Discussion
Effective aperture and directivity are related by \( A_{e} = D\lambda^{2}/4\pi \). What aperture does a directivity of 100 give at 1 m wavelength?
Answer: D
Substituting directly:
\[ A_{e} = \tfrac{100 \times 1}{4\pi} \approx 7.96 \]
giving about 8 square metres. The relation is universal, holding for wire antennas and reflectors alike, and it shows that for a fixed directivity the collecting area shrinks as the square of the frequency. That is one reason why link budgets at high frequency need physically large dishes to keep the same performance.
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