Question E9B02:
What is the front-to-back ratio of the antenna radiation pattern shown in Figure E9-1?  

Choices:  
A: 36 dB  
B: 14 dB  
C: 24 dB  
D: 18 dB    

Correct Answer is  D: 18 dB  

To find the front-to-back ratio (F/B), read the antenna’s polar plot at the forward (0°) and directly opposite (180°) directions.

Key idea:
- F/B is the ratio of radiation in the forward direction to that in the opposite direction (180°), expressed in dB.
- On a normalized plot (forward peak is 0 dB), the F/B in dB is just the magnitude of the back-lobe level.

Useful formulas:
- $$\text{F/B (dB)} = 10\log_{10}\!\left(\frac{P_\text{front}}{P_\text{back}}\right)$$
- $$\text{F/B (dB)} = G_\text{front(dB)} - G_\text{back(dB)}$$
- If the plot is normalized so $G_\text{front}=0$ dB: $$\text{F/B (dB)} = -G_\text{back(dB)}$$

Why 18 dB is correct:
- In Figure E9-1, the back lobe at 180° intersects the −18 dB circle relative to the forward maximum (0 dB).
- Therefore, $$\text{F/B} = 0 - (-18) = 18\ \text{dB}.$$

Why the others are incorrect:
- 14 dB would require the back lobe at −14 dB (not shown).
- 24 dB would require the back lobe at −24 dB (smaller than shown).
- 36 dB would require the back lobe at −36 dB (much smaller than shown).

Rule of thumb:
- On a normalized polar plot, just read the dB value of the back lobe at 180° and take its magnitude as the F/B. An 18 dB F/B corresponds to about a 63:1 power ratio.