TECHNICAL NOTES · AVIONICS & RF
The link budget that passes at zenith and fails at 10°
A link budget is usually presented at one geometry — and often the flattering one. Run the same small-satellite downlink across a pass and the margin moves by more than 10 dB. Here is the whole calculation, so every number can be checked.
The scenario
A satellite in a 550 km circular orbit downlinks at 2 250 MHz (S-band) to a small ground station. The values below are illustrative but typical; the required Eb/N0 in particular comes from your modem's datasheet for your modulation, coding and target bit-error rate.
| PARAMETER | VALUE | NOTE |
|---|---|---|
| Transmit power | 3.01 dBW | 2 W |
| Transmit antenna gain | 6.0 dBi | patch |
| Transmit line loss | −1.0 dB | |
| EIRP | 8.01 dBW | |
| Atmospheric loss | −0.4 dB | |
| Polarisation loss | −0.5 dB | |
| Receive pointing loss | −1.0 dB | |
| Ground station G/T | 2.0 dB/K | |
| Boltzmann constant | −228.6 dBW/K/Hz | |
| Data rate | 63.01 dBHz | 2 Mbit/s |
| Required Eb/N0 | 4.5 dB | from modem datasheet |
| Implementation loss | 2.0 dB |
The two equations that move
Slant range from the satellite to the station at elevation angle ε:
d = √((R⊕ + h)² − (R⊕ cos ε)²) − R⊕ sin ε, with R⊕ = 6 378.137 km, h = 550 km
Free-space path loss:
FSPL [dB] = 20 log₁₀(d [km]) + 20 log₁₀(f [MHz]) + 32.45
Everything else is fixed, so the link closes on:
C/N₀ = EIRP − FSPL − Latm − Lpol − Lpoint + G/T − kEb/N₀ = C/N₀ − 10 log₁₀(R) · margin = Eb/N₀ − required − Limpl
Across the pass
| ELEVATION | SLANT RANGE | FSPL | C/N₀ | Eb/N₀ | MARGIN |
|---|---|---|---|---|---|
| 90° (zenith) | 550.0 km | 154.30 dB | 82.41 dBHz | 19.40 dB | 12.90 dB |
| 20° | 1 293.8 km | 161.73 dB | 74.98 dBHz | 11.97 dB | 5.47 dB |
| 10° | 1 815.7 km | 164.67 dB | 72.04 dBHz | 9.03 dB | 2.53 dB |
| 5° | 2 205.9 km | 166.37 dB | 70.34 dBHz | 7.33 dB | 0.83 dB |
At zenith the link looks enormously over-designed. At 10° — where a low-orbit pass spends much of its time — it falls short of a common 3 dB margin policy, and at 5° it barely closes at all. The only terms that changed are range and path loss: a factor of four in distance is 12 dB.
Three ways to close it
- Halve the data rate at low elevation. 1 Mbit/s adds 3.01 dB, giving 5.54 dB of margin at 10°. Adaptive or stepped rates recover most of the throughput a fixed low rate gives away.
- Raise the elevation mask to 20°. 5.47 dB of margin, at the cost of contact time on every pass — often the most expensive option.
- Buy gain. A larger dish or lower-noise front end raises G/T dB for dB, and helps every pass.
What to check in any link budget
State the geometry the margin applies to; carry the budget across the elevation range you actually use; check that every loss has a source; and confirm the required Eb/N0 matches your modem at your target error rate. A margin quoted without its elevation angle is not a margin. DYNAMIS builds power, link and signal budgets line by line with the arithmetic executed as code, so every row above can be traced and re-run.
Related notes
- Decoding an ARINC 429 BNR word, bit by bit
- How to check an AI's engineering calculation
- Verifiable AI: no hallucinated math
- Writing verifiable requirements with EARS
Published · 31 August 2026 · All technical notes