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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 guide support both TE10 and TE01 modes and no other, is
- a)3.35 GHz < f < GHz
- b)2.5 GHz < f < 3.6 GHz
- c)3 GHz < f < 3.6 GHz
- d)2.5 GHz < f < 4.02 GHz
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refr...
3 GHz < f < 3.6 GHz
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A 6 cm x 4 cm rectangular wave guide is filled with dielectric of refr...
Given Data:
- Dimensions of the rectangular waveguide: 6 cm x 4 cm
- Refractive index of the dielectric: 1.25
TE10 and TE01 Modes:
TE10 mode corresponds to the lowest order transverse electric mode where the electric field is perpendicular to the longer dimension of the waveguide. TE01 mode corresponds to the lowest order transverse electric mode where the electric field is perpendicular to the shorter dimension of the waveguide.
Finding the Cutoff Frequencies:
The cutoff frequency for TE10 mode is given by:
$$ f_{c1} = \frac{c}{2a} = \frac{c}{2(6 cm)} $$
The cutoff frequency for TE01 mode is given by:
$$ f_{c2} = \frac{c}{2b} = \frac{c}{2(4 cm)} $$
where c is the speed of light in free space.
Calculating the Cutoff Frequencies:
Substitute the values of the dimensions of the waveguide and speed of light in the above equations to find the cutoff frequencies for TE10 and TE01 modes.
Considering the Refractive Index:
When the waveguide is filled with a dielectric material, the cutoff frequencies are reduced by the square root of the refractive index of the dielectric material.
$$ f_{c1}^{'} = \frac{f_{c1}}{\sqrt{n}} $$
$$ f_{c2}^{'} = \frac{f_{c2}}{\sqrt{n}} $$
where n is the refractive index of the dielectric.
Range of Frequencies:
The range of frequencies over which the waveguide supports both TE10 and TE01 modes and no other modes is between the cutoff frequencies for TE10 and TE01 modes after considering the refractive index of the dielectric material.
Therefore, the range of frequencies is 3 GHz to 3.6 GHz.
- Dimensions of the rectangular waveguide: 6 cm x 4 cm
- Refractive index of the dielectric: 1.25
TE10 and TE01 Modes:
TE10 mode corresponds to the lowest order transverse electric mode where the electric field is perpendicular to the longer dimension of the waveguide. TE01 mode corresponds to the lowest order transverse electric mode where the electric field is perpendicular to the shorter dimension of the waveguide.
Finding the Cutoff Frequencies:
The cutoff frequency for TE10 mode is given by:
$$ f_{c1} = \frac{c}{2a} = \frac{c}{2(6 cm)} $$
The cutoff frequency for TE01 mode is given by:
$$ f_{c2} = \frac{c}{2b} = \frac{c}{2(4 cm)} $$
where c is the speed of light in free space.
Calculating the Cutoff Frequencies:
Substitute the values of the dimensions of the waveguide and speed of light in the above equations to find the cutoff frequencies for TE10 and TE01 modes.
Considering the Refractive Index:
When the waveguide is filled with a dielectric material, the cutoff frequencies are reduced by the square root of the refractive index of the dielectric material.
$$ f_{c1}^{'} = \frac{f_{c1}}{\sqrt{n}} $$
$$ f_{c2}^{'} = \frac{f_{c2}}{\sqrt{n}} $$
where n is the refractive index of the dielectric.
Range of Frequencies:
The range of frequencies over which the waveguide supports both TE10 and TE01 modes and no other modes is between the cutoff frequencies for TE10 and TE01 modes after considering the refractive index of the dielectric material.
Therefore, the range of frequencies is 3 GHz to 3.6 GHz.
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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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. Can you explain this answer?.
Solutions 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 guide support both TE10 and TE01 modes and no other,isa)3.35 GHz < f < GHzb)2.5 GHz < f < 3.6 GHzc)3 GHz < f < 3.6 GHzd)2.5 GHz < f <4.02 GHzCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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