Efficiency, not gain, sets how far a link reaches. Total efficiency folds in mismatch loss, the radiation pattern shows where the power actually goes, and the 2D²/λ far-field boundary decides whether your range test measured anything real.
| Term | Definition | What it excludes | ||
|---|---|---|---|---|
| Radiation efficiency | Radiated power ÷ power accepted by the antenna | Excludes mismatch at the port | ||
| Total efficiency | Radiated power ÷ power delivered to the feed = η_rad × (1 − | Γ | ²) | Includes mismatch loss |
| Realised gain | Gain (dBi) + 10·log₁₀(η_total) | The number that predicts range | ||
| System efficiency | Add cable loss, connector loss and enclosure detuning | The only number that predicts your range |
Typical radiation efficiency by antenna type:
| Antenna | Typical radiation efficiency |
|---|---|
| External dipole / whip at 868–915 MHz | 80–95 % |
| 2.4 GHz SMD chip antenna on a small board | 40–70 % |
| Ceramic GNSS patch (passive, no LNA) | 40–60 % |
| FPC or PCB internal antenna, well laid out | 60–80 % |
Note the ordering trap: a lossy but well-matched antenna can show a decent peak gain in one direction while radiating less than half the accepted power. Gain measured without efficiency is half a specification.
The pattern is the 3-D map of where power goes. Practical quantities:
For a single main lobe, gain and beamwidth trade directly: G ≈ 41 253 / (θ_E × θ_H). This couples straight back to the gain page: 3 dB more gain, half the beam area.
| Region | Extent | What is true there |
|---|---|---|
| Reactive near field | r < λ/2π (≈ 0.159 λ) | E and H not orthogonal, stored energy dominates, no defined pattern |
| Radiating near field (Fresnel) | λ/2π → 2D²/λ | Pattern still changes with distance |
| Far field (Fraunhofer) | r > 2D²/λ | Pattern and gain are distance-independent; this is where measurements are valid |
where D is the largest linear dimension of the antenna.
| Antenna | D | Frequency | λ | Far field starts at |
|---|---|---|---|---|
| 100 mm whip, 868 MHz | 0.10 m | 868 MHz | 0.346 m | 5.8 cm |
| 25 mm GNSS patch | 0.025 m | 1575 MHz | 0.190 m | 6.6 mm |
| 0.6 m 5.8 GHz grid dish | 0.60 m | 5.8 GHz | 0.052 m | 13.9 m |
The practical consequence: a small chip antenna or patch is in the far field almost immediately, so a bench measurement at 50 cm is legitimate. A large directional antenna at 5.8 GHz is not — you need roughly 14 m or a proper range. This single table explains a large share of bad customer test reports.
FSPL (dB) = 20·log₁₀(d) + 20·log₁₀(f) + 32.44 — d in km, f in MHz (ITU-R P.525-4 prints the constant as 32.4; either is defensible — state which you used.)
| Frequency | 10 m | 100 m | 1 km | 10 km |
|---|---|---|---|---|
| 433 MHz | 45.2 dB | 65.2 dB | 85.2 dB | 105.2 dB |
| 868 MHz | 51.2 dB | 71.2 dB | 91.2 dB | 111.2 dB |
| 915 MHz | 51.7 dB | 71.7 dB | 91.7 dB | 111.7 dB |
| 2.4 GHz | 60.1 dB | 80.1 dB | 100.1 dB | 120.1 dB |
| 5.8 GHz | 67.7 dB | 87.7 dB | 107.7 dB | 127.7 dB |
Treat FSPL as a floor, not a prediction. It assumes free space, isotropic antennas, no ground reflection and no obstruction. Real sub-GHz links in industrial sites lose another 10–30 dB; a 2.4 GHz radio inside a metal cabinet can lose 20–40 dB more. Always add an explicit environment margin line to the budget.
LoRa-style link, 868 MHz, 1 km, SF10 (sensitivity ≈ −137 dBm with a typical SX127x-class receiver — check your own module datasheet):
| Element | Value |
|---|---|
| TX power | +14 dBm |
| TX antenna efficiency | −1.0 dB (80 %) |
| TX antenna gain | +2.0 dBi |
| Cable and connector | −0.5 dB |
| Path loss @ 1 km | −91.2 dB |
| RX antenna gain | +2.0 dBi |
| RX cable | −0.5 dB |
| Signal at receiver | ≈ −75 dBm |
| Environment margin (industrial, walls) | −20 dB |
| Worst case at receiver | ≈ −95 dBm |
| Link margin | ≈ 42 dB |
That margin is why sub-GHz IoT is forgiving — and why a 0.5 dB VSWR argument is usually noise.
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