*Question E9B01:
What is the 3 dB beamwidth of the antenna radiation pattern shown in Figure E9-1?*  

*Correct Answer is  B: 50 degrees*  

### AI Response: (may contain errors)  

To determine the 3 dB beamwidth of an antenna radiation pattern, we need to understand what the 3 dB point represents. The 3 dB beamwidth is the angle between the points where the antenna gain drops to half its maximum value, which corresponds to a decrease of 3 dB in power.

### Explanation of the Correct Answer (50 degrees):
- The correct answer is **50 degrees** because this is the angle where the gain of the antenna is reduced to half of its peak value. This is a common characteristic of many antenna designs, particularly directional antennas, where the beamwidth is specified in degrees.

### Why the Other Choices are Incorrect:
- **A: 75 degrees**: This value is too wide for typical antennas with a focused radiation pattern. A 75-degree beamwidth would indicate a less directional antenna.
  
- **C: 25 degrees**: This value is too narrow for the antenna shown in the figure. A 25-degree beamwidth would suggest a highly directional antenna, which is not the case here.
  
- **D: 30 degrees**: While this is a more reasonable value than 25 degrees, it is still narrower than the 50 degrees indicated by the figure. 

### Useful Formulas and Rules of Thumb:
- The 3 dB beamwidth can often be estimated from the antenna's design and is typically provided in the specifications. For many antennas, the beamwidth can be approximated as:
  
$$
\text{Beamwidth} \approx \frac{70}{\text{Gain (dBi)}}
$$

- This formula gives a rough estimate of the beamwidth in degrees based on the gain of the antenna. Higher gain antennas tend to have narrower beamwidths.

In summary, the 3 dB beamwidth of 50 degrees is consistent with the expected performance of the antenna shown in the figure, while the other options do not align with typical antenna characteristics.