Discussion
Gain follows \( G = 4\pi A \eta / \lambda^{2} \). What gain does a 2 m dish of 60 per cent efficiency give at 10 GHz?
Answer: D
The physical area is pi times one squared, about 3.14 square metres, so:
\[ \begin{aligned} G &= \tfrac{4\pi \times 3.14 \times 0.6}{0.03^{2}} \\ &\approx 26300 \end{aligned} \]
which is about 44 dBi. The relation shows that gain rises as the square of both diameter and frequency, which is why a modest dish gives enormous gain at microwave frequencies and almost none at high frequency. It is the single most used formula in aperture antenna work and is worth being able to evaluate quickly in the head to within a decibel.
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