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Decibels
The logarithmic scale for gain, loss and signal strength.
The logarithmic scale for gain, loss and signal strength.
A decibel (dB) expresses a ratio on a logarithmic scale. It answers "how many times stronger or weaker?" with a small, additive number. Radio needs this because signal levels span an absurd range: a 100 W transmitter can be a hundred billion billion times stronger than a very faint signal a good receiver can still copy. On a log scale that whole span is only about 200 dB.
Learn three anchors and you can estimate almost anything. 3 dB is a doubling, 10 dB is ten times, and every 10 dB is another factor of ten. Gains add as dB, so 6 dB is two doublings (×4), 13 dB is 10 + 3 (×20), and 7 dB is 10 − 3 (×5).
| dB | Power ratio | Voltage ratio |
|---|---|---|
| 1 | 1.26 | 1.12 |
| 3 | 2.0 | 1.41 |
| 6 | 4.0 | 2.0 |
| 10 | 10 | 3.16 |
| 20 | 100 | 10 |
| 30 | 1,000 | 31.6 |
| −3 | 0.5 | 0.71 |
| −10 | 0.1 | 0.32 |
| −20 | 0.01 | 0.1 |
Voltage and current use 20 instead of 10 because power goes as the square of voltage: double the voltage across a fixed resistance and you get four times the power, which is 6 dB, not 3. A factor of 2 is 6 dB if it is voltage and 3 dB if it is power.
A bare dB is a ratio with no absolute level. Adding a letter fixes a reference:
| Unit | Reference | Example |
|---|---|---|
| dBm | 1 milliwatt | 0 dBm = 1 mW, +30 dBm = 1 W, +50 dBm = 100 W |
| dBW | 1 watt | +20 dBW = 100 W |
| dBi | an isotropic radiator (an ideal point source) | a half-wave dipole has 2.15 dBi |
| dBd | a half-wave dipole | a dipole is 0 dBd |
The two antenna units differ by a fixed 2.15 dB: dBi = dBd + 2.15. A gain quoted in dBi sounds bigger than the same antenna in dBd, so check which is meant when comparing antennas. See Gain and directivity.
dB values of the same kind combine freely: a level in dBm plus a gain in dB is a level in dBm. Subtract two levels in dBm and you get a plain dB. Never add two dBm values together, since that would mean multiplying two powers.
Here 3 dB of cable loss halves the power, and a 6 dB antenna gain then multiplies it by four, for a net +3 dB: 100 W becomes about 200 W of effective radiated power. Working in dB turns that chain of multiplying into simple addition; see Feed line loss and velocity factor and Gain and directivity. The same arithmetic describes receiver sensitivity and Noise and signal-to-noise ratio, and one nominal S-meter step is 6 dB, a factor of four in power.