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Signals & Wireless (RF)

How to calculate a radio link budget

A link budget adds up every gain and loss between a transmitter and a receiver, in decibels, to see whether enough signal arrives. Start with what the transmitter sends, subtract what the path loses, add what the amplifiers win back, and compare the result with what the receiver needs. What's left over is the margin: the safety you keep for rain, walls and fading.

Decibels make it a sum

Gains and losses multiply: ÷100 across the path, then ×100 in an amplifier. In decibels they add. For voltages:

dB = 20 × log₁₀(Vout ÷ Vin): ×10 = +20 dB, ×100 = +40 dB, ÷100 = −40 dB

Send 8 V, lose 40 dB on the path and 80 mV arrives; a +40 dB amplifier wins it back to 8 V.

Distance: 6 dB per doubling

A transmitter's power spreads out like light from a bulb. Twice as far away, the same power covers four times the area, so each patch gets a quarter: −6 dB. Four times as far costs 12 dB, and ten times 20 dB. In free space the whole path loss is roughly:

loss ≈ 20 log₁₀(d in km) + 20 log₁₀(f in MHz) + 32.4 dB

Wi-Fi at 2400 MHz over 100 m: −20 + 67.6 + 32.4 ≈ 80 dB.

Win it back: the LNA

The first amplifier in a receiver, the low-noise amplifier, wins back most of the loss. A non-inverting op-amp gives 1 + Rf ÷ Rg, so 99 kΩ over 1 kΩ is ×100, +40 dB. Move twice as far and the link falls 6 dB short until Rf is 199 kΩ: ×200, +46 dB.

Live experiment

Close the link

TX sends 8 V at 20 kHz, the path across the garden loses 40 dB, and an op-amp LNA with gain 1 + Rf ÷ 1 kΩ wins it back. Set Rf and watch the budget add up and LINK light, then move twice as far away: 6 dB more to find.

Try it yourself: free lesson

“Close the link” is lesson 6 of 6 in Airwave Atoll, Signals & Wireless (RF) World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.

Keep a margin

A link with no margin works on a good day only. Rain, walls, a passing lorry or a hand over the antenna can each steal several decibels. Real links keep 10 dB or more spare, and satellite and microwave links budget for fading on purpose.

Power in dBm

Engineers usually budget power in dBm, decibels above 1 mW: 1 W is +30 dBm and 1 mW is 0 dBm. Power ratios use 10 × log₁₀; voltages use 20 because power goes as voltage squared. A typical budget: transmit +20 dBm, two antennas at +2 dBi each, a 100 dB path, so −76 dBm arrives. A receiver that needs −90 dBm then has 14 dB of margin. GPS signals arrive near −130 dBm, below the noise, and receivers still find them.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Close the link” is lesson 6 of 6 in Airwave Atoll, Signals & Wireless (RF) World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.

Or start from the very first lesson, no account needed

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3Why keep a margin?
    Show the answer

    Answer: Rain, walls and fading can steal decibels at any moment. A link with zero margin works on a good day and fails on a bad one. Real links keep 10 dB or more spare.

    • Why not “It isn't needed”? Without margin the link fails as soon as anything steals a few decibels.
    • Why not “To make the signal sound louder”? Margin is about the link staying up, not about how loud the result sounds.
    • Why not “To use less power”? Margin costs power, not saves it: it means sending or amplifying more than the bare minimum.
  2. Question 2 of 3Rg = 1 kΩ. For ×200 (+46 dB), Rf is…
    Show the answer

    Answer: 199 kΩ. Gain = 1 + Rf ÷ Rg, so Rf = 199 × 1 kΩ. 99 kΩ is last time's ×100, and 20 kΩ gives only ×21.

    • Why not “20 kΩ”? 20 kΩ gives 1 + 20 = ×21, about 26 dB.
    • Why not “46 kΩ”? 46 is the gain in decibels, not the ratio. ×200 needs Rf = 199 × Rg.
    • Why not “99 kΩ”? 99 kΩ gives ×100, +40 dB: 6 dB short of what twice the distance needs.
  3. Question 3 of 3The path loses 40 dB. The LNA must give…
    Show the answer

    Answer: ×100, so Rf = 99 kΩ over Rg's 1 kΩ. 40 dB is ×100 in voltage, and 1 + 99 kΩ ÷ 1 kΩ is 100.

    • Why not “×10, so Rf = 9 kΩ”? ×10 is only 20 dB, leaving the link 20 dB short.
    • Why not “×40”? ×40 is only about 32 dB. 40 dB is a voltage ratio of 100.
    • Why not “×1000”? ×1000 is 60 dB, 20 dB more than the path takes, and it could overload the stages after it.
Keep practising: free lesson

“Close the link” is lesson 6 of 6 in Airwave Atoll, Signals & Wireless (RF) World 3. Free with an account. Lessons unlock in order, so you’ll do the 19 before it first.

Questions people ask

What is a link budget?

An account of every gain and loss from transmitter to receiver: transmit power, antenna gains, cable and path losses, and amplifier gains, added in decibels. If the received level beats the receiver's sensitivity, the link works, and the difference is the margin.

How much does signal strength drop with distance?

In free space, 6 dB for every doubling of distance and 20 dB for every tenfold increase, because the power spreads over an area that grows with the distance squared. Walls, terrain and the ground usually add more.

How much link margin do I need?

Commonly 10 dB or more for a fixed link indoors or across a garden, and more for links through rain, trees or moving obstacles. In free space each extra 6 dB of margin roughly doubles the range.

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