The electromagnetic field expressions for TEmn mode in an air-filled rectangular waveguide are given by; mi пл H₂(x, y,

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The electromagnetic field expressions for TEmn mode in an air-filled rectangular waveguide are given by; mi пл H₂(x, y, z)= Amn cos x cos a bye-18z jßmn mi 127 H₂(x, y, z)= Amn Sin-x cos ka a bye-18z mi TUTT Hy(x, y, z)=1 jßnn kab Amn cos-xsin- a -ye-1Bz b mi пл jωμηπ Ex(x, y, z)= Amn Cosxsin kab ye-1Bz a αξωμηπ mi пл Ey(x, y, z)= ka Amn sin- xcosye-18z a where; Amn is an arbitrary constant for the TEmn mode and ß is the corresponding propagation constant. The wide dimension (a) of the waveguide equals 19.05 mm. i. Find the other waveguide dimension (b) so that it might be [7 marks] possible that only the fundamental mode will propagate over a bandwidth of more than 15 GHz. ii. Specify the excitation system to only support the required [7 marks] fundamental mode propagation. iii. Plot the surface current on both the upper and right-side walls corresponding to the TE11 mode. [9 marks] iv. Plot the electric field along the cross section (x-y plane) of the WG for the TE11 mode. [10 marks]