Understanding decibels (dB)
The decibel is widely used as a measure of the loudness of sound, but it is actually only a convenient way of specifying the ratio between two quantities, so a 6' 7" man could be said to be 1dB taller than a 6' man! An engineer might use it for such things in jest, but in general the dB is commonly used to express a wide variety of measurements in acoustics and electronics, where it helps in giving a manageable view of things that can cover huge range of values, where only geometric increase or decrease is important. It is especially useful in audio because our ears follow a roughly logarithmic law, referred to by psychologists as Weber's law. The smallest change in loudness that we can detect is about 1dB, or a ten percent change, regardless of whether the sound is very quiet or very loud, in other words we hear loudness 'geometrically' rather than 'arithmetically'.
The decibel is a dimensionless unit like percent and only has meaning when levels are specified relative to a reference level. In audio, the reference level is often specified with a suffix after the dB notation and a brief summary of the most commonly used standards follows:
dBm specifies a power level on a line, referenced to 1mW. In the early days of audio signals were passed along 'matched' transmission lines, meaning that both the source impedance and the load impedance were the same as the 'characteristic impedance' of the line, usually 600 ohms. This ensured that all energy sent down the line ended up in the load resistance, with non reflected back to cause frequency response anomalies or echoes.
dBu specifies that the voltage amplitude of an audio signal is referenced to 0.775 volts rms. This is the same voltage as would be needed to dissipate 1mW into a 600 ohm resistor, and is kept for historical reasons, though 600 ohm matched transmission is rarely used today. The standard for studio interconnection today uses low source impedance (<50 ohms) and high input impedance (10 or 20k ohm). The use of a 'solid' drive ensures more accurate levels, and reflections are not a problem over short paths (say <50m). The u is thought to stand for 'universal' or maybe 'unloaded'. 0dBu is the universal 'Alignment level' within many broadcast organisations and recording studios, with signal levels allowed into the 'headroom' region which may be 24dB, 18dB (EBU recommendation for programme interchange) or 8dB (EBU standard for radio and TV broadcasts and paths).
dBV specifies that the reference amplitude is 1V. This is sometimes used for consumer levels, but dBu are to be preferred because most audio instruments are calibrated in dBu.
This is a measure of sound pressure level, relative to 20 micropascals (µPa = 1×10^-6 Pa), an arbitrary figure chosen as being about the quietest sound a human can hear. This is roughly the sound of a mosquito flying 3 metres away!
This means relative to full-scale or the point at which clipping occurs in a system. It is frequently used in referring to digital signal levels which do not in themselves correspond to any particular voltage, until they are converted using a D-A convertor.
dB AL (Recommended by Lindos)
This means dB relative to Alignment Level, which is a reference level or anchor point against which all else in an audio system is measured. Alignment level may correspond to different voltage levels in various part of the system or signal path (though commonly it will be 0dBu), and in a digital recording it may correspond with varying digital values, though commonly it will be -18dB FS (or -24 or -12) as defined in EBU recommendations. Importantly it is the reference at any point in a system above which Headroom is defined and relative to which noise is measured.
The great merit of this system is that a noise measurement made relative to Alignment Level will always be a reasonable guide to the true intrusiveness of the noise onto typical material, regardless of the headroom. Where less headroom is available for transmission, compression or limiting will usually be used to reduce brief peaks, but this has little effect on overall perceived loudness. A recording may start life with 24dB of headroom, and end up with only 9dB of headroom at the listeners radio or television. Its dynamic range has indeed been reduced, but it will not sound any noisier, assuming that it is the peaks that have been limited. Instead it will have lost sparkle and impact. Specifying noise and headroom separately reflects these different qualities properly.
Decibels in Audio Recording and Reproduction
The dynamic range of the human ear is phenomenal, through a complex gain adjustment system a range of around 140dB is covered. Accurately capturing and reproducing the quietest and loudest sounds audible by humans is a formidable task.
The diagram below shows the range of levels handled by various stages in a typical audio chain, from live sound to loudspeaker. Note how most devices cannot cope with the full range without the use of compression or limiting.
Useful Conversion Tables
It is useful to remember that 6dB is approximately a factor of 2.0, 10dB a factor of 3, and 20 dB exactly 10 times, when referring to voltage levels. When levels are multiplied, dB are added. Thus 26dB represents 20 times.
Power levels, being proportional to the square of the voltage, have different ratios, so that 3dB is twice the power, 6dB is 4 times the power, and 10dB is ten times the power. Usually, these days, it is voltage ratios that are relevant, and the following table will be found useful to commit to memory:
0dB x 1
+1dB x 1.1
0dB x 1
+1dB x 1.1
+3dB x 1.414 (root 2)
+6dB x 2
+10dB x 3
+20dB x 10
+30dB x 30
+40dB x 100
+50dB x 300
+60dB x 1000 etc
-1dB x 0.9
-3dB x 0.707
-6dB x 0.5
-10dB x 0.3
-20dB x 0.10
-40dB x 0.01
-60dB x 0.001 etc