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A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25
Que: The range of frequencies over which single mode operation will occur is
- a)2.24 GHz < f <3.33 GHz
- b)2 GHz < f < 3 GHz
- c)4.48 GHz < f < 7.70 GHz
- d)4 GHz < f < 6 GHz
Correct answer is option 'A'. Can you explain this answer?
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To determine the range of frequencies over which single mode operation will occur in a rectangular waveguide filled with a dielectric, we can use the cutoff frequency formula. The cutoff frequency is the frequency below which the waveguide can support only one mode of propagation.
The cutoff frequency for the dominant mode in a rectangular waveguide is given by the formula:
fc = (c/2π) * sqrt((m/a)^2 + (n/b)^2)
Where:
- fc is the cutoff frequency
- c is the speed of light in a vacuum (3 x 10^8 m/s)
- m and n are the mode numbers (m is the number of half-wavelength variations along the x-axis, and n is the number of half-wavelength variations along the y-axis)
- a and b are the dimensions of the waveguide cross-section (in this case, a = 6 cm and b = 4 cm)
To determine the range of frequencies over which single mode operation will occur, we need to find the cutoff frequency for the next higher mode (m+1, n) and the next higher mode (m, n+1). The range of frequencies between these two cutoff frequencies will be the range for single mode operation.
Calculation:
- For the dominant mode (m=1, n=0):
- fc1 = (c/2π) * sqrt((1/6)^2 + (0/4)^2) = 1.92 GHz
- For the next higher mode (m=2, n=0):
- fc2 = (c/2π) * sqrt((2/6)^2 + (0/4)^2) = 3.84 GHz
- For the next higher mode (m=1, n=1):
- fc3 = (c/2π) * sqrt((1/6)^2 + (1/4)^2) = 4.32 GHz
Therefore, the range of frequencies over which single mode operation will occur is 1.92 GHz to 4.32 GHz.
Since option 'A' (2.24 GHz to 3.33 GHz) falls within this range, it is the correct answer.
The cutoff frequency for the dominant mode in a rectangular waveguide is given by the formula:
fc = (c/2π) * sqrt((m/a)^2 + (n/b)^2)
Where:
- fc is the cutoff frequency
- c is the speed of light in a vacuum (3 x 10^8 m/s)
- m and n are the mode numbers (m is the number of half-wavelength variations along the x-axis, and n is the number of half-wavelength variations along the y-axis)
- a and b are the dimensions of the waveguide cross-section (in this case, a = 6 cm and b = 4 cm)
To determine the range of frequencies over which single mode operation will occur, we need to find the cutoff frequency for the next higher mode (m+1, n) and the next higher mode (m, n+1). The range of frequencies between these two cutoff frequencies will be the range for single mode operation.
Calculation:
- For the dominant mode (m=1, n=0):
- fc1 = (c/2π) * sqrt((1/6)^2 + (0/4)^2) = 1.92 GHz
- For the next higher mode (m=2, n=0):
- fc2 = (c/2π) * sqrt((2/6)^2 + (0/4)^2) = 3.84 GHz
- For the next higher mode (m=1, n=1):
- fc3 = (c/2π) * sqrt((1/6)^2 + (1/4)^2) = 4.32 GHz
Therefore, the range of frequencies over which single mode operation will occur is 1.92 GHz to 4.32 GHz.
Since option 'A' (2.24 GHz to 3.33 GHz) falls within this range, it is the correct answer.
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A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer?.
A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refractive index 1.25Que: The range of frequencies over which single mode operation will occur isa)2.24 GHz < f <3.33 GHzb)2 GHz < f < 3 GHzc)4.48 GHz < f < 7.70 GHzd)4 GHz < f < 6 GHzCorrect answer is option 'A'. Can you explain this answer?.
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