The Decibel

The unit of the decibel is used widely in sound engineering, often in preference to other units such as volts, watts, or other such absolute units, since it is a convenient way of representing the ratio of one signal’s amplitude to another’s. It also results in numbers of a convenient size which approximate more closely to one’s subjective impression of changes in the amplitude of a signal, and it helps to compress the range of values between the maximum and minimum sound levels encountered in real signals. For example, the range of sound intensities which can be handled by the human ear covers about 14 powers of ten, from 0.000000000001Wm-2 to around 100Wm-2, but the equivalent range in decibels is only from 0 to 140dB. Decibels are not only used to describe the ratio between two signals, or the level of a signal above a reference, they are also used to describe the voltage gain of a device. For example, a microphone amplifier may have a gain of 60 dB, which is the equivalent of multiplying the input voltage by a factor of 1000, as shown in the example below:

The decibel is based on the logarithm of the ratio between two numbers. It describes how much larger or smaller one value is than the other. It can also be used as an absolute unit of measurement if the reference value is fixed and known. Some standardized references have been established for decibel scales in different fields of sound engineering. The decibel is strictly ten times the logarithm to the base ten of the ratio between the powers of two signals:

For example, the difference in decibels between a signal with a power of 1 watt and one of 2 watts is 10log(2/1)= 3dB. If the decibel is used to compare values other than signal powers, the relationship to signal power must be taken into account. Voltage has a square relationship to power (from Ohm’s law: W=(V*V)/ R); thus to compare two voltages:

For example, the difference in decibels between a signal with a voltage of 1 volt and one of 2 volts is 20log(2/1)= 6 dB. So a doubling in voltage gives rise to an increase of 6 dB, and a doubling in power gives rise to an increase of 3 dB. A similar relationship applies to acoustical sound pressure (analogous to electrical voltage) and sound power (analogous to electrical power)

Decibel with Reference

If a signal level is quoted in decibels, then a reference must normally be given, otherwise the figure means nothing; e.g. ‘Signal level= 47dB’ cannot have a meaning unless one knows that the signal is 47 dB above a known point. ‘+8 dB ref. 1 volt’ has a meaning since one now knows that the level is 8 dB higher than 1 volt, and thus one could calculate the voltage of the signal.

Sound pressure levels (SPLs) are an example, since the reference level is defined worldwide as 2x10-5 Nm-2 (20 μPa). Thus to state ‘ SPL=77 dB’ is probably acceptable, although confusion can still arise due to misunderstandings over such things as weighting curves. In sound recording, 0 dB or ‘ zero level ’is a nominal reference level used for aligning equipment and setting recording levels, often corresponding to 0.775 volts (0 dBu) although this is subject to variations in studio centers in different locations. (Some studios use 4 dBu as their reference level, for example.) ‘ 0 dB ’ does not mean ‘ no signal ’ , it means that the signal concerned is at the same level as the reference. Often a letter is placed after ‘ dB ’to denote the reference standard in use (e.g. ‘ dBm ’ ), and a number of standard abbreviations are in use, some examples of which are given below. Sometimes the suffix denotes a particular frequency weighting characteristic used in the measurement of noise (e.g. ‘ dBA ’ )

Here are some useful dB equivalents of different voltage or SPL relationships and multiplication factors:

Bibliography:

1. Sound and Recording, Sixth Edition, Francis Rumsey and Tim McCormick.

2. Designing Sound, MIT

3. Sound Design, Maurizio Giri.