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Question 9.1: A lossless transmission line has a characteristic impedance ......

A lossless transmission line has a characteristic impedance 100[Ω] . When it operates at a frequency 200[MHz], the phase constant is 5[rad/s] on the line. Determine the capacitance and inductance per unit length of the line.

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The phase constant is, from Eq. (9-23a),

\gamma = j\beta = j\omega \sqrt{LC}                      (propagation constant)                     (9-23a)

\beta = \omega \sqrt{LC} = 2\pi \times 2\times 10^{8} \sqrt{LC} = 5

The characteristic impedance is, from Eq. (9-23b),

Z_{o}= R_{o} = \sqrt{L / C}                      (characteristic resistance)                      (9-23b)

Z_{o} = \sqrt{L / C} = 100

The product of β and Z_{o} gives

2\pi \times 2\times 10^{8} L = 500

Thus

L = 0.40[μH/m]

C = 40[pF/m] .

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