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A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectively
- a)0.212 ∠48.55°, 1.538
- b)0.486 ∠68.4°, 2.628
- c)0.486 ∠41.45°, 2.682
- d)0.212 ∠68.4°, 1.538
Correct answer is option 'A'. Can you explain this answer?
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A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage...
Given information:
- Coaxial cable impedance (Zc) = 60 Ω
- Dipole antenna impedance (Za) = 75 + j25 Ω
To find:
- Voltage reflection coefficient (Γ)
- Standing wave ratio (s)
1. Calculate the reflection coefficient (Γ):
The reflection coefficient is given by the formula:
Γ = (Za - Zc) / (Za + Zc)
Substituting the given values:
Γ = (75 + j25 - 60) / (75 + j25 + 60)
= (15 + j25) / (135 + j25)
= (15/160 + j25/160) / (135/160 + j25/160)
= (15 + j25) / (135 + j25)
To simplify the expression, we can multiply the numerator and denominator by the complex conjugate of the denominator:
Γ = [(15 + j25) / (135 + j25)] * [(135 - j25) / (135 - j25)]
= [(15 * 135 + j25 * 135 + j25 * 135 - j25 * j25) / (135 * 135 + j25 * 135 - j25 * 135 - j25 * j25)]
= [(15 * 135 + j50 * 135 + 25 * 135 + 25 * 25) / (135 * 135 + 25 * 25)]
= (2025 + j3375 + j3375 + 625) / (18225 + 625)
= (5025 + j6750) / 18850
= (2515 + j3375) / 9425
The magnitude of the reflection coefficient can be found using the formula:
|Γ| = sqrt(Re(Γ)^2 + Im(Γ)^2)
Substituting the values:
|Γ| = sqrt((2515/9425)^2 + (3375/9425)^2)
= sqrt(0.0676 + 0.1272)
= sqrt(0.1948)
= 0.441
The phase angle of the reflection coefficient can be found using the formula:
∠Γ = atan(Im(Γ) / Re(Γ))
Substituting the values:
∠Γ = atan(3375/2515)
= 53.6°
Therefore, Γ = 0.441 ∠53.6°
2. Calculate the standing wave ratio (s):
The standing wave ratio is given by the formula:
s = (1 + |Γ|) / (1 - |Γ|)
Substituting the value of |Γ|:
s = (1 + 0.441) / (1 - 0.441)
= 1.441 / 0.559
= 2.578
Therefore, the correct answer is option 'A': 0.441 ∠53.6°, 2.578
- Coaxial cable impedance (Zc) = 60 Ω
- Dipole antenna impedance (Za) = 75 + j25 Ω
To find:
- Voltage reflection coefficient (Γ)
- Standing wave ratio (s)
1. Calculate the reflection coefficient (Γ):
The reflection coefficient is given by the formula:
Γ = (Za - Zc) / (Za + Zc)
Substituting the given values:
Γ = (75 + j25 - 60) / (75 + j25 + 60)
= (15 + j25) / (135 + j25)
= (15/160 + j25/160) / (135/160 + j25/160)
= (15 + j25) / (135 + j25)
To simplify the expression, we can multiply the numerator and denominator by the complex conjugate of the denominator:
Γ = [(15 + j25) / (135 + j25)] * [(135 - j25) / (135 - j25)]
= [(15 * 135 + j25 * 135 + j25 * 135 - j25 * j25) / (135 * 135 + j25 * 135 - j25 * 135 - j25 * j25)]
= [(15 * 135 + j50 * 135 + 25 * 135 + 25 * 25) / (135 * 135 + 25 * 25)]
= (2025 + j3375 + j3375 + 625) / (18225 + 625)
= (5025 + j6750) / 18850
= (2515 + j3375) / 9425
The magnitude of the reflection coefficient can be found using the formula:
|Γ| = sqrt(Re(Γ)^2 + Im(Γ)^2)
Substituting the values:
|Γ| = sqrt((2515/9425)^2 + (3375/9425)^2)
= sqrt(0.0676 + 0.1272)
= sqrt(0.1948)
= 0.441
The phase angle of the reflection coefficient can be found using the formula:
∠Γ = atan(Im(Γ) / Re(Γ))
Substituting the values:
∠Γ = atan(3375/2515)
= 53.6°
Therefore, Γ = 0.441 ∠53.6°
2. Calculate the standing wave ratio (s):
The standing wave ratio is given by the formula:
s = (1 + |Γ|) / (1 - |Γ|)
Substituting the value of |Γ|:
s = (1 + 0.441) / (1 - 0.441)
= 1.441 / 0.559
= 2.578
Therefore, the correct answer is option 'A': 0.441 ∠53.6°, 2.578
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A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer?
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A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 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 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer?.
A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 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 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer?.
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A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A 60 Ω coaxial cable feeds a 75 + j 25Ω + dipole antenna. The voltage reflection coefficient Γ and standing wave ratio s are respectivelya)0.212 ∠48.55°, 1.538b)0.486 ∠68.4°, 2.628c)0.486 ∠41.45°, 2.682d)0.212 ∠68.4°, 1.538Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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