Table of Contents
What is a Decibel?
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. It was originally developed by Bell Telephone Laboratories and named after Alexander Graham Bell. The decibel scale is logarithmic because human perception of sound, light, and other stimuli follows a logarithmic rather than linear relationship.
One bel represents a ten-fold increase in power. Since the bel is often too large a unit for practical use, the decibel (one-tenth of a bel) is the standard unit. Decibels are used extensively in acoustics, electronics, signal processing, and telecommunications because they allow very large or very small ratios to be expressed as manageable numbers.
Decibel Formulas
Power and voltage decibels differ by a factor of 2 because power is proportional to the square of voltage (P = V²/R). When converting between the two, remember that 20 dB of voltage gain equals 20 dB of power gain, but the underlying ratios differ: a 20 dB power ratio is 100:1, while a 20 dB voltage ratio is 10:1.
Common dB Values
| dB Value | Power Ratio | Voltage Ratio | Example |
|---|---|---|---|
| 0 dB | 1:1 | 1:1 | No change |
| 3 dB | 2:1 | 1.41:1 | Double power |
| 6 dB | 4:1 | 2:1 | Double voltage |
| 10 dB | 10:1 | 3.16:1 | 10x power |
| 20 dB | 100:1 | 10:1 | 100x power |
| -3 dB | 0.5:1 | 0.71:1 | Half power |
Applications
- Acoustics: Sound pressure level (SPL) in dB relative to 20 μPa
- Electronics: Amplifier gain, filter attenuation, signal-to-noise ratio
- Telecommunications: Link budgets, antenna gain, cable loss
- Audio: Speaker sensitivity, microphone output levels
Frequently Asked Questions
What is the difference between dB and dBm?
Plain dB is a relative measurement comparing two values. dBm is an absolute measurement referenced to 1 milliwatt. So 0 dBm = 1 mW, 10 dBm = 10 mW, and 30 dBm = 1 W. Other absolute dB units include dBW (referenced to 1 watt), dBV (referenced to 1 volt), and dBu (referenced to 0.775 V).
Why do we use logarithmic scales?
Logarithmic scales compress large ranges into manageable numbers. Audio signals can vary by a factor of a million or more in power. Using decibels, this becomes a 60 dB range, which is much easier to work with. Additionally, gains and losses in a signal chain can be simply added rather than multiplied when expressed in dB.
How do I add dB values?
You cannot simply add dB values of individual sources. You must first convert to linear values, add them, then convert back. For two equal sources, the combined level is the original level plus 3 dB (double the power). For sources differing by more than 10 dB, the weaker source adds negligibly to the total.