Variable permittivity dielectric material loaded stepped-horn antenna

24where Γwghnk and r wg enk are the complex modal amplitudes of the k-th reflected mode producedby Mn, for T E and T M modes, respectively.Using (2.35) and (2.51), a single element of the magnetic current density on theaperture plane is expressed as,Multiplying each side of (2.55) by (ft x eh, ) and (ii x eel ) and integrating over theaperture cross section and from orthogonality, all terms in the summation are zero exceptk = 1 term, leads toAdmittance matrix of waveguide region Y wgmn (2.42)is then expressed asIf testing function is chosen as the same as expansion function (also called Galerkin method),Wm = Mn , aperture admittance can be expressed asUtilizing the image theory, the tangential magnetic field of incident wave on the conductingsurface that replaces the aperture is twice of the tangential component of the incidentmagnetic field