Correct Answer - Option 3 : R ≪ ωL, G ≪ ωC
Concept:
Propagation constant for the transmission line is given by:
\(\gamma = \alpha + j\beta = \sqrt {\left( {R + j\omega L} \right)\left( {G + j\omega C} \right)} \)
For lossless line α = 0
If R ≪ ωL and a ≪ ωC, the propagation constant becomes:
\(\gamma = \sqrt {\left( {j\omega L} \right)\left( {j\omega C} \right)} \)
\(\gamma = j\omega \sqrt {LC} \) ---(1)
Comparing equation (1) with α + jβ:
α = 0. Hence the line is lossless.
Important points:
A transmission line is also lossless when:
R = 0 and G = 0.
\(\gamma = j\omega \sqrt {LC} \)
Here also α = 0 and the line is lossless
∴ The conditions for lossless line includes:
1) R = 0; G = 0, or
2) ωL ≫ & ωC ≫ G
