Variable permittivity dielectric material loaded stepped-horn antenna

CHAPTER 2MATHEMATICAL MODELTypical pyramidal horn antenna geometry is shown in Figure 2.1. Analysis of this radiatingstructure is done by separating the antenna into two parts. The first part is the taperedsection of the horn starting at the feed waveguide and ending at the aperture. This sectionis modelled by a set of NI cascaded dielectric loaded uniform waveguide sections as shownin Figure 2.2. The mode matching method is performed to obtain the generalized scatteringmatrix at each step discontinuity. The overall scattering matrix of the tapered region is thencomputed by cascading the scattering matrices of the junctions involved in the model.The second part of the problem is an aperture radiating into the half-space assumingthe horn to be terminated by an infinite metallic plane as shown in Figure 2.3. The methodof moments is then invoked to determine the generalized reflection matrix of this apertureand then the unknown aperture field distribution.2.1 Mode MatchingThe tapered region of the horn antenna is approximated in terms of NI rectangular waveguidesections each of length A/ LINT filled with dielectric material of permittivity, εi εriεo ,i 1, 2, . . . , NI. Each section begins at zi (i — 1)A/ where z = 0 corresponds tothe junction adjacent to the feed waveguide (i 1), and the aperture plane is located atz = L. The cross-sectional dimensions of the i-th waveguide section, ai and bi being thewaveguide dimensions in the transverse (x, y) plane, are defined as5