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The constants of a transmission line are R=6Ω/km, L=2.2 mH/Km.G=0.25×10-6 ℧/km, C=0.005×10-6 F/km. Determine the characteristics impedance, propagation constant and attenuation constant at 1 KHZ.
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Answer : $Z=R+j\omega L =6+j2 \pi \times 1000\times 2.2 \times 10^{-3}=15.07\measuredangle66.54 ^0 \Omega /km$

$Y=G+j\omega C=0.25 \times 10^{-6}+j2\pi\times 1000\times 0.005\times 10^{-6}=3.14 \times 10^{-5}\measuredangle 89.54^0\mho/km$

Characteristic impedance $Z_0=\sqrt{\dfrac{Z}{Y}}=\sqrt{\dfrac{15.07\measuredangle66.54^0}{3.14\times 10^{-5}\measuredangle89.54^0}}=692.77\measuredangle-11.5^0\Omega $

Propogation constant $\gamma=\sqrt{ZY}=\sqrt{15.07\measuredangle66.54^0\times 3.14 \times 10^{-5} \measuredangle 89.54^0}=0.022\measuredangle78.014^0/km=(4.55 \times 10^{-3}+j0.022)/km$

Since $\gamma=\alpha+j\beta$

where , $\alpha =$attenuation constant

$\beta=$phase shift

Now, attenuation constant at 1kHz $\alpha =4.55 \times 10^{-3}neper/km$.

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