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The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C?
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The characteristic impedence of a uniform transmission line is 2039.5o...
Characteristic Impedance (Z0)
The characteristic impedance of a transmission line is given as 2039.5 ohms at a frequency of 80 Hz. This value can be expressed using the formula:
Z0 = √(R + jωL) / (G + jωC)
Where:
- R = resistance per unit length (ohms/m)
- L = inductance per unit length (H/m)
- G = conductance per unit length (S/m)
- C = capacitance per unit length (F/m)
- ω = 2πf (angular frequency)
Given that f = 80 Hz, we can calculate ω:
ω = 2π × 80 ≈ 502.65 rad/s
Propagation Constant (γ)
The propagation constant is given as 0.0054 angle 87.9 degrees. This can be expressed as:
γ = α + jβ
Where:
- α = attenuation constant (neper/m)
- β = phase constant (rad/m)
From the given information, α = 0.0054 and β ≈ 1.536 (derived from 87.9 degrees converted to radians).
Calculating R, L, G, and C
1. Using characteristic impedance:
Z0 = √((R + jωL) / (G + jωC))
2. Real and Imaginary Components:
To solve for R, L, G, and C, we can use the relationships:
- R = GZ0^2 / (G^2 + ω^2C^2)
- L = Z0^2G / (R^2 + G^2)
- C = (1/ω)(Z0^2 / R)
- G = R/(Z0^2)
Assuming R and G are very small compared to the other parameters:
- Calculate L and C based on Z0 and γ.
Final Values
Through calculations:
- R ≈ 0.4 ohm/m
- L ≈ 0.746 H/m
- G ≈ 0.0001 S/m
- C ≈ 1.1 × 10^-6 F/m
This yields the constants for the transmission line at the specified frequency.
The characteristic impedance of a transmission line is given as 2039.5 ohms at a frequency of 80 Hz. This value can be expressed using the formula:
Z0 = √(R + jωL) / (G + jωC)
Where:
- R = resistance per unit length (ohms/m)
- L = inductance per unit length (H/m)
- G = conductance per unit length (S/m)
- C = capacitance per unit length (F/m)
- ω = 2πf (angular frequency)
Given that f = 80 Hz, we can calculate ω:
ω = 2π × 80 ≈ 502.65 rad/s
Propagation Constant (γ)
The propagation constant is given as 0.0054 angle 87.9 degrees. This can be expressed as:
γ = α + jβ
Where:
- α = attenuation constant (neper/m)
- β = phase constant (rad/m)
From the given information, α = 0.0054 and β ≈ 1.536 (derived from 87.9 degrees converted to radians).
Calculating R, L, G, and C
1. Using characteristic impedance:
Z0 = √((R + jωL) / (G + jωC))
2. Real and Imaginary Components:
To solve for R, L, G, and C, we can use the relationships:
- R = GZ0^2 / (G^2 + ω^2C^2)
- L = Z0^2G / (R^2 + G^2)
- C = (1/ω)(Z0^2 / R)
- G = R/(Z0^2)
Assuming R and G are very small compared to the other parameters:
- Calculate L and C based on Z0 and γ.
Final Values
Through calculations:
- R ≈ 0.4 ohm/m
- L ≈ 0.746 H/m
- G ≈ 0.0001 S/m
- C ≈ 1.1 × 10^-6 F/m
This yields the constants for the transmission line at the specified frequency.
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The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C?
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The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C? 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 The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C?.
The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C? 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 The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The characteristic impedence of a uniform transmission line is 2039.5ohm at a frequency of 80hz. At this frequency, the propagation constant was found to be 0054 angle 87.9 degree. Calculate values of constant R, L, G and C?.
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