*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)  

When two antennas are combined in a specific configuration, such as stacking them vertically, their combined gain can be increased compared to a single antenna. Here's how it works for this question:

1. **Correct Answer Explanation (B: Approximately 3 dB higher):**
   - When two identical antennas are spaced and phased correctly, their combined gain is typically increased by about 3 dB. This is because the power from each antenna adds constructively, effectively doubling the power in the desired direction.
   - In decibels, doubling the power results in a gain increase of 3 dB. This is a fundamental property of logarithmic scales used in measuring power gain.

2. **Why Other Choices Are Incorrect:**
   - **A: Approximately 1.5 dB higher**: A 1.5 dB increase would imply less than doubling the power, which is not the case when two antennas are combined correctly.
   - **C: Approximately 6 dB higher**: A 6 dB increase would imply quadrupling the power, which would require four antennas, not just two.
   - **D: Approximately 9 dB higher**: A 9 dB increase would imply an eightfold increase in power, which is not achievable with just two antennas.

3. **Useful Formula:**
   - The general rule of thumb for combining two identical antennas is:
     $$ \text{Gain increase} = 10 \log_{10}(2) \approx 3 \text{ dB} $$

This rule applies when the antennas are properly spaced and phased, as in the case of the two three-element Yagi antennas spaced vertically 1/2 wavelength apart. This configuration allows the signals to add constructively, resulting in the 3 dB gain increase.