Question E9A10:
Which of the following improves the efficiency of a ground-mounted quarter-wave vertical antenna?  

Choices:  
A: Installing a ground radial system  
B: Isolating the coax shield from ground  
C: Shortening the radiating element  
D: All these choices are correct    

Correct Answer is  A: Installing a ground radial system  

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Correct answer: A — Installing a ground radial system

1) Why A is correct
- A ground-mounted quarter-wave vertical returns RF current through the earth. Soil is lossy, so without radials much of the power is dissipated as heat in the ground.
- A radial system provides a low-resistance return path, reducing ground loss and increasing efficiency.
- Antenna efficiency:
  $$\eta = \frac{R_{\text{rad}}}{R_{\text{rad}} + R_{\text{loss}}}$$
  Adding radials reduces $R_{\text{loss}}$, so $\eta$ increases.
- For a quarter-wave vertical over perfect ground, $R_{\text{rad}} \approx 36.5\,\Omega$. Real ground adds series loss; radials push the feedpoint resistance closer to this ideal value.

2) Why the others are incorrect
- B: Isolating the coax shield from ground  
  This does not reduce ground loss. In fact, the coax shield should be bonded to the radial system at the feedpoint. “Isolation” can increase common-mode currents and does not improve radiation efficiency. A common-mode choke may clean up pattern/RFI, but it doesn’t address ground loss.
- C: Shortening the radiating element  
  A shorter vertical has lower radiation resistance and requires loading (e.g., a coil), which adds loss. Lower $R_{\text{rad}}$ and added loading resistance both reduce $\eta$. For a short monopole of height $h$:
  $$R_{\text{rad}} \approx 40\pi^2 \left(\frac{h}{\lambda}\right)^2 \;\Omega$$
  So shortening reduces $R_{\text{rad}}$ roughly with the square of height, worsening efficiency for the same ground loss.
- D: All these choices are correct  
  False because B and C do not improve efficiency.

3) Useful formulas and rules of thumb
- Efficiency:
  $$\eta = \frac{R_{\text{rad}}}{R_{\text{rad}} + R_{\text{loss}}}$$
- Quarter-wave vertical over perfect ground:
  $$R_{\text{rad}} \approx 36.5\,\Omega$$
- Short (loaded) vertical:
  $$R_{\text{rad}} \approx 40\pi^2 \left(\frac{h}{\lambda}\right)^2 \;\Omega$$
- Radial system tips:
  - More and longer radials reduce $R_{\text{loss}}$.
  - Rule of thumb: 16–32 radials of length ≈ $0.25\lambda$ give good efficiency; 60+ is excellent. If many radials are used, shorter lengths still help.
  - Lay radials on or just under the ground; bond coax shield to the radial hub at the base.

Bottom line: Only a ground radial system directly improves the efficiency of a ground-mounted quarter-wave vertical.