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A printed transition is proposed to overcome problems limiting the performances of SIW horn antennas when built in thin substrates (thickness <; λ0/10). An analytical model to analyze its behavior is given along with design guidelines. The development of a possible transmission line model is also presented. This transition is associated with a H-plane sectoral SIW horn antenna to both show the validity of the proposed model and the significant improvements it can bring in terms of matching, bandwidth and radiation.