Question E9H05:
What challenge is presented by a small wire-loop antenna for direction finding?  

Choices:  
A: It has a bidirectional null pattern  
B: It does not have a clearly defined null  
C: It is practical for use only on VHF and higher bands  
D: All these choices are correct    

Correct Answer is  A: It has a bidirectional null pattern  

To calculate the ERP:  
$$ERP = P_T \times G_A$$  
where:
- $P_T$ = transmitter power in watts
- $G_A$ = antenna gain (linear)

This shows how to compute the effective radiated power for the given setup.

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Correct answer: A — It has a bidirectional null pattern.

1) Why A is correct
- A small wire-loop (electrically small loop) has a figure-8 reception pattern with two deep nulls 180° apart. When you rotate the loop for a null, you get an excellent bearing line but cannot tell which of the two opposite directions is the true source without additional information. This creates a 180-degree ambiguity.
- For a small loop, received voltage varies with angle roughly as:
  $$|V(\phi)| \propto |\sin \phi| \quad \text{or} \quad |\cos \phi|$$
  depending on how you define the reference angle. In either case, there are two nulls separated by 180°.

2) Why the other choices are incorrect
- B: It does not have a clearly defined null — Incorrect. Small loops are prized for direction finding precisely because their nulls are very sharp and well defined.
- C: It is practical for use only on VHF and higher bands — Incorrect. Small loops are widely and effectively used on LF/MF/HF (e.g., AM broadcast-band DF). They are not limited to VHF+.
- D: All these choices are correct — Incorrect because B and C are false.

3) Useful formulas and rules of thumb
- Small loop response (magnitude) versus azimuth angle:
  $$|V(\phi)| \propto |\sin \phi| \quad \text{(two nulls 180° apart)}$$
- Magnetic flux linkage (conceptual):
  $$V \propto N A \omega B \cos \theta$$
  where $N$ = turns, $A$ = loop area, $\omega$ = angular frequency, $B$ = magnetic field, $\theta$ = angle between $B$ and loop normal. Zero response occurs when the field is in the plane of the loop (a null), which happens in two opposite directions.
- Rule of thumb to resolve the 180° ambiguity: Add a “sense” antenna (e.g., short vertical) and phase it with the loop to create a cardioid pattern:
  $$V_{\text{total}}(\phi) = V_{\text{loop}}\sin \phi + V_{\text{sense}}$$
  Proper amplitude/phase yields a single null, removing the front/back ambiguity.