On the basis of the difference of the patterns in two principal planes of a multimode pyramidal horn that are predicted by numerical method

the mode ratio is determined to be inthe range from 0. 68 to 3. 73. By means of solving a set of mode matching matrix equations

themode ratio and phase at a E-plane symmetrie step in a rectangular waveguide are accurately obtained. The usually used formula of propogation constant of an infinite extension taper rectangularwaveguide is revised so that the phase difference between TE10 and TE12/TM12 modes at the hornaperture can be predicted more reasonably. The results from theoretical calculation and experimentare compared

and the ways to broaden the band are discussed.