Question E9H03:
What is receiving directivity factor (RDF)?  

Choices:  
A: Forward gain compared to the gain in the reverse direction  
B: Relative directivity compared to isotropic  
C: Relative directivity compared to a dipole  
D: Peak antenna gain compared to average gain over the hemisphere around and above the antenna    

Correct Answer is  D: Peak antenna gain compared to average gain over the hemisphere around and above the antenna  

Correct answer: D

1) Why D is correct
- Receiving Directivity Factor (RDF) quantifies how “selective” a receiving array is by comparing its strongest response to the average response to noise and signals from all directions above ground.
- Formally, it is the ratio of the peak gain to the average gain over the upper hemisphere (2π steradians), which is what a ground-mounted receive antenna “sees.”

Useful formulas:
$$G_{\text{avg,hem}}=\frac{1}{2\pi}\int_{0}^{2\pi}\int_{0}^{\pi/2} G(\theta,\phi)\,\sin\theta\,d\theta\,d\phi$$
$$\text{RDF}=\frac{G_{\text{peak}}}{G_{\text{avg,hem}}},\qquad \text{RDF}_{\text{dB}}=10\log_{10}\!\left(\frac{G_{\text{peak}}}{G_{\text{avg,hem}}}\right)$$
If both are in dBi (with the average computed in linear units first, then converted to dB), then:
$$\text{RDF}_{\text{dB}}=G_{\text{peak}}(\text{dBi})-G_{\text{avg,hem}}(\text{dBi})$$

2) Why the other choices are incorrect
- A: “Forward gain compared to the gain in the reverse direction” is the front-to-back ratio, not RDF. F/B only compares two directions; RDF averages over all directions in the upper hemisphere.
- B: “Relative directivity compared to isotropic” describes directivity (or gain in dBi) in free space relative to an isotropic radiator over the full sphere (4π), not the hemisphere-average used for RDF.
- C: “Relative directivity compared to a dipole” is gain in dBd (relative to a half-wave dipole), not RDF.

3) Rules of thumb
- Higher RDF means better receive SNR in noise-limited conditions; every additional 3 dB of RDF is a noticeable improvement.
- Typical RDF values:
  - Beverage: ~8–12 dB
  - 4-square/phased arrays: ~12–14+ dB
  - Large, optimized receiving arrays: >15 dB
- RDF is about pattern quality (noise rejection), not absolute gain; a low-gain antenna with high RDF can outperform a high-gain antenna for reception.