Parabolic Antenna Gain
Gain of a dish antenna rises with aperture area and falls with wavelength, scaled by aperture efficiency.
Formula
Variables
Example
1 m dish at λ 0.03 m, η 0.55: G ≈ 0.55×(π×1÷0.03)² ≈ 6030 (≈38 dBi)
How it works
A parabolic dish concentrates radio energy into a narrow beam because its curved surface makes signals from across the aperture arrive in phase at the focus. The larger the effective collecting area, the more power the antenna can capture and redirect, so gain scales with D²; shorter wavelengths also fit more wave cycles across the dish, increasing directivity, which is why gain scales with 1/λ². The efficiency factor η accounts for real-world losses such as spillover, surface errors, blockage, and imperfect feed illumination, so actual gain is always below the ideal geometric value.
When to use it
Use this formula when estimating the receive or transmit gain of a parabolic reflector in communications, radar, satellite links, or avionics antenna design. It is especially useful for link budgets, comparing dish sizes/frequencies, or checking whether a given antenna can meet a required beamwidth or sensitivity.
Worked example, step by step
Given: D = 0.75 m, λ = 0.025 m, η = 0.62 Step 1: Compute the diameter-to-wavelength ratio: πD/λ = π×0.75/0.025 = 94.248 Step 2: Square the result: (94.248)^2 = 8882.6 Step 3: Apply efficiency: G = 0.62×8882.6 = 5505.2 Final answer: G ≈ 5.5×10^3 (linear gain) In dBi: 10 log10(5505.2) ≈ 37.4 dBi
Common mistakes to avoid
- Using diameter instead of radius in the formula; the dish gain depends on D, not D/2
- Forgetting that λ must be in the same units as D, otherwise the ratio is wrong
- Confusing linear gain with dBi and reporting the raw value as if it were already in decibels
Did You Know?
Doubling a dish’s diameter quadruples its gain, so weather-radar and satcom performance improves fast with antenna size — limited only by what fits in the nose radome.
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