*Question G9C09:
In free space, how does the gain of two three-element, horizontally polarized Yagi antennas spaced vertically 1/2 wavelength apart typically compare to the gain of a single three-element Yagi?*  

*Correct Answer is  B: Approximately 3 dB higher*  

### AI Response: (may contain errors)  

To understand the gain comparison between two vertically spaced three-element Yagi antennas and a single three-element Yagi, we need to consider how antenna gain works in relation to spacing.

### Correct Answer Explanation:
- **Correct Answer: Approximately 3 dB higher**  
  When two identical antennas are spaced vertically by a distance of 1/2 wavelength, they can combine their gains effectively. The gain from two antennas in this configuration can be approximated using the formula for combining gains:

  $$ G_{total} = G_1 + G_2 + 10 \log_{10}(N) $$

  where:
  - $G_1$ and $G_2$ are the gains of the individual antennas (in dB),
  - $N$ is the number of antennas (in this case, $N = 2$).

  Since both antennas have the same gain, the formula simplifies to:

  $$ G_{total} = G + G + 10 \log_{10}(2) $$

  The term $10 \log_{10}(2)$ is approximately 3 dB. Therefore, the total gain of the two antennas is approximately 3 dB higher than that of a single antenna.

### Incorrect Answer Explanations:
- **A: Approximately 1.5 dB higher**  
  This value does not accurately reflect the gain increase from two antennas. The gain increase from combining antennas is more significant than 1.5 dB.

- **C: Approximately 6 dB higher**  
  A 6 dB increase would imply a doubling of power, which is not the case with two antennas spaced 1/2 wavelength apart. The gain increase is limited to about 3 dB due to the nature of combining antennas.

- **D: Approximately 9 dB higher**  
  A 9 dB increase would suggest a tripling of power, which is not achievable with just two antennas. The maximum gain increase from two antennas in this configuration is capped at around 3 dB.

### Summary:
- The gain of two vertically spaced three-element Yagi antennas is approximately 3 dB higher than a single three-element Yagi due to the effective combination of their gains.
- The other choices are incorrect because they overestimate the gain increase based on the number of antennas and their spacing. 

This understanding is crucial for the Extra Class exam, as it highlights the principles of antenna gain and the effects of spacing on performance.