Question E9B04:
What is the front-to-back ratio of the radiation pattern shown in Figure E9-2?  

Choices:  
A: 15 dB  
B: 28 dB  
C: 3 dB  
D: 38 dB    

Correct Answer is  B: 28 dB  

To find front-to-back (F/B) ratio, read the maximum (forward) gain and the gain 180° opposite (back) from the radiation pattern, then take the difference in dB.

Key formulas:
- $$F/B\ (\mathrm{dB}) = G_\text{front}(\mathrm{dB}) - G_\text{back}(\mathrm{dB})$$
- Equivalently, $$F/B\ (\mathrm{dB}) = 10\log_{10}\!\left(\frac{P_\text{front}}{P_\text{back}}\right) = 20\log_{10}\!\left(\frac{E_\text{front}}{E_\text{back}}\right)$$

Why 28 dB is correct:
- In Figure E9-2 the pattern is normalized so the main lobe is at 0 dB.
- The back lobe (at 180°) is about −28 dB.
- Thus, $$F/B = 0 - (-28) = 28\ \mathrm{dB}.$$
- This means the back power is about $10^{28/10} \approx 630$ times lower than the front.

Why the other choices are incorrect:
- 15 dB: Would imply the back lobe is at −15 dB; the figure shows a deeper back lobe.
- 3 dB: That’s a half-power difference (used for beamwidth), not the front-to-back level difference.
- 38 dB: Would require a back lobe near −38 dB, deeper than shown in the figure.

Rule of thumb:
- On normalized polar plots (front at 0 dB), the F/B ratio in dB is simply the magnitude of the back-lobe level (positive number). For many Yagis, F/B is typically 20–30 dB.