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An exact full-wave model for a design of multi band horns based on the hybrid mode matching and Winner-Hopf method is described. The model is well suited for optimization owing to the mode-matching approach. The complex horn structure is constructed from a set of fundamental building blocks, and the scattering matrix of the entire device is found by cascading of the scattering matrices of the individual components. The main steps of the realization for a three-band (S/X/Ka) feed horn compatible with VLBI2010 standards are considered.

horn antennas; mode-matching technique