Question

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 (in Np/m) is
1. 500
2. 5
3. 0.014
4. 0.002

Answer 1

Correct Answer - Option 4 : 0.002

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

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