Link Budgets: Decibels, Path Loss and Margin

A link budget answers one question: does enough signal arrive for the receiver to read it? It is a single sum. Gains are positive, losses are negative, and if the total is above what the receiver needs, the link works.

The adding up is easy. Getting the units right is not.

Decibels

A decibel is a ratio written on a log scale. That turns multiplication into addition, which is the only reason anyone uses them.

dB = 10 · log10(P_out / P_in)

A few values are worth memorising, because you can add them together:

dB	Ratio
3 dB	2×
6 dB	4×
10 dB	10×
20 dB	100×
30 dB	1000×

So 23 dB is 20 + 3, which means 100 × 2 = 200 times. And −3 dB means half the power.

WARNING

dB and dBm are not the same thing. dB is a ratio, so it has no units. dBm is an actual amount of power, measured against one milliwatt.

You can add a dB to a dBm — that is a gain applied to a power, and the answer is a dBm. You can subtract one dBm from another, and the answer is a dB. But adding two dBm values together means nothing, and it is the most common mistake in a first link budget.

Antennas use a third unit: dBi, which compares the antenna to one that radiates equally in every direction. It is a ratio, so it adds like a dB.

Free-space path loss

Most of your signal is lost simply because the wave spreads out as it travels. No weather, nothing in the way — just distance.

FSPL(dB) = 20·log10(d) + 20·log10(f) + 32.44
           d in km, f in MHz

Both of those 20·log10 terms lead to the same rule:

Double the distance, lose 6 dB. At any frequency.
Double the frequency, lose 6 dB. This is why moving from UHF to X-band is not free. You gain bandwidth and pay for it in path loss, then buy it back with a bigger or more focused antenna.

For a satellite 500 km away on 437 MHz:

FSPL = 20·log10(500) + 20·log10(437) + 32.44
     = 53.98 + 52.81 + 32.44
     = 139.2 dB

That is about 10¹⁴ times less power, lost to spreading alone. It is also why every other number in the budget is worth fighting for.

The whole sum

budget.txt

  Transmit power                      +30.0 dBm   (1 W)
  Loss in the transmit cable           −1.0 dB
  Transmit antenna gain                +2.0 dBi    (satellite, near-omni)
  ──────────────────────────────────────────────
  EIRP                                +31.0 dBm
 
  Free-space path loss               −139.2 dB    (500 km, 437 MHz)
  Atmosphere and polarisation          −2.0 dB
  Pointing error                       −1.0 dB
  ──────────────────────────────────────────────
  Power arriving                     −111.2 dBm
 
  Receive antenna gain                +14.0 dBi   (ground station yagi)
  Loss in the receive cable            −1.5 dB
  ──────────────────────────────────────────────
  Signal at the receiver              −98.7 dBm
 
  What the receiver needs            −110.0 dBm   (at this data rate)
  ──────────────────────────────────────────────
  LINK MARGIN                          +11.3 dB

A positive margin means the link works. +11.3 dB is comfortable — about 13 times more power than the minimum.

How much margin you actually need

3 dB is not enough. It sounds like plenty, since it means twice the power you need. But the things it has to cover are neither small nor rare:

Distance changes during a pass. The budget above assumed 500 km, which is the satellite straight overhead. When it is low on the horizon at 10°, it is about 1,700 km away — another 10 dB of loss. And a pass spends most of its time low on the horizon.
Rain. It does not matter at UHF. Above 10 GHz it matters a lot, and heavy rain can cost 10 dB or more at Ka-band.
Pointing error, which gets worse as the antenna gets more focused and more useful.
Tumbling. A satellite that cannot control its orientation swings its antenna around, and the gain changes by many dB as it turns. The +2.0 dBi above is optimistic for anything that is not stabilised.

Working numbers: 6 dB for a steady link when the satellite is high, 10 dB if you want the whole pass, and 20 dB above Ku-band where rain is a real problem.

Do this before you trust a budget

Work it out again for the worst case, not for the satellite overhead. A budget that works overhead and fails at 10° gives you a usable window of a few tens of seconds — and you will not find that out until you are watching a receiver that only decodes in the middle of a pass.

Here is the distance to a satellite at a given angle above the horizon:

slant_range.py

import math
 
RE = 6378.137  # km
 
 
def slant_range(altitude_km: float, elevation_deg: float) -> float:
    """Distance to a satellite seen at a given angle above the horizon."""
    eps = math.radians(elevation_deg)
    return -RE * math.sin(eps) + math.sqrt(
        (RE * math.sin(eps)) ** 2 + altitude_km**2 + 2 * RE * altitude_km
    )
 
 
for elevation in (90, 30, 10, 5):
    d = slant_range(500, elevation)
    fspl = 20 * math.log10(d) + 20 * math.log10(437) + 32.44
    print(f"{elevation:3d}°   {d:7.1f} km   {fspl:6.1f} dB")

output.txt

 90°     500.0 km    139.2 dB
 30°     902.3 km    144.3 dB
 10°    1702.4 km    149.8 dB
  5°    2077.6 km    151.5 dB

Between straight overhead and 5° above the horizon you lose 12.3 dB. That is the entire margin of a budget that looked healthy, spent on distance alone.

Part of the working notes behind SatLab.