Decibel

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Decibel: a simple guide

What is a decibel?
The decibel (dB) is a unit for expressing how big one value is compared to another, using a logarithmic scale. It is one tenth of a bel, a name that comes from Alexander Graham Bell. A decibel by itself doesn’t measure an absolute amount; it measures a ratio between two quantities such as power or amplitude (root-power).

Power versus amplitude
- Power ratio: dB = 10 log10(P / P0)
- Amplitude or root-power ratio (like voltage or sound pressure): dB = 20 log10(A / A0)
Two signals that differ by 1 dB have a power ratio of about 1.26 (P / P0 ≈ 1.26) or an amplitude ratio of about 1.12 (A / A0 ≈ 1.12).

Absolute reference values (suffixes)
Sometimes the decibel is used with a reference value to give an absolute level, written with a suffix:
- dBm: reference is 1 milliwatt (mW)
- dBW: reference is 1 watt (W)
- dBV, dBu: references for voltage levels
- dB SPL: sound pressure level, reference is 20 micropascals in air
The suffix tells you what the ratio is measured against. If the reference isn’t stated, the number is usually understood as a relative level (a gain or loss).

Why use decibels?
- They’re great for very large or very small ratios because the numbers stay manageable.
- They make multipath or chained effects easy: gains and losses add in decibels. If you have several stages, you can add their dB values to get the total gain or loss.

Common rules and quick facts
- A change of 10 dB means a tenfold change in power (or about a 3.16-fold change in amplitude). More precisely, power changes by exactly a factor of 10^(dB/10).
- A change of 20 dB means a tenfold change in amplitude.
- A 3 dB change is roughly a doubling or halving of power (10^(±3/10) ≈ 2.00).
- In acoustics, the common reference for sound levels is dB SPL, using 20 log10(p/p_ref) because sound pressure is a root-power quantity.
- The decibel is not an SI unit, but it is widely used in engineering, electronics, telecommunications, and acoustics.

Caution with adding decibels
Because dB are logarithmic, you can’t simply add or subtract dB values like ordinary numbers when sounds or signals interact. To combine levels accurately, you convert to the linear scale, add or subtract, then convert back to dB (logarithmic addition).

In everyday use
You’ll see decibels everywhere: measuring sound levels (dB SPL) in a room, rating the gain of amplifiers and attenuators, calculating link budgets in communications, and describing dynamic range in cameras and audio gear.