A standard air-filled rectangular waveguide with dimensions a = 8.636 cm, b = 4.318 cmis fed by a 4-GHz carrier from a coaxial cable. Determine if a TE10 mode will be propagated.Repeat the same question for the mode TM11
Question
A standard air-filled rectangular waveguide with dimensions a = 8.636 cm, b = 4.318 cmis fed by a 4-GHz carrier from a coaxial cable. Determine if a TE10 mode will be propagated.Repeat the same question for the mode TM11
Solution
To determine if a certain mode will propagate in a waveguide, we need to calculate the cut-off frequency for that mode and compare it with the frequency of the signal. The cut-off frequency for a certain mode in a rectangular waveguide is given by:
f_c = (c/2) * sqrt[(m/a)^2 + (n/b)^2]
where:
- c is the speed of light (3 * 10^8 m/s),
- m and n are the indices of the mode,
- a and b are the dimensions of the waveguide.
- For the TE10 mode, m=1 and n=0. So, the cut-off frequency is:
f_c = (3 * 10^8 m/s / 2) * sqrt[(1/0.08636 m)^2 + (0/0.04318 m)^2] = 1.73 GHz
Since the signal frequency (4 GHz) is higher than the cut-off frequency, the TE10 mode will propagate in the waveguide.
- For the TM11 mode, m=1 and n=1. So, the cut-off frequency is:
f_c = (3 * 10^8 m/s / 2) * sqrt[(1/0.08636 m)^2 + (1/0.04318 m)^2] = 3.46 GHz
Since the signal frequency (4 GHz) is also higher than the cut-off frequency, the TM11 mode will also propagate in the waveguide.
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