Before this:What is a radio wave?
Decibels & signal power
Key takeaways A decibel (dB) is a logarithmic way to express a ratio of power. dBm pins that ratio to a real reference (1 milliwatt) so it names an absolute signal strength; dBFS does the same against a digital maximum inside your SDR. Radio uses decibels because signals span a trillion-to-one range and logarithms make that manageable — and because gains and losses along a path simply add up. The numbers that matter most: every 10 dB = 10× power, every 3 dB ≈ 2×, and a signal is only usable when it sits well above the noise floor.
Decibels trip up almost every newcomer, because they’re negative, logarithmic, and come in confusing flavours. Spend ten minutes here and they’ll click — after which GopherTrunk’s signal meters turn from noise into a clear story about whether a signal is good enough to decode.
Why does radio measure everything in decibels?
The signals you care about cover an absurd dynamic range. A handheld radio across
the street might deliver a billion times more power to your antenna than a repeater
on a distant hilltop. Writing those values in watts means juggling numbers like
0.000000000002 — error-prone and unreadable.
A decibel solves this by taking the logarithm of the ratio between two powers:
dB = 10 × log₁₀(P₁ ÷ P₂)
The logarithm squashes that trillion-to-one span into a friendly range of about 120 units. Two consequences fall out of this and they’re the whole reason engineers love decibels:
- Multiplication becomes addition. An amplifier that multiplies power by 4 and a cable that cuts it in half become “+6 dB” and “-3 dB” — you just add them: net +3 dB. Tracing a signal through a chain of gains and losses is arithmetic you can do in your head.
- It matches how we perceive change. A 10× jump in power “feels” like one step, whether you’re going from weak to medium or medium to strong.
What do the magic numbers 3 dB and 10 dB mean?
You don’t need a calculator for most day-to-day decibel thinking — just two anchors:
| Change in dB | Change in power | Mnemonic |
|---|---|---|
| +3 dB | ×2 (double) | “3 to double” |
| −3 dB | ÷2 (half) | |
| +10 dB | ×10 | “10 for ten-fold” |
| +20 dB | ×100 | |
| +30 dB | ×1000 |
Combine them: +13 dB is ×10 then ×2 = ×20. −6 dB is half and half again = ¼. This mental arithmetic is enough to reason about almost any antenna, amplifier, or cable spec you’ll meet.
What is dBm, and how is it different from dB?
Plain dB is only a ratio — it tells you about a change, not an actual level. “This amplifier gives 15 dB of gain” says nothing about how strong the output is until you know the input.
dBm fixes a reference: it’s decibels relative to 1 milliwatt. That turns it into an absolute unit of power, so it can name a real signal strength on its own:
| dBm | Power | Typical meaning |
|---|---|---|
| 0 dBm | 1 mW | A reference point |
| −30 dBm | 1 µW | A very strong received signal |
| −80 dBm | 10 pW | A solid, easy-to-decode signal |
| −100 dBm | 0.1 pW | A weak signal, near many noise floors |
| −120 dBm | 1 fW | Often buried in the noise |
Two things to internalise. First, received signals are negative — they’re tiny fractions of a milliwatt. Second, closer to zero is stronger: −80 dBm beats −100 dBm by 20 dB, which is 100× the power.
Power ↔ dBm converter
Edit either field. 1 W = 30 dBm; 1 mW = 0 dBm; a 5 W handheld transmits at +37 dBm.
What is the noise floor, and why does it decide what you can hear?
No receiver sees pure silence. There’s always a background hiss — thermal noise in the electronics plus random RF energy from the environment. That background level is the noise floor, and like signal strength it’s measured in dBm (often around −110 to −90 dBm for an SDR, depending on bandwidth and surroundings).
A signal is only useful if it pokes up above the noise floor. The gap between the two is the signal-to-noise ratio (SNR), measured in dB:
SNR (dB) = signal level (dBm) − noise floor (dBm)
A signal at −85 dBm with a noise floor at −105 dBm has 20 dB of SNR — plenty. Digital voice modes each need a minimum SNR to decode; drop below it and the decoder starts dropping symbols and you get gaps or silence. This is why, in GopherTrunk’s tuning meters, you watch not just the raw signal but how far it stands above the noise.
