The one calculation every comms engineer does
A link budget is an accounting sheet in decibels. You start with what the transmitter radiates, subtract everything the universe takes away, add what the receiver contributes, and see whether enough is left to decode bits at the rate you want. If the answer is "yes, with margin", the link works. If not, you change something — a bigger dish, more power, a lower data rate, a better code.
Free-space path loss
Signal spreads out as it travels; power density falls with the square of distance. Expressed in dB, with distance in km and frequency in GHz:
FSPL (dB) = 20·log10(d_km) + 20·log10(f_GHz) + 92.45
Some anchors: a LEO satellite at 1,000 km slant range on X-band loses ~171 dB. A GEO satellite at 38,000 km on Ku-band loses ~206 dB. Mars at 2.5 AU on X-band loses ~282 dB — and yet Deep Space Network links close, because the other terms are enormous.
Noise: the floor you are shouting over
The receiver's ability to hear is captured by G/T — antenna gain divided by system noise temperature, in dB/K. A hot, noisy receiver behind a huge dish and a cold, quiet receiver behind a small one can have the same G/T. Boltzmann's constant k sets the noise power per hertz: 10·log10(k) = −228.6 dBW/K/Hz.
Putting it together
C/N₀ (dB-Hz) = EIRP − FSPL − other losses + G/T + 228.6
C/N₀ is carrier power over noise density — how much signal you have per hertz of noise. To decode bits you need energy per bit over noise:
Eb/N₀ (dB) = C/N₀ − 10·log10(R_bits/s)
Margin (dB) = Eb/N₀ − Eb/N₀ required by your modulation & code
The "required Eb/N₀" comes from the next lesson; QPSK with a decent forward-error-correction code needs around 2–5 dB for a 10⁻⁶ bit error rate. Engineers usually want at least 3 dB of margin after rain and pointing losses.
The levers, ranked by cost
| Lever | Gain | What it costs |
|---|---|---|
| Halve the data rate | +3 dB | Half the data per pass |
| Double transmitter power | +3 dB | Mass, heat, solar array |
| Double ground dish diameter | +6 dB | Money on the ground (cheap) |
| Better coding (e.g. LDPC vs. convolutional) | 2–4 dB | Processing, licensing |
| Move from X to Ka | +10 dB antenna gain both ends | Rain margin, pointing |
Worked example
EIRP 51 dBW (last lesson), 2,000 km slant range at 8.4 GHz, 3 dB of pointing and atmospheric losses, a 1.2 m ground station with G/T 20 dB/K, 100 Mbps:
- FSPL = 20·log10(2000) + 20·log10(8.4) + 92.45 = 66.0 + 18.5 + 92.45 = 176.9 dB
- C/N₀ = 51 − 176.9 − 3 + 20 + 228.6 = 119.7 dB-Hz
- Eb/N₀ = 119.7 − 10·log10(10⁸) = 119.7 − 80 = 39.7 dB
Against a 4.5 dB requirement that is a luxurious 35 dB of margin — the point at which a designer starts trading the excess for a smaller antenna or a higher rate. Change the numbers below and watch which terms move the answer. The site's full tool at /link-budget-calculator adds rain models and antenna noise temperature.