How do antenna gain and directivity relate to each other?

• A. Gain equals Directivity × Impedance
• B. Gain equals Directivity plus Efficiency
• C. Gain equals Efficiency
• D. Gain equals Directivity × Efficiency

Answer: (D)

Gain measures how much power is effectively radiated in a preferred direction, taking into account both how focused the pattern is (directivity) and how much of the input power is actually radiated (efficiency). Directivity describes the antenna’s radiation pattern shape, assuming all input power is radiated; it reflects how well the antenna concentrates energy in a given direction. Efficiency accounts for losses—ohmic, dielectric, and other losses—that cause some input power to be wasted as heat rather than radiated. Since those losses reduce the power that actually leaves the antenna in the favored direction, they multiply the ideal focus provided by directivity. Therefore the relationship is gain equals directivity times efficiency. If the antenna were perfect (efficiency = 1), gain would equal directivity. If there are losses (efficiency < 1), gain is reduced accordingly. The other options misstate this relationship: impedance is a separate parameter and does not determine gain; adding directivity and efficiency isn’t the correct combination; and gain is not simply equal to efficiency alone.