black box model for a split-power CVT is presented. The CVT can be run in two modes, using two clutches to perform the mode shift. By combining matching two-mode CVTs, the model can be extended to include an arbitrary number of modes. The planetary gear arrangement in the CVT is described by a set of basic speed ratios. For any configuration, there are restrictions on the basic speed ratios to obtain a useful two-mode transmission. The model is used to determine permitted values of the basic speed ratios for a general CVT, containing a planetary gear arrangement with an arbitrary number of shafts. Application examples are shown. The results presented can be used for developing CVT concepts with several modes, as efficient, jerk-free automatic transmissions for heavy vehicles.