Question E9A12:
How much gain does an antenna have compared to a half-wavelength dipole if it has 6 dB gain over an isotropic radiator?  

Choices:  
A: 3.85 dB  
B: 6.0 dB  
C: 8.15 dB  
D: 2.79 dB    

Correct Answer is  A: 3.85 dB  

To compare antenna gain referenced to isotropic (dBi) versus a half-wave dipole (dBd), use:

$$G_{\text{dBd}} = G_{\text{dBi}} - 2.15\ \text{dB}$$

- A half-wave dipole has about $2.15\ \text{dB}$ gain over an isotropic radiator, so $0\ \text{dBd} = 2.15\ \text{dBi}$.

1) Why the correct answer is correct:
- Given $G_{\text{dBi}} = 6.0\ \text{dB}$,
  $$G_{\text{dBd}} = 6.0 - 2.15 = 3.85\ \text{dB}$$
- So, the antenna has 3.85 dB gain over a dipole.

2) Why the other choices are incorrect:
- 6.0 dB (B): Fails to convert from dBi to dBd; it’s still referenced to isotropic.
- 8.15 dB (C): Incorrectly adds the dipole’s 2.15 dB instead of subtracting.
- 2.79 dB (D): Uses an incorrect offset for the dipole reference (not 2.15 dB).

3) Useful formulas / rules of thumb:
- Conversion: $$G_{\text{dBd}} = G_{\text{dBi}} - 2.15\ \text{dB}$$
- Dipole reference: half-wave dipole ≈ $2.15\ \text{dBi}$ = $0\ \text{dBd}$.