GATE EC 2018 Set 1 — Question 31
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Electromagnetics → Transmission Lines → Characteristic Impedance & Propagation
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Question
A lossy transmission line has resistance per unit length . The line is distortionless and has characteristic impedance of . The attenuation constant (in Np/m, correct to three decimal places) of the line is ________.
Correct answer
0.001 to 0.001
Solution
For a distortionless transmission line, the condition is , where is resistance per unit length, is capacitance per unit length, is conductance per unit length, and is inductance per unit length.The attenuation constant () for a transmission line is generally given by:
For a distortionless line (), the attenuation constant simplifies to:
We also know that for a distortionless line, the characteristic impedance () is given by:
From , we can write , which implies .Now substitute into the attenuation constant formula:
Given values:
Resistance per unit length,
Characteristic impedance, Calculate the attenuation constant:
Correct to three decimal places, the attenuation constant is 0.001 Np/m.The final answer is .
For a distortionless line (), the attenuation constant simplifies to:
We also know that for a distortionless line, the characteristic impedance () is given by:
From , we can write , which implies .Now substitute into the attenuation constant formula:
Given values:
Resistance per unit length,
Characteristic impedance, Calculate the attenuation constant:
Correct to three decimal places, the attenuation constant is 0.001 Np/m.The final answer is .
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