Question

Surge impedance of a lossless transmission line is (if \( L \) = inductance/m and \( C \) = capacitance/m):

• A. \( \sqrt{\frac{C}{L}} \)
• B. \( \sqrt{\frac{L}{C}} \)
• C. \( \frac{1}{\sqrt{LC}} \)
• D. \( \sqrt{LC} \)

Hint:

The surge impedance of a lossless transmission line is \( Z_0 = \sqrt{\frac{L}{C}} \). It plays a crucial role in impedance matching and wave propagation.

Answer 1

The Correct Option is B

Step 1: The characteristic impedance (or surge impedance) of a lossless transmission line is given by: \[ Z_0 = \sqrt{\frac{L}{C}} \] where:
- \( L \) is the inductance per unit length (H/m),
- \( C \) is the capacitance per unit length (F/m). 
Step 2: This formula is derived from the transmission line equation, considering a lossless line where resistance (\( R \)) and conductance (\( G \)) are negligible. 
Step 3: Evaluating options:
- (A) Incorrect: The correct formula has \( L \) in the numerator, not \( C \).
- (B) Correct: \( \sqrt{\frac{L}{C}} \) is the correct surge impedance expression.
- (C) Incorrect: \( \frac{1}{\sqrt{LC}} \) is incorrect.
- (D) Incorrect: \( \sqrt{LC} \) does not represent surge impedance.