The decibel (dB) measures power and amplitude ratios on a logarithmic scale. It equals one-tenth of a bel and was named after Alexander Graham Bell.
Power and Root-Power Relationships
The decibel expresses two main types of ratios:
- For power quantities: $$ L_P = 10\log_{10}(P/P_0) $$ dB
- For root-power quantities: $$ L_F = 20\log_{10}(F/F_0) $$ dB
A one decibel change represents a power ratio of approximately 1.26 and an amplitude ratio of about 1.12.
Historical Development
The Bell System created the decibel in the 1920s to measure signal loss in telephone circuits. Before this, they used “miles of standard cable” (MSC) as their unit. In 1924, they introduced the Transmission Unit (TU), which later became the decibel in 1928.
Common Applications
Acoustics
Sound pressure levels use dB SPL, referenced to 20 micropascals – the typical human hearing threshold. A normal conversation measures about 60 dB SPL, while a rock concert can reach 120 dB SPL.
Electronics
Engineers use decibels to express:
- Amplifier gains
- Signal attenuation
- Signal-to-noise ratios
The dBm unit references 1 milliwatt of power, while dBV references 1 volt.
Telecommunications
Network engineers measure:
- Signal strength in dBm
- Cable losses in dB/meter
- Antenna gains in dBi (compared to an isotropic radiator)
Key Properties
The decibel’s logarithmic nature offers two main advantages:
- It compresses large value ranges into manageable numbers
- It allows multiplication of power ratios through simple addition
For example, three amplifiers with gains of 10 dB, 8 dB, and 7 dB have a total gain of 25 dB.
Practical Conversions
Some useful reference points:
- 3 dB represents approximately double the power
- 10 dB represents a 10-fold increase in power
- 20 dB represents a 100-fold increase in power
The decibel remains fundamental to audio, telecommunications, and electronics, providing an intuitive way to work with exponential relationships in signal processing and transmission.
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power ratio of 101/20 (approximately 1.12).
| decibel | |
|---|---|
| Unit system | Non-SI accepted unit |
| Symbol | dB |
| Named after | Alexander Graham Bell |
| Conversions | |
| 1 dB in ... | ... is equal to ... |
| bel | 1/10 bel |
The unit fundamentally expresses a relative change but may also be used to express an absolute value as the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "V" (e.g., "20 dBV").
Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm with base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.
The definition of the decibel originated in the measurement of transmission loss and power in telephony of the early 20th century in the Bell System in the United States. The bel was named in honor of Alexander Graham Bell, but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and engineering, most prominently for sound power in acoustics, in electronics and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.