Which statement correctly describes the relationship between antenna gain and directivity?

• A. Gain and directivity are identical.
• B. Gain is the directivity plus efficiency factors; Directivity is focused radiation pattern.
• C. Directivity measures impedance match; Gain measures beam width.
• D. Gain includes efficiency; Directivity is only how focused the radiation is.

Answer: (D)

Gain includes efficiency; Directivity is only how focused the radiation is. The key relationship is G = η D, where η is the radiation efficiency (the fraction of input power actually radiated). Directivity describes how concentrated the pattern would be if there were no losses, purely a function of antenna geometry. Efficiency accounts for losses (ohmic, dielectric, etc.), so actual gain is the directivity scaled by η. If the antenna is lossless (η = 1), gain equals directivity; with real antennas (η < 1), gain is lower than directivity by that factor. The statement captures that gain depends on both the pattern concentration and the efficiency, which is why it’s the best description.