Decibels Demystified, Part 2

Aug 1, 2001 12:00 PM, By Scott Wilkinson

V, L AND G

Among the many terms tossed around when discussing audio systems, perhaps the most misused are volume, level, and gain. All three words have something to do with the amplitude of an AC electrical signal, and they also relate to decibels, but their precise meaning is not clear to the many people who use them with reckless abandon.

People often use volume to describe acoustic sound intensity or the amplitude of an AC electrical signal. Technically speaking, however, volume is defined as power, and it is typically applied to the output of a power amplifier. If you turn up the volume, you are increasing the power output in watts.

The word level is often used in conjunction with voltage or power values, as in “the power level is so many watts” or “the voltage level is so many volts.” However, level is defined as the magnitude of a quantity with respect to a particular reference value. (Sound familiar?) As a result, the word is correctly used only in conjunction with decibels. For example, the audio-signal level in professional audio equipment is expressed in dBm, which is referenced to 1 mW.

Gain is defined in several ways, which doesn't help matters. Unless otherwise specified, it usually refers to the change in a signal's power and is measured in decibels. In that case, gain has no standard reference value. Instead, the gain compares the signal's power values before and after the change. For example, if a signal's power increases by a factor of two, the gain is 3 dB.

dBV Versus dBm/dBu

dBV	Volts RMS	dBm (into 600•) or dBu
+6.00	2.000	+8.2
+4.00	1.600	+6.2
+1.78	1.228	+4.0
0.00	1.000	+2.2
-2.20	0.775	0.0
-6.00	0.500	-3.8
-8.20	0.388	-6.0
-10.00	0.316	-7.8
-12.00	0.250	-9.8
-12.20	0.245	-10.0
-20.00	0.100	-17.8

IT'S ALL RELATIVE

The concept of gain brings up another application of decibels: they are often used to compare two voltage or power values without respect to a standard reference level. When decibels are used to relate two arbitrary values in that way, they are expressed in dB without a modifier (such as m or V) because they use no standard reference. That approach is typically used to describe the change in a signal that is altered by adjusting a control. For example, you might manipulate an equalizer control to reduce the level of a frequency band by 3 dB.

In addition, it doesn't matter whether power or voltage values are compared; the number of decibels remains the same in either case. If you change the power flowing through any circuit with a given impedance, the voltage also changes but by a different factor than the change in power. The factor by which the power changes is the square of the factor by which the voltage changes. For example, if the power increases by a factor of four, the voltage increases by a factor of two (the square root of four). That is due to the fact that power is proportional to the square of the voltage, as revealed in Joule's law:

P = K × V × I
= K × V²/Z

Remember that K is a constant that depends on the reactance of the circuit, and it can be ignored for these purposes. Of course, V is voltage, I is current, and Z is impedance.

PRACTICAL EXAMPLES

It's time to look at a few practical examples. You've probably seen frequency-response specifications, which identify the range of frequencies that a piece of audio gear can effectively pass from its input to its output at a given gain. For example, a piece of gear might have a frequency response of 50 Hz to 18 kHz, ±3 dB. That means that all frequencies between 50 Hz and 18 kHz will pass from the input to the output with no more than 6 dB of variation in gain (3 dB above the input level and 3 dB below) from one frequency to another.

Equalizers include one or more boost/cut controls that amplify or attenuate different ranges, or bands, of frequencies. For example, many EQs boost or cut the frequencies in each band by ±12 dB. At maximum boost (+12 dB), the signal's power in that frequency band is increased by a factor of 16, and the voltage is increased by a factor of 4.

Another characteristic of most audio gear is the signal-to-noise ratio (which is often abbreviated S/N). S/N is the difference in decibels between the nominal signal level and the noise floor of the equipment. For example, in many analog tape decks, the noise floor is 45 to 65 dB below the nominal signal level, which corresponds to 0 on the tape deck's volume unit (VU) meters, so S/N = 45 to 65 dB.

You can record signals at a level as much as 5 dB above the nominal level on an analog tape deck, which determines the dynamic range of the deck. By definition, dynamic range is the difference in decibels between the maximum undistorted signal level and the noise floor. In the example from the previous paragraph, the dynamic range is 50 to 70 dB.

Decibels are critical to understanding and effectively using audio equipment. Now that you have a basic understanding of decibels, you should be able to make the most of your studio and the signals that flow through it.

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Scott Wilkinson has never met an electrical decibel he didn't like.