Decibel

The decibel may be a mysterious unit of measurement to many and most people do not understand it's definition and use. The actual unit of measurement is the "Bel" and was named in honor of Alexander Graham Bell. It is almost almost always used with the standard prefix "deci" which means tenths. This is done because it results in nicer numbers. If an amplifier doubles the power of a signal its gain is 0.3 Bels. Most people prefer to say 3 decibels instead.

The Bel is the base 10 logarithm of the ratio of the measured power with respect to the reference power.
Bels = Log10 (Power / RefrencePower)
decibels = 10 * Log10 (Power / RefrencePower)
An amplifier that has a power gain of ten has a gain of 1 Bel or 10 decibels. (power gain is the output power with respect to the input power).

The advantage of a logarithmic unit is that when we cascade amplifiers and pads we can calculate the total gain and loss both addition and subtraction instead of multiplication and division. (cascade == to connect in series i.e.: mic into mic preamp, mic preamp into EQ, EQ into compressor, compressor into line amp, etc.)

Some common symbols that indicate decibels (db) with respect to a reference level.

Symbol Power reference
dbm 1 milliwatt Very common in audio and many other places
dbW 1 Watt
dbK 1 Kilowatt Used in high power RF work - such as Broadcast transmitters.
dbu 1 uV at 75 ohms The power equal to 1 microvolt across 75 ohms - Used in cable TV and receive antenna signals

Although Bels (and decibels) are the logarithm of a power ratio, we often use them to measure voltage gain as if the input and output impedance of the amplifier are the same. In audio this is rarely true but it is such an extremely useful fiction that we do this all the time. The big problem is that many people do not understand that we are doing this and get confused.

When we are using this very useful fiction, the Bel is twice the base 10 logarithm of the ratio of the measured voltage with respect to the reference voltage. We multiply the result by two since power is proportional to the square of the voltage across a constant load resistance. (Power = Voltage * Voltage / Resistance)

Bels = 2 * Log10 (Voltage / RefrenceVoltage)
decibels = 20 * Log10 (Voltage / RefrenceVoltage)

Some common symbols that indicate decibels (db) with respect to a reface level using voltage and pretending the input and output impedanceare the same:

Symbol Power reference
dbV 1 Volt
dbmv 1 millivolt
dbu 1 microvolt (as used in cable TV and receive antennas but ignoring and impedance differences)

Some examples of approximate db readings converted to power and voltage ratios:

The ratio of two levels according to a scale where a certain percentage change is one unit. [NOUN]
Useful Notes in using the Decibel Unit:
1. One dB represents approximately the smallest volume change which can be heard if listened for carefully. One dB represents an approximate change in pressure of 12%.
2. Three dB represents a small but noticeable change in volume.
3. Six dB represents a change in level of twice (or half) as much pressure.
4. A certain amount of dB represents a change of level (a change from what was before or from a standard level).
5. A certain percentage change in level will always be the same amount of change in dB.
6. Adding dB represents a multiplication of level.
7. 0 dB a is starting point in the comparison and does not mean no level.
Important Note About Decibels: It is recommended that you read all of the notes about the decibel as this is one of the most confusing terms in audio.

History and Original Use

The unit was originally invented by Bell Telephone Labs as the Bel and given its name after Alexander Graham Bell. The decibel is 1/10 of this original unit. The Bel unit was defined as a ratio of power levels of 10 to 1(ten times the power or one-tenth the power).
In Telephones, amplifiers are driving speakers and doing so over long lines. To drive speakers there needs to be a power transfer. So if you are in the business of driving speakers, you will analyze how much power there is available and how much power was lost in getting the signal to the speaker.

What does Power have to do with Volume?

More power means more volume can be achieved in the speaker but these two factors don't directly relate. Volume has to do with the amount of Sound Pressure there is. The ear is a pressure sensitive device. Power (in an electrical circuit) is not just the pressure but also the flow. In electricity, the pressure is the voltage and the amount of flow is the amount of current. If you put twice as much voltage into a device (say a light bulb) there would be twice as much current; because both the voltage doubled and the current doubled, the power has been multiplied by a factor of four. In order to double the pressure of the sound pressure wave out of a speaker, you need 4 times the amplifier power to drive it.

Does Pressure and Voltage Directly Relate To Volume?

For all practical purposes, yes. Although the ear is not exactly pressure sensitive, it is closer to being pressure sensitive than to being anything else.
Many studies have been done regarding how changes in perceived loudness (volume) relate to level changes in dB. All of these studies suffered from problems in getting exact figures in that the personal opinion of listeners had to be consulted to get data for the studies.
The results of the studies did show that the perceived change in loudness varied greatly (by some 30% difference) depending on the starting volume, the frequency of the sound and the complexity of the wave. The Audio Cyclopedia, Second Edition, pages 17-18] Furthermore, the greenest recording student listening to music played through a console with a meter can quickly discover that an increase in level of a certain number of dB is much easier to hear than a reduction of level by the same amount of dB.
Someone (or some people) interpreted test data and made a generalization that a 10 dB change in level was twice (or half) the volume and many texts compound this useless and deceiving assertion. In practice the 6 dB change for full fidelity music represents twice (or half) the volume better than the confusing 10 dB. It has good scientific basis in that twice the pressure is an increase in 6 dB.

The following is presented as factors supporting this:

1. For centuries, composers and conductors have used a formula that it takes four times the musicians to get twice the volume. If a composer/conductor wanted the violins to be twice as loud, they would specify 4 times as many. This is four times the power or a 6 dB volume increase.
2. If 10 dB is twice the volume, then 10 people talking (10 times the power) would be twice as loud as one person talking. Any day care worker can tell you that 10 kids are much louder than twice the volume of one kid. If 6 dB is twice the volume, four kids would be twice the volume of one kid; you might have a chance of a day care worker agreeing with you on this.

Modern Use of The Decibel Unit

Statements such as "voltage ratios cannot be expressed in decibels because decibels are, by definition, a ratio of power levels," ignores the current use of the unit and published standard decibel notation. What is the case here is that the use of the term in the profession demands a new definition of the term. It is common in language for the manner that the word is used in society to be the final determining standard for what a word means and technical terms are no exception. When a technical term is being commonly used by professionals differently than the dictionaries say it should be, it is time for the dictionaries to be re-written.

When you were little, it's possible that your teacher would not allow you to use the word "can" in asking a question. She may not have let you leave the room until you said, "May I go to the bathroom?" She was simply trying to get you to use words correctly. Most dictionaries of today allow you to use the word "can" when asking a question - it is too common in society for the writers of dictionaries to ignore. The same kind of thing has happened to the decibel. Except for the final amplifier that drives a speaker almost all equipment used in recording and sound reproduction is voltage sensitive. A change in voltage gain is a change in level, something to be measured, observed and used by recording engineers and design engineers. The dB, as read on meters, as specified for the level in and out of equipment, and as given in overload levels are voltage levels. The units dBV and dBu are based on standard levels of voltage completely divorced of current in the circuit or power levels.