A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω /m. If the line is distortionless, the attenuation constant is

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This question was previously asked in

UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper

Answer 1

Concept:

For distortionless transmission line, we have

\(LG = RC\)

Characteristic impedance:

\({Z_o} = \sqrt {\frac{L}{C}} = \sqrt {\frac{R}{G}} \) ---(1)

Attenuation constant:

\(\alpha = \sqrt {RG} \) --- (2)

Calculation:

From equation (1) and (2), we get

\(\alpha = \sqrt R \frac{{\sqrt R }}{{{Z_o}}} = \frac{R}{{{Z_o}}}\;\)

Putting the values of R and Z0, we get

\( \Rightarrow \alpha = \frac{{0.1}}{{50}} = 0.002\;Np/m\)