Question E9F02:
Which of the following has the biggest effect on the velocity factor of a transmission line?  

Choices:  
A: The characteristic impedance  
B: The transmission line length  
C: The insulating dielectric material  
D: The center conductor resistivity    

Correct Answer is  C: The insulating dielectric material  

Correct answer: C — The insulating dielectric material

1) Why C is correct
- Velocity factor (VF) is the ratio of wave speed in the line to the speed of light. For TEM lines:
  $$v_p = \frac{1}{\sqrt{L' C'}} \quad\text{and}\quad Z_0 = \sqrt{\frac{L'}{C'}}$$
  In typical transmission lines, the permeability is near that of free space, so the dielectric mainly sets the capacitance per unit length. This gives:
  $$v_p \approx \frac{c}{\sqrt{\epsilon_{\text{eff}}}} \quad\Rightarrow\quad \text{VF} = \frac{v_p}{c} \approx \frac{1}{\sqrt{\epsilon_{\text{eff}}}}$$
- Changing the insulating dielectric (and thus its relative permittivity, $\,\epsilon_r\,$) strongly changes VF. Examples:
  - Solid polyethylene: VF ≈ 0.66
  - Foam PE: VF ≈ 0.78–0.85
  - Air dielectric: VF ≈ 0.95–1.00

2) Why the other choices are incorrect
- A: The characteristic impedance  
  - $Z_0$ depends on geometry and dielectric. You can change $Z_0$ by changing conductor dimensions while using the same dielectric, with little change in VF. VF is tied primarily to $\,\epsilon_{\text{eff}}\,$, not directly to $Z_0$.

- B: The transmission line length  
  - Length changes total delay, not the wave speed. VF is a material/structure property per unit length and does not depend on how long the line is.

- D: The center conductor resistivity  
  - Resistivity affects loss (attenuation) and heating, not phase velocity. It has negligible effect on VF in normal ham applications.

3) Useful formulas and rules of thumb
- Velocity factor:
  $$\text{VF} \approx \frac{1}{\sqrt{\epsilon_{\text{eff}}}}$$
- Wavelength in the line:
  $$\lambda_{\text{line}} = \text{VF} \cdot \lambda_0 = \text{VF} \cdot \frac{c}{f}$$
- Electrical length of a physical segment $L$:
  $$\theta\ (\text{degrees}) = 360^\circ \cdot \frac{L}{\lambda_{\text{line}}}$$

Rule of thumb: Pick the dielectric to get the VF you need; geometry mostly sets $Z_0$, not VF.