Question E9H11:
What feature of a cardioid pattern antenna makes it useful for direction-finding antennas?  

Choices:  
A: A very sharp peak  
B: A single null  
C: Broadband response  
D: High radiation angle    

Correct Answer is  B: A single null  

To find the bearing with a cardioid-pattern DF antenna, operators use its single, very deep null. This gives high angular precision and removes the 180-degree ambiguity found in bidirectional patterns.

Why B (A single null) is correct:
- A cardioid has one deep null in its azimuth pattern. Pointing that null toward the signal source yields a precise bearing.
- Nulls are sharper than peaks, so small changes in angle cause large changes in received signal near the null, improving accuracy.
- It also resolves the front/back ambiguity (only one null direction).

Why the others are incorrect:
- A: A very sharp peak — Cardioid maxima are relatively broad; DF typically relies on the sharp null, not the peak.
- C: Broadband response — Not inherent to a cardioid; bandwidth depends on the antenna design, not the cardioid shape.
- D: High radiation angle — Irrelevant for azimuth DF; elevation angle doesn’t provide the DF advantage here.

Useful formulas/rules of thumb:
- A cardioid can be formed by summing an omnidirectional “sense” antenna with a bidirectional loop/dipole:
  $$E(\theta) = E_s + E_l \cos\theta$$
  If amplitudes are equal and phases aligned,
  $$E(\theta) = 1 + \cos\theta \quad \Rightarrow \quad \text{null at } \theta = 180^\circ$$
  or with opposite phase,
  $$E(\theta) = 1 - \cos\theta \quad \Rightarrow \quad \text{null at } \theta = 0^\circ.$$
- Bearing accuracy near a null improves with the steepness of the pattern slope:
  $$\Delta \theta \approx \frac{\Delta V}{\left|\frac{dV}{d\theta}\right|}$$
  The large slope at the null makes $\Delta \theta$ small for a given signal change $\Delta V$.