An antenna does not amplify — it focuses
A transmitter puts out a fixed number of watts. An antenna cannot add power; it can only decide where the power goes. Gain is how much stronger the signal is in the antenna's favourite direction compared with an imaginary antenna that radiates equally in all directions (an isotropic radiator). It is quoted in dBi — decibels relative to isotropic.
For a parabolic dish of diameter D at wavelength λ:
G = η · (π · D / λ)² (as a ratio)
G_dBi = 10 · log10(G)
η is the aperture efficiency — how much of the dish actually contributes — typically 0.5–0.7. Because λ = c / f, gain rises with the square of both diameter and frequency.
Feel for the numbers (η = 0.6)
| Dish | S-band (2.2 GHz) | X-band (8.4 GHz) | Ka-band (26 GHz) |
|---|---|---|---|
| 0.3 m (CubeSat-class) | ~14 dBi | ~26 dBi | ~36 dBi |
| 1.2 m (small ground station) | ~26 dBi | ~38 dBi | ~48 dBi |
| 13 m (commercial teleport) | ~47 dBi | ~59 dBi | ~69 dBi |
The price of gain: beamwidth
Focusing power means narrowing the beam. The half-power beamwidth of a dish is roughly:
θ₃dB ≈ 70° · λ / D
A 13 m dish at Ka-band has a beam about 0.06° wide — narrower than the Moon as seen from Earth. Point it 0.1° off and the link is gone. That is why high-gain, high-frequency systems need tracking mounts, star trackers on the spacecraft, and money.
EIRP: what the far end actually sees
Equivalent Isotropically Radiated Power combines transmitter power and antenna gain into one number — the power an isotropic antenna would need to produce the same signal in the beam direction:
EIRP (dBW) = P_tx (dBW) + G_tx (dBi) − line losses (dB)
Decibels turn multiplication into addition, which is why every link engineer thinks in dB. 20 W is 13 dBW; add a 38 dBi dish and you have an EIRP of 51 dBW — the equivalent of a 126 kW isotropic transmitter.
Design intuition
- Doubling transmitter power buys you 3 dB. Doubling dish diameter buys you 6 dB. Antennas are usually the cheaper decibel.
- On a small satellite, mass and pointing limit the antenna, so power and ground-station size do the work.
- On a ground station, the dish is cheap relative to a spacecraft — which is why 13 m teleport dishes exist.
Try the numbers below, then carry your EIRP into the next lesson.