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In a Loss-Less transmission line, for a λ /8 long short circuit section, the input impedance will be:
1. Inductive
2. Infinite
3. Capacitive
4. Zero

1 Answer

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Best answer
Correct Answer - Option 1 : Inductive

Concept:

The input impedance of a transmission line is given by:

\({Z_{in}} = {Z_o}\frac{{\left( {{Z_L} + j{Z_0}tanβ l} \right)}}{{\left( {{Z_0} + j{Z_L}tanβ l} \right)}}\)  ---(1)

Z0 = Characteristic impedance

ZL = Load impedance

Application:

For l = λ/8

\(β l=\frac{2\pi}{\lambda}\times \frac{\lambda}{8}\)

\(\beta l=\frac{\pi}{4}\)

Putting this Equation (1), we get:

\({Z_{in}} = {Z_o}\frac{{\left( {{Z_L} + j{Z_0}} \right)}}{{\left( {{Z_0} + j{Z_L}} \right)}}\)

For short circuit load (ZL= 0), the input impedance becomes:

\({Z_{in}} = {Z_o}\frac{{\left( {{0} + j{Z_0}} \right)}}{{\left( {{Z_0} + j{0}} \right)}}\)

\({Z_{in}} = j{Z_o}\)

Since Impedance has a positive imaginary part, the transmission line behaves as an inductive Transmission Line.

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