1 An air-filled rectangular waveguide has a cross section of 6 X 4 an.

(a) Calculate the cutoff frequency of the dominant mode.

(b) Determine how many modes are passed at three times cutoff frequency of dominant mode.

2 An air-filled waveguide has a = 6 cm and b = 4 cm. What modes are possible if a wave of frequency f = 6 GHz is to be propagated down the guide?

3 A rectangular waveguide (2.28 X 1.01 cm) is filled with polyethylene (ε_r = 2.25). Calculate the cutoff frequencies for the following modes:
Molt TE₁₀, TE₁₁, TE₀₂, TE₂₂, TM₁₁, TM₁₂, TM₂₁. Assume that polyethylene is lossless.

4 A 2 X 1 cm waveguide is filled with deionized water with e, = 81. If the operating frequency is 4.5 GHz, determine (a) all possible propagating modes and their cutoff frequencies, (b) the intrinsic impedance of the highest mode, (c) the group velocity of the lowest mode.

5 Design a rectangular waveguide with an aspect ratio of 3 to 1 for use in the K band (18-26.5 GHz). Assume that the guide is air filled.

6 A tunnel is modeled as an air-filled metallic rectangular waveguide with dimensions a = 8 m and b16 m. Determine whether the tunnel %till pass (a) a 1.5 wiz AM broadcast signal, (b) a 120 MHz FM broadcast signal.

12.7 In an air-filled rectangular waveguide, the cutoff frequency of a TE₁₀ mode is 5 GHz whereas that of TE₀, mode is 12 GHz. Calculate
(a) The dimensions of the guide

(b) The cutoff frequencies of the next three higher TE modes

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