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A transmission line whose characteristic impedance is purely resistive
- a)must be lossless line
- b)must be a distortionless line
- c)may not be a lossless line
- d)may not be a distortionless line
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A transmission line whose characteristic impedance is purely resistive...
If the transmission line is to have neither frequency nor delay distortion, then α (attenuation constant) and velocity of propagation cannot be functions of frequency.
V = ω/β β
must be a direct function of frequency to achieve this condition
LG = CR
L/C = R/G
z0 = √((R + jωL)/(G + jωC))
For a lossless line,
z0 = √(L/C)
α = √(RG) = 0 for R = 0, G = 0
β = ω√(LC)
A loss less line is always a distortion less line.
V = ω/β β
must be a direct function of frequency to achieve this condition
LG = CR
L/C = R/G
z0 = √((R + jωL)/(G + jωC))
For a lossless line,
z0 = √(L/C)
α = √(RG) = 0 for R = 0, G = 0
β = ω√(LC)
A loss less line is always a distortion less line.
Most Upvoted Answer
A transmission line whose characteristic impedance is purely resistive...
Characteristic Impedance of a Transmission Line
A transmission line is a medium that carries electrical signals from one point to another. It is used in various applications such as telecommunications, power distribution, and data transmission. The characteristic impedance of a transmission line is an important parameter that determines the behavior of the line. It is defined as the ratio of voltage to current in a wave traveling on the line.
Purely Resistive Characteristic Impedance
When the characteristic impedance of a transmission line is purely resistive, it means that the line has no reactive components such as capacitance or inductance. In such a case, the characteristic impedance is equal to the resistance of the line. This condition is also known as a matched condition, which means that the load impedance is equal to the characteristic impedance of the line.
Lossless and Distortionless Line
A lossless transmission line is one that has no power loss due to resistance or leakage. This means that the power delivered to the load at the end of the line is the same as the power input at the source. A distortionless transmission line is one that does not introduce any distortion in the signal being transmitted. This means that the signal at the output of the line is a replica of the signal at the input.
Characteristic Impedance and Lossless Line
When the characteristic impedance of a transmission line is purely resistive, it implies that the line is lossless. This is because a purely resistive line has no reactive components that can cause power loss. Therefore, the power delivered to the load at the end of the line is the same as the power input at the source, making it a lossless line.
Conclusion
In conclusion, a transmission line whose characteristic impedance is purely resistive must be a lossless line because it has no reactive components that can cause power loss.
A transmission line is a medium that carries electrical signals from one point to another. It is used in various applications such as telecommunications, power distribution, and data transmission. The characteristic impedance of a transmission line is an important parameter that determines the behavior of the line. It is defined as the ratio of voltage to current in a wave traveling on the line.
Purely Resistive Characteristic Impedance
When the characteristic impedance of a transmission line is purely resistive, it means that the line has no reactive components such as capacitance or inductance. In such a case, the characteristic impedance is equal to the resistance of the line. This condition is also known as a matched condition, which means that the load impedance is equal to the characteristic impedance of the line.
Lossless and Distortionless Line
A lossless transmission line is one that has no power loss due to resistance or leakage. This means that the power delivered to the load at the end of the line is the same as the power input at the source. A distortionless transmission line is one that does not introduce any distortion in the signal being transmitted. This means that the signal at the output of the line is a replica of the signal at the input.
Characteristic Impedance and Lossless Line
When the characteristic impedance of a transmission line is purely resistive, it implies that the line is lossless. This is because a purely resistive line has no reactive components that can cause power loss. Therefore, the power delivered to the load at the end of the line is the same as the power input at the source, making it a lossless line.
Conclusion
In conclusion, a transmission line whose characteristic impedance is purely resistive must be a lossless line because it has no reactive components that can cause power loss.
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