====== Decibel ======

The **decibel (dB)** expresses a logarithmic ratio. Radio engineers use it for gains, losses, signal-to-noise ratios and power levels referenced to a stated value. A bare dB value is a ratio, not an absolute power.

===== Power and voltage ratios =====

<code>
Gain_dB = 10 log10(P_out / P_in)
Gain_dB = 20 log10(V_out / V_in)   (equal resistances)
</code>

The second formula represents the same power ratio only when the voltages are compared across equal resistances, or when the impedance conditions otherwise justify it.

^ Power ratio ^ Change ^
| 2 | about +3.01 dB |
| 10 | +10 dB |
| 100 | +20 dB |
| 0.5 | about -3.01 dB |
| 0.1 | -10 dB |

Gains and losses add when expressed in decibels. A 20 dB amplifier followed by a 3 dB cable loss gives 17 dB net gain, assuming the specified gains apply to the actual operating conditions.

===== dBm and dBW =====

<code>
P_dBm = 10 log10(P / 1 mW)
P_dBW = 10 log10(P / 1 W)
P_dBm = P_dBW + 30
</code>

0 dBm is 1 mW, 30 dBm is 1 W, and 4 W is approximately 36.02 dBm. A negative dBm value represents a positive power smaller than 1 mW. It is not negative physical power.

===== Reading signal reports =====

An SNR in decibels compares signal power with noise power in a stated bandwidth. [[ft8|FT8]] and [[wspr|WSPR]] reports use a reference noise bandwidth; a negative report does not mean the decoder is working without signal energy. Reports from different bandwidths or measurement methods cannot be compared directly.

An antenna gain figure also needs its reference. The label following dB is part of the measurement and should be preserved when documenting a station.

===== References =====

  * [[https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8|NIST Guide to the SI: logarithmic quantities]].
  * [[https://wsjt.sourceforge.io/FT4_FT8_QEX.pdf|Franke, Somerville and Taylor: FT4 and FT8 communication protocols]].