Question E4A11:
Which of the following can be measured with an antenna analyzer?  

Choices:  
A: Velocity factor  
B: Cable length  
C: Resonant frequency of a tuned circuit  
D: All these choices are correct    

Correct Answer is  D: All these choices are correct  

To see why “All these choices are correct” is the right answer, remember what an antenna analyzer does: it measures complex impedance (R + jX), SWR/return loss, and often phase versus frequency. From those, you can determine resonance, electrical length, cable velocity factor, and even length.

Why D is correct (All these choices are correct):
- Antenna analyzers can:
  - Sweep frequency and find where reactance crosses zero (resonance).
  - Identify quarter/half-wave resonances of a transmission line to compute length and/or velocity factor.
  - Some models also include TDR-like functions to estimate cable length directly.

Why A, B, and C aren’t the best single answers:
- Each of A–C is true by itself, but the analyzer can do all of them. Therefore, the most complete answer is D.

How each item is measured:
- Velocity factor (VF):
  - Find a resonance of a known-length coax (open or short at the far end). Use quarter- or half-wave conditions to solve for VF.
  - Using a half-wave resonance:
    $$L \approx \frac{\lambda_{\text{line}}}{2} = \frac{VF \cdot c}{2f} \quad \Rightarrow \quad VF \approx \frac{2Lf}{c}$$
  - Using a quarter-wave resonance:
    $$L \approx \frac{\lambda_{\text{line}}}{4} = \frac{VF \cdot c}{4f} \quad \Rightarrow \quad VF \approx \frac{4Lf}{c}$$

- Cable length (L):
  - If VF is known (datasheet), find a quarter- or half-wave resonance frequency and solve for L.
  - Half-wave:
    $$L \approx \frac{VF \cdot c}{2f}$$
  - Quarter-wave:
    $$L \approx \frac{VF \cdot c}{4f}$$
  - Many analyzers also estimate length via TDR mode.

- Resonant frequency of a tuned circuit:
  - Connect the analyzer across the LC network and sweep frequency. Resonance is where reactance crosses zero and impedance is purely resistive:
    $$f_0 \approx \frac{1}{2\pi\sqrt{LC}}$$

Useful formulas and rules of thumb:
- Speed of light: $$c \approx 3.00 \times 10^8\ \text{m/s}$$
- Free-space wavelength (meters): $$\lambda \approx \frac{300}{f_{\text{MHz}}}$$
- In a line: $$\lambda_{\text{line}} = VF \cdot \lambda = \frac{VF \cdot c}{f}$$
- Impedance repeats every half-wavelength on a transmission line; strong series/parallel resonance effects occur at quarter-wavelengths for open/shorted stubs.