Question E9G11:
In what units are the wavelength scales on a Smith chart calibrated?  

Choices:  
A: In fractions of transmission line electrical frequency  
B: In fractions of transmission line electrical wavelength  
C: In fractions of antenna electrical wavelength  
D: In fractions of antenna electrical frequency    

Correct Answer is  B: In fractions of transmission line electrical wavelength  

Correct answer: B — In fractions of transmission line electrical wavelength

Why B is correct:
- The outer scales of a Smith chart are calibrated in distance along a transmission line, expressed as a fraction of the line’s electrical wavelength.
- This “electrical wavelength” depends on the line’s propagation velocity (velocity factor), not free-space wavelength.
- The scale typically reads in wavelengths toward the generator (clockwise) and toward the load (counterclockwise), and repeats every $0.5\,\lambda$ due to periodicity.

Why the others are incorrect:
- A: Frequency is not the unit on the rim scales; the chart’s periphery measures distance (phase) along the line, not frequency.
- C: It’s not in terms of the antenna’s wavelength; it’s the transmission line’s electrical wavelength, which can differ due to the dielectric (velocity factor).
- D: Same issue—frequency of the antenna is not what’s shown; the Smith chart rim shows fractions of the line’s wavelength.

Useful formulas and tips:
- Free-space wavelength:
  $$\lambda_0 = \frac{c}{f}$$
- Line velocity factor and line wavelength:
  $$\lambda_{\text{line}} = VF \cdot \lambda_0 = \frac{v_p}{f}$$
  where $VF = v_p/c$.
- Electrical length of a line section:
  $$\theta\ (\text{degrees}) = 360^\circ \cdot \frac{\ell}{\lambda_{\text{line}}}$$
- On the Smith chart, moving along a constant-SWR circle:
  - Clockwise: toward generator
  - Counterclockwise: toward load
  - Impedance patterns repeat every $0.5\,\lambda_{\text{line}}$.