Decibels (dB and dBm)

In radio, power levels span a colossal range: a strong signal can be a billion times more powerful than a weak one. To keep things readable, we work on a logarithmic scale: the decibel.

The dB expresses a ratio between two powers:

dB = 10 · log₁₀(P₁ / P₂)

A few landmarks worth memorising:

• +3 dB ≈ ×2 (double the power)
• +10 dB = ×10
• −10 dB = ÷10
• +20 dB = ×100

The dBm is an absolute dB, referenced to 1 milliwatt: 0 dBm = 1 mW, −30 dBm = 1 µW, −90 dBm = a very weak yet perfectly usable radio signal.

On your analyser, the spectrum's vertical axis is in dB. Careful: with a HackRF these values are relative (they depend on the gain you set) — excellent for seeing and comparing signals, but not a calibrated absolute dBm measurement.

What really matters is not the raw value but the gap between a signal and the floor: that's SNR — see Bruit de fond, SNR et sensibilité.

The decibel cheat sheet

Everything combines by addition: +13 dB = +10 then +3 = ×20. That's the whole magic of the logarithm.

dBm, dBi, dBd — three cousins not to confuse

• dBm: an absolute power, referenced to 1 mW (0 dBm = 1 mW; +30 dBm = 1 W).
• dBi: an antenna gain, referenced to the ideal isotropic antenna.
• dBd: the same gain referenced to a dipole — 0 dBd = 2.15 dBi (a classic exam trap).

A chain example: transmitter +30 dBm → cable −3 dB → antenna +5 dBi ⇒ EIRP ≈ +32 dBm. You just add, nothing else.

Your turn

Swapping antennas, your signal goes from −90 to −70 dBm. How many times more received power? (+20 dB → ×100.)

👉 Read the dB axis on a real spectrum: First contact