# Decibels Demystified, Part 2

Illustration: Karyn Kraft

In the past two issues, I've presented the underlying ideas necessary to understand decibels. Now that those concepts have been discussed, it's time to dig into information that is more practical and that relates directly to audio equipment.

There are several standard reference values to which power and voltage are compared using decibels (see the table “The Decibel Zoo”). Unfortunately, that leads to much confusion. Remember that all voltage in audio equipment is based on alternating current and measured using the root mean square (RMS) method.

As mentioned last month, power-referenced decibels are used for circuits that draw a significant amount of current from the voltage source. In the following equations, the amount of power being used as a reference is represented by P0, and the amount of power being measured is P1. If the measured power is equal to the reference power (P1 = P0), the difference is 0 dB. In other words, 0 dB is the *reference level*. (Recall from last month, if a = 10b, then b = log a.)

The Decibel Zoo Decibel Type Standard Reference (0 dB)

dBm 1 mW dBu 0.775 VRMS dBV 1 VRMS

*10 log (P1/P0) = 10 log 1= 10 × 0= 0 dB*

If the measured power is twice the reference value (P1 = 2P0), the difference is about 3 dB.

*10 log (P1/P0) = 10 log (2P0/P0)= 10 log 2= 10 × 0.301= 3.01 dB*

If the measured power is ten times the reference value (P1 = 10P0), the difference is 10 dB.

*10 log (P1/P0) = 10 log (10P0/P0)= 10 log 10= 10 × 1= 10 dB*

The most common power-referenced decibels are denoted dBm, and the reference power value (P0) is 1 milliwatt (mW), or 0.001W. In other words,

*0 dBm = 1 mW*

That type of decibel is handy when talking about small but significant power values such as those that exist in most professional audio equipment. In fact, dBm is typically used to specify the nominal signal level in professional gear.

## HIGH-VOLTAGE DECIBELS

Voltage-referenced decibels are used when a circuit draws negligible current from the voltage source (that is, when the impedance is high and the load is small). That applies to most consumer and semipro gear, including synthesizers. The reference level is still 0 dB; however, if the measured voltage is twice the reference value (V1 = 2V0), the difference is 6 dB, not 3 dB as in power-referenced decibels.

*20 log (V1/V0) = 20 log (2V0/V0)= 20 log 2= 20 × 0.301= 6.02 dB*

If the measured voltage is ten times the reference value (V1 = 10V0), the difference is 20 dB.

*20 log (V1/V0) = 20 log (10V0/V0)= 20 log 10= 20 × 1= 20 dB*

One common voltage-referenced decibel is denoted dBu. The *u* stands for unloaded and refers to the very small load that high-impedance circuits present to the voltage source. The reference voltage for dBu is 0.775V. In other words,

*0 dBu = 0.775V*

Perhaps the most common voltage-referenced decibel is denoted dBV, for which the reference voltage is 1V. In other words,

*0 dBV = 1V*

That type of decibel is generally used to measure the signal level in consumer and semipro gear. (See the table “dBV Versus dBm/dBu” to compare decibel types.)

You might occasionally come across a similar decibel designation, dBv, which is completely equivalent to dBu. Don't let the *v* fool you; it is not the same as that in dBV. The dBv decibel is not used much today.

## 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.

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