7. EyEO HO Hr €0. 40 The above figure represents a section of rectangular waveguide, half of which is completely filled

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7 Eyeo Ho Hr 0 40 The Above Figure Represents A Section Of Rectangular Waveguide Half Of Which Is Completely Filled 1 (532.42 KiB) Viewed 12 times

7. EyEO HO Hr €0. 40 The above figure represents a section of rectangular waveguide, half of which is completely filled with a non-magnetic dielectric of relative permittivity &r, the other half being empty. The guide has dimensions a × b (a = 3.00 cm > b) and supports the TE10 mode with the electric field and the transverse component of the magnetic field intensity in the empty section given by π.χ E₁ E, sin(Xexp (@t-B,z), = a Bo π.χ H₁ -Î = Eosin exp j(wt - Boz), ωμο a where Bo is the propagation constant in the empty guide. In this question, assume that the field is launched from the left side of the guide by means of a matched oscillator operating at a frequency of 6.00 GHz and that the guide is terminated in a matched load somewhere along the guide on the dielectric-filled side. (i) Draw a two-dimensional diagram in a plane parallel to the y-z plane, representing the incident transverse fields E; and H₁, the corresponding reflected fields E, and H₁, and the transmitted fields E, and H, at the boundary (z = 0). [8 marks] (ii) Apply the boundary conditions to obtain the following reflection and transmission coefficients: Eor B-Bo. Г = ; Eoi B + Bo Eot 2ß T = = Eoi B + Bo where ß is the propagation constant in the dielectric side of the waveguide. [18 marks] (iii) I is measured at z = 0 and found to be 0.200 -j 0.100. Find &r. [22 marks] (iv) Calculate by what fraction the E field amplitude drops after penetrating 3 cm into the dielectric. [12 marks] y = 2