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The broad wall dimension of a waveguide having a cut off frequency of 7.5 GHz is
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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The broad wall dimension of a waveguide having a cut off frequency of ...
Answer: b
Explanation: The cut off frequency and the broad wall dimension are related by fc = mc/2a. On substituting for m = 1 and fc = 7.5 GHz, we get a = 0.02 or 2 cm.
Explanation: The cut off frequency and the broad wall dimension are related by fc = mc/2a. On substituting for m = 1 and fc = 7.5 GHz, we get a = 0.02 or 2 cm.
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The broad wall dimension of a waveguide having a cut off frequency of ...
Understanding Waveguide and Cut-off Frequency
Waveguides are structures that guide electromagnetic waves, typically used in microwave applications. The cut-off frequency is the frequency below which a particular mode cannot propagate in the waveguide. For rectangular waveguides, the dominant mode is typically the TE10 mode.
Cut-off Frequency Formula
The cut-off frequency (fc) can be determined using the formula:
fc = (c / 2) * (m / a)
Where:
- c = Speed of light (approximately 3 x 10^8 m/s)
- m = Mode number (for TE10, m = 1)
- a = Broad wall dimension of the waveguide
Calculation Steps
1. Given Cut-off Frequency: 7.5 GHz (which is 7.5 x 10^9 Hz)
2. Using the Formula:
- Rearranging the formula gives: a = (c / 2) * (m / fc)
- For TE10, m = 1, so:
- a = (3 x 10^8 m/s) / (2 * 7.5 x 10^9 Hz)
3. Calculating a:
- a = (3 x 10^8) / (15 x 10^9) = 0.02 meters = 2 cm
Conclusion
The broad wall dimension of the waveguide with a cut-off frequency of 7.5 GHz is 2 cm, which corresponds to option 'B'. This value ensures that the waveguide can effectively support the propagation of the desired mode while filtering out frequencies below the cut-off.
Waveguides are structures that guide electromagnetic waves, typically used in microwave applications. The cut-off frequency is the frequency below which a particular mode cannot propagate in the waveguide. For rectangular waveguides, the dominant mode is typically the TE10 mode.
Cut-off Frequency Formula
The cut-off frequency (fc) can be determined using the formula:
fc = (c / 2) * (m / a)
Where:
- c = Speed of light (approximately 3 x 10^8 m/s)
- m = Mode number (for TE10, m = 1)
- a = Broad wall dimension of the waveguide
Calculation Steps
1. Given Cut-off Frequency: 7.5 GHz (which is 7.5 x 10^9 Hz)
2. Using the Formula:
- Rearranging the formula gives: a = (c / 2) * (m / fc)
- For TE10, m = 1, so:
- a = (3 x 10^8 m/s) / (2 * 7.5 x 10^9 Hz)
3. Calculating a:
- a = (3 x 10^8) / (15 x 10^9) = 0.02 meters = 2 cm
Conclusion
The broad wall dimension of the waveguide with a cut-off frequency of 7.5 GHz is 2 cm, which corresponds to option 'B'. This value ensures that the waveguide can effectively support the propagation of the desired mode while filtering out frequencies below the cut-off.
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The broad wall dimension of a waveguide having a cut off frequency of 7.5 GHz isa)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?
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