Question

In a lossless transmission line with a capacitance of 30 pF/m and a velocity of propagation of 2.5×10 m/s at 10 MHz, find the phase constant and the inductance of the line.

a) Phase constant
b) Inductance
c) Characteristic impedance
d) None of the above

Answer 1

The phase constant of the transmission line is 0.251 rad/m and the inductance of the line is 1.087 μH.

Step-by-step explanation:

To find the phase constant and inductance of the transmission line, we can use the following formulas:

Phase constant (β) = 2πf/v

Inductance (L) = (1/β²) / (Cω²)

Given:

Capacitance (C) = 30 pF/m

Velocity of propagation (v) = 2.5 × 10⁸ m/s

Frequency (f) = 10 MHz = 10 × 10⁶ Hz

Using the given values, we can calculate:

Phase constant (β) = 2π(10 × 10⁶)/(2.5 × 10⁸) = 0.251 rad/m

Inductance (L) = (1/(0.251)²) / (30 × 10⁻¹² (2π(10 × 10⁶))²) = 1.087 μH

Therefore, the phase constant is 0.251 rad/m and the inductance of the line is 1.087 μH.