What is dBFS, and where does it show up?
Inside the SDR, after the antenna signal is digitised, levels are measured against the maximum number the analog-to-digital converter (ADC) can represent. That scale is dBFS — decibels relative to full scale. Here 0 dBFS is the ceiling, and every real sample sits below it as a negative number, like −12 dBFS.
dBFS matters for one practical reason: if a signal (or the sum of all signals in your bandwidth) reaches 0 dBFS, the ADC clips — it can’t go higher, so the waveform is flattened and distortion sprays across the spectrum, wrecking nearby decodes. The fix is setting gain so strong signals peak comfortably below 0 dBFS. dBm describes the world outside the radio; dBFS describes the digital world inside it.
How do gain and path loss add up along a signal path?
Here’s where decibels pay off. Walk a signal from antenna to decoder and every stage is just a number you add:
-70 dBm antenna picks up the signal
+20 dB low-noise amplifier (LNA)
-2 dB coax cable loss
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-52 dBm at the SDR input
No multiplying microwatts — just running addition. The same logic covers path loss (the signal weakening as it spreads from the transmitter, which can be 100+ dB over a few kilometres) and antenna gain (a directional antenna concentrating energy, adding several dB in its favoured direction). Master this and you can predict, roughly, whether a system will be receivable before you ever tune to it.
Worked example: “will I hear it?”
Put it all together. A repeater transmits +47 dBm (about 50 W). You’re far enough away that path loss is −120 dB. Your antenna adds +3 dB, but coax and connectors cost −4 dB. Just add them up:
+47 dBm transmitter power
-120 dB path loss
+3 dB antenna gain
-4 dB feedline + connector loss
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-74 dBm signal at the SDR
Now compare against the noise floor. If yours is around −100 dBm, your SNR ≈ −74 − (−100) = 26 dB — comfortably above what any digital voice mode needs, so it’ll decode cleanly. Drop to a worse antenna (−74 → say −90 dBm signal) and SNR falls to 10 dB — still workable, but closer to the edge. This back-of-the- envelope sum, done entirely in decibels, is exactly how you reason about whether a system is worth chasing and what a better antenna or location would buy you.
Quick check: how much more power is −60 dBm than −80 dBm?
Recap
- A dB is a logarithmic ratio of power; +10 dB = ×10, +3 dB ≈ ×2.
- dBm is absolute power vs. 1 mW; received signals are negative, and closer to zero is stronger.
- dBFS is the digital scale inside the SDR; 0 dBFS is the clipping ceiling.
- The noise floor sets the bar a signal must clear; SNR is how far it clears it, and decoders need a minimum.
- Gains and losses along a path add, which is the whole point of decibels.
Next, we’ll look at how the spectrum is divided into bands — and then start putting information onto these waves with modulation.
Frequently asked questions
What is the difference between dB, dBm, and dBFS?
dB is a ratio between two powers — it expresses a change, like “6 dB of gain.” dBm is an absolute power referenced to one milliwatt, so it names an actual signal strength, like “-95 dBm.” dBFS is decibels relative to digital full scale, used inside the SDR to describe how close a sample is to clipping the analog-to-digital converter; 0 dBFS is the maximum and real signals sit below it as negative numbers.
Why does radio use decibels instead of plain numbers?
Radio signals span an enormous range — a strong local signal can be a trillion times more powerful than the faint one you’re straining to hear. Decibels compress that range with a logarithm, so instead of writing 0.000000000001 watts you write a tidy -90 dBm. Logarithms also turn the multiplication of gains and losses along a signal path into simple addition.
What is the noise floor?
The noise floor is the background level of random RF energy and receiver noise that’s always present, measured in dBm. A signal must rise above the noise floor to be usable. The gap between your signal and the noise floor is the signal-to-noise ratio (SNR), and digital modes need a minimum SNR to decode cleanly.
Is a signal of -80 dBm stronger or weaker than -100 dBm?
-80 dBm is stronger. Because these are negative numbers, the one closer to zero is larger. -80 dBm is 100 times (20 dB) more powerful than -100 dBm. A useful rule — every 10 dB is a 10x change in power, and every 3 dB is roughly a doubling or halving.