The electromagnetic field expressions for TMmn mode in rectangular waveguide are given by; mi n E(x,...

Transcribed Image Text:

The electromagnetic field expressions for TMmn mode in rectangular waveguide are given by; mi nπ E₂(x, y, z) = Amn sin x sin- b a Ex(x, y, z) = Ey (x, y, z)= H₂(x, y, z) = -jpmn k²a -jpnn mi Amn cos x sin- a mi Amnsin- x cos a mi k²b joenn k²b -joemn ka Amn sin -ye-jßz NIT a -x cos bye-jßz nπ bye-jßz пл bye-1Bz mл -X xsin ye a nπ Hy(x, y, z)= Amncos- where; Amn is an arbitrary constant for the TMmn mode and ß is the corresponding propagation constant. The waveguide has dimensions: a-19.05 mm and (b/a) = 0.65. The waveguide is filled with dielectric material of er=4. i. Find the cutoff frequency of the first TMmn mode. ii. If the frequency of operation is 8 GHz, find all possible propagating modes, find also the corresponding propagation constant for each propagating mode. bye-jßz iii. Plot the surface current on both the upper and right-side walls corresponding to the TM₁1 mode. iv. Plot the electric field along the cross section (x-y plan) of the WG for the TM₁1 mode. v. Find the appropriate placement for a narrow slot on the metallic walls which might be needed to measure the electric field inside the waveguide for the TM₁1 mode along the direction of propagation without affecting the field distribution. [5 marks] [5 marks] [5 marks] [5 marks] [5 marks] The electromagnetic field expressions for TMmn mode in rectangular waveguide are given by; mi nπ E₂(x, y, z) = Amn sin x sin- b a Ex(x, y, z) = Ey (x, y, z)= H₂(x, y, z) = -jpmn k²a -jpnn mi Amn cos x sin- a mi Amnsin- x cos a mi k²b joenn k²b -joemn ka Amn sin -ye-jßz NIT a -x cos bye-jßz nπ bye-jßz пл bye-1Bz mл -X xsin ye a nπ Hy(x, y, z)= Amncos- where; Amn is an arbitrary constant for the TMmn mode and ß is the corresponding propagation constant. The waveguide has dimensions: a-19.05 mm and (b/a) = 0.65. The waveguide is filled with dielectric material of er=4. i. Find the cutoff frequency of the first TMmn mode. ii. If the frequency of operation is 8 GHz, find all possible propagating modes, find also the corresponding propagation constant for each propagating mode. bye-jßz iii. Plot the surface current on both the upper and right-side walls corresponding to the TM₁1 mode. iv. Plot the electric field along the cross section (x-y plan) of the WG for the TM₁1 mode. v. Find the appropriate placement for a narrow slot on the metallic walls which might be needed to measure the electric field inside the waveguide for the TM₁1 mode along the direction of propagation without affecting the field distribution. [5 marks] [5 marks] [5 marks] [5 marks] [5 marks]

Answer rating: 100% (QA)

for TM mode Ez 2 42 An sin max sintrany eBz 065 b1238mm a 1905 mm Er 4 cis cutoff frequ... View the full answer