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A rectangular metal waveguide filled with a dielectric of relative permittivity εr = 4, has the inside dimensions 3 x 1.2 cm, the cut off frequency for the dominant mode is
- a)2.5 GHz
- b)5 GHz
- c)10 GHz
- d)12.5 GHz
Correct answer is option 'B'. Can you explain this answer?
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Given parameters:
- Inside dimensions of rectangular waveguide: 3 x 1.2 cm
- Dielectric constant: εr = 4
To find:
- Cut-off frequency for the dominant mode
Solution:
1. Calculate the cut-off wavelength (λc) for the dominant mode:
- For a rectangular waveguide, the cut-off wavelength is given by:
λc = 2a / m1√(εr-1)
where a is the smaller dimension of the waveguide and m1 is the mode number for the dominant mode (m1 = 1 for TE10 mode)
- Substituting the values, we get:
λc = 2 x 1.2 / √(4-1) = 1.385 cm
2. Calculate the cut-off frequency (fc) for the dominant mode:
- The cut-off frequency is given by:
fc = c / λc
where c is the speed of light in free space (3 x 10^8 m/s)
- Converting the cut-off wavelength to meters, we get:
λc = 0.01385 m
- Substituting the values, we get:
fc = 3 x 10^8 / 0.01385 = 21.66 GHz
3. Calculate the frequency for the dominant mode:
- The frequency for the dominant mode is given by:
f = m1c / 2a√(εr-1)
- Substituting the values, we get:
f = (1 x 3 x 10^8) / (2 x 0.012)√(4-1) = 5 GHz
Therefore, the cut-off frequency for the dominant mode is 5 GHz (option B).
- Inside dimensions of rectangular waveguide: 3 x 1.2 cm
- Dielectric constant: εr = 4
To find:
- Cut-off frequency for the dominant mode
Solution:
1. Calculate the cut-off wavelength (λc) for the dominant mode:
- For a rectangular waveguide, the cut-off wavelength is given by:
λc = 2a / m1√(εr-1)
where a is the smaller dimension of the waveguide and m1 is the mode number for the dominant mode (m1 = 1 for TE10 mode)
- Substituting the values, we get:
λc = 2 x 1.2 / √(4-1) = 1.385 cm
2. Calculate the cut-off frequency (fc) for the dominant mode:
- The cut-off frequency is given by:
fc = c / λc
where c is the speed of light in free space (3 x 10^8 m/s)
- Converting the cut-off wavelength to meters, we get:
λc = 0.01385 m
- Substituting the values, we get:
fc = 3 x 10^8 / 0.01385 = 21.66 GHz
3. Calculate the frequency for the dominant mode:
- The frequency for the dominant mode is given by:
f = m1c / 2a√(εr-1)
- Substituting the values, we get:
f = (1 x 3 x 10^8) / (2 x 0.012)√(4-1) = 5 GHz
Therefore, the cut-off frequency for the dominant mode is 5 GHz (option B).
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A rectangular metal waveguide filled with a dielectric of relative permittivity εr = 4, has the inside dimensions 3 x 1.2 cm, the cut off frequency for the dominant mode isa)2.5 GHzb)5 GHzc)10 GHzd)12.5 GHzCorrect answer is option 'B'. Can you explain this answer?
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