A new inhomogeneous waveguide transformer with hard walls is presented. Mod
e matching technique along with an optimization routine is used to design t
he transformer. The generalized scattering matrix (GSM) of the whole block
is calculated which can be used to predict the fields at the output given t
he incident excitations. An example of a three-section transformer, which r
eplaces a tapered hard horn, is shown. The transformer has better performan
ce in the bandwidth of interest compared to the tapered hard horn having tw
ice the length of the transformer. This type of transformers could be usefu
l for excitation of quasi-optical amplifiers and reflector feeds.