*Question E9C01:
What type of radiation pattern is created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase?*  

*Correct Answer is  D: A figure-eight oriented along the axis of the array*  

### AI Response: (may contain errors)  

To understand the radiation pattern created by two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase, we need to analyze the configuration:

1. **Correct Answer Explanation**:
   - When two antennas are fed 180 degrees out of phase, they create a destructive interference pattern in certain directions and constructive interference in others. 
   - The spacing of 1/2-wavelength causes the antennas to produce a figure-eight pattern oriented along the axis of the array. This means that the maximum radiation occurs in the directions perpendicular to the line connecting the two antennas, while there are nulls (areas of reduced radiation) along the axis of the array.

2. **Why Other Choices Are Incorrect**:
   - **A: Cardioid**: This pattern typically results from a single antenna with a specific feed arrangement or from two antennas with a different phase relationship. It does not apply here since we have a figure-eight pattern.
   - **B: Omni-directional**: An omni-directional pattern radiates equally in all horizontal directions. The configuration described does not produce this type of pattern due to the phase difference and spacing.
   - **D: A figure-eight oriented along the axis of the array**: This is incorrect because the figure-eight pattern is actually oriented perpendicular to the axis of the array, not along it.

3. **Useful Formulas and Rules of Thumb**:
   - The general rule for antenna arrays is that the spacing and phase difference significantly affect the resulting radiation pattern. 
   - For two antennas spaced $d$ apart and fed with a phase difference $\phi$, the pattern can be analyzed using the principle of superposition, where the resultant field is the vector sum of the fields from each antenna.

In summary, the correct answer is that the configuration creates a figure-eight pattern oriented along the axis of the array due to the specific phase relationship and spacing of the antennas.