*Question E9C02:
What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase?*  

*Correct Answer is  A: Cardioid*  

### AI Response: (may contain errors)  

To understand the radiation pattern created by two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase, we need to analyze the configuration and the resulting pattern.

### Correct Answer: Cardioid

1. **Why the correct answer is correct:**
   - When two antennas are spaced 1/4-wavelength apart and fed 90 degrees out of phase, they create a radiation pattern known as a cardioid. 
   - The cardioid pattern has a single lobe in one direction and a null in the opposite direction. This is due to the phase difference causing constructive interference in one direction and destructive interference in the opposite direction.

### Why the other choices are incorrect:

2. **Choice A: Cardioid**
   - This is the correct answer, as explained above.

3. **Choice B: A figure-eight end-fire along the axis of the array**
   - A figure-eight pattern typically occurs when antennas are fed in phase or with a specific phase difference that aligns them along the axis. In this case, the 90-degree phase difference does not create a figure-eight end-fire pattern.

4. **Choice C: A figure-eight broadside to the axis of the array**
   - A broadside figure-eight pattern is produced when antennas are spaced and fed in a way that maximizes radiation perpendicular to the line connecting them. The 90-degree phase difference and the specific spacing do not yield this pattern.

5. **Choice D: Omni-directional**
   - An omni-directional pattern would imply equal radiation in all directions. The specific configuration of these antennas with a 90-degree phase difference creates a directional pattern (cardioid), not an omni-directional one.

### Useful Formulas or Rules of Thumb:
- **Phase Difference and Antenna Patterns:**
  - The phase difference between antennas affects the directionality of the radiation pattern. A 90-degree phase difference typically results in a cardioid pattern.
- **Spacing Considerations:**
  - The spacing of antennas relative to their wavelength is crucial. For 1/4-wavelength spacing, the resulting patterns can be significantly different based on the phase relationship.

In summary, the configuration of two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase results in a cardioid radiation pattern, while the other options do not accurately describe the resulting pattern.