SatBase

Link Budget

Link margin and maximum data rate for an RF downlink at the worst-case range of a pass.

Inputs

Spacecraft transmitter

What leaves the spacecraft antenna. Together these set the EIRP.

W
dB
dBi

Path

The worst case the pass must close at: the longest range, at the minimum elevation the station tracks.

GHz
km
°
dB
dB

Ground station

The receiving dish and the noise it adds. Together these set the G/T.

m
%
K

Link

Mbps
dB
dB

Results

Link

Link margin +4.6dB
Maximum data rate 72.8Mbps
Received Eb/N0 8.1dB
Threshold Eb/N0 3.5dB

Transmitter

EIRP 8.0dBW

Path

Slant range 1,695km
Free-space path loss 175.3dB
Total path loss 176.3dB

Ground station

Dish gain 47.8dBi
G/T 24.8dB/K
Received power −120.5dBW
C/N0 85.1dB-Hz

Method

The standard RF link budget after SMAD: the energy per bit that reaches the demodulator, held against what the modulation and coding need, at the worst-case range of a pass.

Eb/N0 = EIRP − Ls − La − Lpp + Gr − 10 log k − 10 log Ts − 10 log R The link equation in decibels: what the transmitter radiates, less what the path takes, plus what the dish collects, over the noise in each bit. With a dish on the ground, frequency cancels: its gain rises as f² exactly as fast as the path loss does.

Derivation

1
Find the worst-case range The spacecraft is farthest from the station when it is lowest in the sky. A link sized at the minimum elevation closes for the whole pass above it. Rₑ is the Earth’s equatorial radius, 6,378 km. λ = c / f, S = √((Re + h)² − (Re cos ε)²) − Re sin ε
2
Radiate: EIRP Transmit power in dBW, plus the antenna’s gain toward the station, less what the cabling loses on the way to it. EIRP = 10 log P + Gt − Ll
3
Cross the path Free-space loss is the spreading of the wavefront over the range, measured against an isotropic receiver of one wavelength. The atmosphere, rain, mispointing and polarization mismatch take their share on top. Ls = 20 log(4πS / λ), Lpath = Ls + La + Lpp
4
Collect: gain and G/T A dish’s gain grows with its area in wavelengths, derated by its aperture efficiency. Divided by the system noise temperature it gives G/T, the single figure ground-station datasheets quote. Gr = 10 log(η (πD / λ)²), G/T = Gr − 10 log Ts
5
Compare signal to noise Thermal noise density is Boltzmann’s constant times the system temperature, −228.6 dBW/(K·Hz) plus 10 log Tₛ. C/N₀ is the received power over it, a figure independent of the data rate. C = EIRP − Lpath + Gr, C/N0 = C − 10 log k − 10 log Ts
6
Spend it on bits: the margin Spreading C/N₀ over R bits per second gives the energy per bit. The margin is how far that sits above the modulation and coding threshold, after the modem’s own implementation loss. Eb/N0 = C/N0 − 10 log R, M = Eb/N0 − (Eb/N0)req − Limpl
7
Solve for the fastest rate Setting the margin equal to the required margin and solving for R gives the fastest rate the link supports with that reserve. Every 3 dB of margin you give up doubles it. Rmax = 10^((C/N0 − (Eb/N0)req − Limpl − Mreq) / 10)

Symbols

Input Description Unit
P Transmit power W
Ll Transmit line loss dB
Gt Transmit antenna gain dBi
f Carrier frequency GHz
h Spacecraft altitude km
ε Minimum elevation angle °
La Atmospheric and rain loss dB
Lpp Pointing and polarization loss dB
D Ground-station dish diameter m
η Dish aperture efficiency %
Ts System noise temperature K
R Data rate Mbps
Eb/N0req Required Eb/N0 of the modulation and coding dB
Limpl Modem implementation loss dB
Mreq Required link margin dB
Derived Description Unit
λ Wavelength: c / f m
S Slant range at the minimum elevation km
EIRP Effective isotropic radiated power dBW
Ls Free-space path loss dB
Gr Ground-station dish gain dBi
G/T Receive figure of merit dB/K
C Received carrier power dBW
C/N0 Carrier-to-noise density ratio dB-Hz
Eb/N0 Received energy per bit over noise density dB
M Link margin dB
Rmax Maximum data rate that meets the required margin Mbps

Reference values

First-order figures for sanity-checking inputs.

Band Downlink GHz Typical use
UHF 0.40–0.45 CubeSat telemetry, amateur
S 2.20–2.29 TT&C, low-rate science
X 8.025–8.4 Earth-observation payload data
Ku 10.7–12.75 GEO broadcast and relay
Ka 25.5–27.0 High-rate EO and relay
Modulation and coding Eb/N0 at 10⁻⁵ dB
Uncoded BPSK / QPSK 9.6
Convolutional, R ½ K 7 Viterbi 4.4
Reed-Solomon (255,223) + convolutional 2.5

This is the RF link equation after SMAD, evaluated at the worst-case slant range over a spherical Earth. A link sized here closes for the whole pass above the minimum elevation, and the higher parts of the pass have margin to spare. Atmospheric, rain, pointing and polarization losses are your figures, not a climate or antenna-pattern model; at Ku and Ka band a rain fade can exceed them. The noise temperature is referred to the antenna terminal, so there is no separate receive line loss. Treat these results as first-pass sizing, not a link design.