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Question

# Find $\alpha$ and $Z_{0}$ of a distortionless line whose $R^{\prime}=2 \Omega / \mathrm{m}$ and $G^{\prime}=2 \times 10^{-4} \mathrm{S} / \mathrm{m}$.

Solution

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From Problem 2.13, we know that

$\alpha = \sqrt{R'G'}.$

With $R' = 2\;\Omega/$m and $G' = 2\times10^{-4}$ S/m, we find

$\alpha = \sqrt{2\times2\times10^{-4}} = 0.02\;\mathrm{(Np/m)}.$

Again from Problem 2.13, we realize that

$Z_0 = \sqrt{\frac{L'}{C'}} = \sqrt{\frac{L'G'}{CG'}} = \sqrt{\frac{R'C'}{C'G'}} = \sqrt{\frac{R'}{G'}},$

where we used $R'C' = L'G'$ (the distortionless-line condition). Thus

$Z_0 = \sqrt{\frac{2}{2\times10^{-4}}} = 100\;(\Omega).$

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