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ESE Electronics 2019: Official Paper

Option 3 : 50 Ω

CT 1: Determinants and Matrices

2969

10 Questions
10 Marks
12 Mins

__Concept__:

Characteristic Impedance of a transmission line is defined as:

\(Z_0=\sqrt{{\frac{R+jω L}{G+jω C}}}\) --- (1)

R = Resistance per unit length of the line

G = Conductance per unit length of the line

L = Inductance per unit length of the line

C = Capacitance per unit length of the line

For a lossless line,

R = G = 0

Using Equation (1), the characteristic impedance of the lossless transmission line will become:

\(Z_0=\sqrt{{\frac{ L}{C}}}\)

__Calculation__:

With L = 0.25 μH/m and C = 100 pF/m, we get:

\(Z_0=\sqrt{{\frac{0.25\times 10^{-6}}{100\times 10^{-12}}}}\)

\(Z_0=\sqrt{2500}\)

**Z _{0} = 50 Ω**