Discussion
An antenna has a directivity of 20 dBi and an efficiency of 50 per cent. What is its gain?
Answer: A
Halving the power is a loss of three decibels, so:
\[ G = 20 - 3 = 17 \]
giving 17 dBi. Efficiency can only reduce gain below directivity, never raise it, which immediately rules out the largest option. Doing the arithmetic in decibels rather than in ratios is quicker here, and remembering that a factor of two is three decibels covers a surprising proportion of the calculations that arise in practice.
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