Question E9A04:
Which of the following factors affect the feed point impedance of an antenna?  

Choices:  
A: Transmission line length  
B: Antenna height  
C: The settings of an antenna tuner at the transmitter  
D: The input power level    

Correct Answer is  B: Antenna height  

To understand feed point impedance, think “what the antenna itself measures right at its terminals.” That value depends on the antenna’s geometry and environment, not on what happens back at the transmitter.

Why B (Antenna height) is correct:
- Height above ground changes the antenna’s coupling to its “image” in the ground, which changes both radiation resistance and reactance at the feed point.
- As height (in wavelengths) changes, the reflected field from the ground adds in- or out-of-phase, altering the current distribution and thus the feed point impedance.
- Examples (typical values):
  - Half-wave dipole in free space: about $73\,\Omega$ (resistive).
  - Half-wave dipole low over ground (e.g., $0.1$–$0.2\,\lambda$ high): often closer to $50$–$60\,\Omega$.
  - Quarter-wave vertical over perfect ground: about $36.5\,\Omega$; poor ground raises the resistive part due to ground loss.

Why the other choices are incorrect:
- A: Transmission line length
  - Line length can transform the impedance seen at the shack but does not change the antenna’s actual feed point impedance. The line input impedance is
    $$Z_{\text{in}} = Z_0 \frac{Z_L + j Z_0 \tan(\beta \ell)}{Z_0 + j Z_L \tan(\beta \ell)}$$
    where $Z_L$ is the antenna feed point impedance. $Z_L$ itself is unchanged by line length.
- C: The settings of an antenna tuner at the transmitter
  - A tuner at the transmitter only matches the line to the transmitter. It does not change the impedance at the antenna terminals (and it doesn’t reduce SWR on the line). Only a matching network located at the antenna feed point would change the antenna’s feed point impedance.
- D: The input power level
  - In normal (linear) operation, antenna impedance is essentially independent of power. Only at extreme power levels causing heating, arcing, or material nonlinearity would it change—outside exam scope.

Useful formulas and rules of thumb:
- Antenna feed point impedance:
  $$Z_{\text{antenna}} = R_r + R_\ell + jX$$
  where $R_r$ is radiation resistance (set by geometry and environment), $R_\ell$ is loss resistance, and $X$ is reactance.
- Short dipole radiation resistance:
  $$R_r \approx 80\pi^2 \left(\frac{\ell}{\lambda}\right)^2$$
- Typical reference values:
  - Half-wave dipole (free space): $R_r \approx 73\,\Omega$
  - Quarter-wave monopole over perfect ground: $R_r \approx 36.5\,\Omega$
- Rule of thumb: Changing antenna height (in wavelengths) noticeably changes feed point impedance; transmission line length or a shack-side tuner only change what the transmitter “sees,” not the antenna’s own feed point impedance.