Question E9F01:
What is the velocity factor of a transmission line?  

Choices:  
A: The ratio of its characteristic impedance to its termination impedance  
B: The ratio of its termination impedance to its characteristic impedance  
C: The velocity of a wave in the transmission line multiplied by the velocity of light in a vacuum  
D: The velocity of a wave in the transmission line divided by the velocity of light in a vacuum    

Correct Answer is  D: The velocity of a wave in the transmission line divided by the velocity of light in a vacuum  

Correct answer: D — The velocity of a wave in the transmission line divided by the velocity of light in a vacuum.

Why D is correct:
- Velocity factor (VF) is defined as the ratio of the wave’s phase velocity in the line to the speed of light in vacuum:
  $$VF = \frac{v_p}{c}$$
- Because the dielectric in the line slows the wave, $VF < 1$ for real transmission lines.

Why the other choices are incorrect:
- A and B: These describe ratios of impedances (characteristic vs termination), which relate to matching and reflections, not wave speed. VF is not an impedance ratio.
- C: Multiplying velocities is dimensionally incorrect. VF is a dimensionless ratio, not a product of speeds.

Useful formulas and rules of thumb:
- Phase velocity in a transmission line:
  $$v_p = \frac{1}{\sqrt{L' C'}}$$
  where $L'$ and $C'$ are inductance and capacitance per unit length.
- Characteristic impedance (for context):
  $$Z_0 = \sqrt{\frac{L'}{C'}}$$
- For non-magnetic dielectrics ($\mu_r \approx 1$):
  $$VF \approx \frac{1}{\sqrt{\epsilon_r}}$$
- Wavelength in the line is shorter by VF:
  $$\lambda_{\text{line}} = VF \cdot \lambda_0$$
- Quarter-wave physical length in a line:
  $$\ell_{1/4} = VF \cdot \frac{c}{4f}$$

Typical VFs:
- Solid polyethylene coax: ≈ 0.66
- Foam PE coax: ≈ 0.78–0.85
- Open-wire/twin-lead: ≈ 0.90–0.98