Variable permittivity dielectric material loaded stepped-horn antenna

37It should be mentioned that even though the step does not excite T Em„, n 0 andT M modes, they might be still present at the aperture if the size of aperture is large enoughto support these modes, because of reflection from aperture and the presence of the taperedsection of the horn antenna.The H-plane step dimension for TEn0 mode excitation is determined as a functionof the step ratio, a, which is defined as a = a s/aA. as is the vertical dimension of thelast section of the tapered region and a A is the vertical dimension of the step waveguideadjacent to the aperture as shown in Figure 3.1. Using continuity of the electromagneticfields across the aperture of step, the coupling integral of TEm0 mode with unit amplitudein the smaller waveguide, last section of the tapered part, to TEn0 mode amplitude in stepwaveguide is evaluated analytically as a function of a, εn and εr2 aswhere b, is the y-dimension of the smaller waveguide, and bA is the y-dimension of the stepwaveguide.Since in this study of H-plane step, only x dimension is changed symmetrically,b, = bA . Zhn0 is the wave impedance of the T En0-th mode in the step waveguide (aperture)and Zhm0 is the wave impedance of the T Em0-th mode at the smaller waveguide (taperedsection) aswhere j = m,n and k is the wave number in the step waveguide as k = ko εEri for smallerwaveguide, j = n, and k = loo εr2 for step waveguide, j = m. k0 is the free spacewavenumber. k, kcj0is TE-th mode.the cut-off wavenumber of theThe formula given above is valid for all TEn0 mode excitations from the incidentTEm0 mode. In this study, only TE30 mode optimization is considered. The goal is to