# Solved Problems-7

Problem-7
In an air-filled rectangular waveguide, the cut-off frequency of a TE10 mode is 5 GHz, whereas that of TE01 mode is 2 GHz. Calculate
1. The dimension of the guide
2. The cut-off frequencies of the next three higher TE modes
3. The cut-off frequency for TE11 mode if the guide is filled with a lossless material having Îµr = 2.25 and Î¼r = 1
Solution
Here,

(a) Since the cut-off frequency is lowest in TE01 mode, this is the dominant mode. This implies that for the rectangular waveguide, b > a.

Now, for TE01 mode, the cut-off frequency is given as,

Also, for TE10 mode, the cut off frequency is given as,

So, the dimension of the rectangular waveguide is 3 cm Ã— 7.5 cm.

(b) The cut-off frequency for TEmn mode is given as,

Next higher order modes will be TE02, TE11, TE03.

The corresponding cut-off frequencies are given as follows.

(c) If the guide is filled with a lossless material having Îµr = 2.25 and Î¼r = 1, the cut-off frequency for TE11 mode is,