Variable permittivity dielectric material loaded stepped-horn antenna

16where D is a diagonal matrix of the size NT x NT whose diagonal elements are given asdue to the uniform waveguide sections of length A/ between the steps. The process isrepeated iteratively to include all discontinuities into an equivalent taper representation interms of the input and output ports. The input port corresponds to the feed waveguide whilethe output port is the radiating aperture of the horn antenna. This permits us to determinethe incident fields at the aperture in terms of the complex amplitudes of the modes excitingthe horn.In order to preserve numerical accuracy, the direct combination of the involved scatteringmatrices at all step discontinuities of the total tapered section are used as opposed tothe common treatment by transmission matrices. Although analytically more extensive,such as a need to take the inverse of 2NT x 2NT matrix twice, this technique leads tomatrix elements only containing exponential functions with negative argument, [13] whereevanescent modes decrease relatively quickly with distance between adjacent discontinuities.This direct combination of scattering matrices avoids numerical instabilities caused by theotherwise known situation of interacting discontinuities. There are two important factorswhich affect the accuracy of the stepped-waveguide aproximation: the size of the step,