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The decibel in practice

In audio and in nature itself, the phenomena under study project results with numerical values that are too large and difficult to handle.

Possibly in the world of audio there is not a word as mentioned and applied (especially empirically) as the decibel (dB).

dBm, dBu, dBA, dBV, etc., are all decibels but do not mean the same thing. In the domains of electroacoustics and acoustics of enclosures we will always be doomed to use in some way the decibel in the design stages and that obviously concerns directly to electronic engineers, telecommunications and acoustic physicists.

If we think about the daily work of musical sound capture in the studio or simply in a cinematographic documentary, situations often arise in which we have to interconnect various elements, whether microphones, recorders, processors, etc.

The audio input and output levels are different depending on whether we are using professional equipment or for the "general public" and its value can be specified in decibels. Urban and industrial ambient noise are equally measured in decibels but they are not the same as those I mentioned earlier.

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To understand it clearly you have to know first of all that the decibel is a mathematical representation to reduce very large numbers to smaller values of 2 or 3 figures. In the audio and in nature itself the phenomena under study are projected results with numerical values too large and difficult to handle. In addition to this, the analysis of magnitudes can be much clearer when comparing values: how much one value is greater or less than another.

Well, that is precisely what the decibel (dB) does, quickly compare and evaluate the relationship between magnitudes of the same nature. It should be noted that the decibel is not a unit in itself but a form of relative measure in which a logarithm of base 10 intervenes.

I hope that people who are not very familiar with mathematics will not abandon the article at this point as I will try to explain it in the simplest way.

Graham Bell

The decibel (dB) is one-tenth of a Bel (B), in honor of Alexander Graham Bell, which is defined as follows:

Bel= log (P2/P1)

The decibel is strictly defined by 10 times the decimal logarithm based on 10 of the power ratio of two signals.

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dB=10 log (P2/P1)

The decibel can be used as the absolute unit of measurement if the reference value P1 is fixed and known. In the case of sound engineering, several standardized reference levels were adopted.

It is clear that to do the calculations you have to use a calculator but I will present the values of logarithms most used.

log 2 = 0.3

log 4 = 0.6

log10 = 1

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log 100 = 2

log 1000 = 3

For example, the difference in decibels between a signal of 1 Watt of power and another of 2 Watts will be:

dB= 10 log (2/1)= 10 log 2= 10 x 0.3 = 3 dB

If we consider values different from those of electrical or sound powers such as voltages or acoustic pressures then we have to take into account how these are related to the powers. In the electrical case according to Ohm's law P = V2/R (V squared) and applying the laws of logarithms we obtain:

dB= 20 log(V2/V1)

For example, the difference in decibels between a voltage of 1 volt and another of 2 volts is 20 log

(2/1)= 20 log 2= 20 x 0.3= 6 dB

Doubling the voltage is equivalent to increasing it by 6 dB; doubling the electrical power is equivalent to increasing it by 3 dB.

In practice

Let's now look at some practical examples:

1. What is the gain of an amplifier of 50 Watts of power when we feed it with 0.5 Watts?

G (gain)= 10 log (50/0.5)= 10 log 100= 10 x 2= 20 dB

2. A microphone produces a voltage of 2 mV (0.002 Volts) and the console preamplifier 2 Volts. What is the gain of the preamplifier?

G= 20 log (2/0.002)= 20 log 1000= 20 x 3= 60 dB

When the level of a signal is expressed in decibels it always has to be referenced to something otherwise the value does not make sense. There are different levels of reference in the world of audio and here we will only mention the most used.

Reference 1 milliwatt: corresponds to a voltage of 0.775 volts applied to a resistance of 600 ohms and dissipating a power of 1 milliwatt.

0 dBm= 1 milliwatt (0.775 volts over 600 ohms)

0 dBm does not mean "absence of signal" but the signal considered is at the same level as the reference signal.

When it comes simply to voltage we talk about dBu (Europe) or dBv (USA).

Reference 0.775 volts:

0 dBv= 0 dBu= 0.775 volts

+ 4 dBv= 1.23 volts; +6 dBv= 1.66 volts; - 60 dBv= 0.775 volts

Reference 1 volt ("general public" equipment):

0 dBV= 1 volt

+ 6 dBV= 2 volts; - 60 dBV= 1 millivoltium (mV); - 10 dBV = 0.316 volts.

Level indicators such as PPM modulometers have markings of 0 dB on their scales indicating the maximum level allowed to avoid saturation. The corresponding electrical voltage differs according to countries and international standardization bodies.

With regard to the sound pressure level SPL (Sound Pressure Level) the reference level is universally recognized: 0.00002 N/meters squared = 20 μPa (microPascals) = 0.00002 Pa

Example: in a sound booth 8 Pa (Pascals) are measured. What is the sound pressure level?

G= 20 log (8/0.00002)= 20 log (0.00004)= 112 dB SPL

A pressure of 1 Pa corresponds to a level of 94 dB SPL.

Electroacoustic applications

Returning to electroacoustic applications, it is important to know that the levels of the signals coming from the microphones are between -40 dBv and -60 dBv (capacitors and dynamics respectively).

Professional line signals generally work at +4 dBm (1.23 V) and "general public" at -10 dBV (0.316 V), that is, 4 times less strong than the first, that is, 12 dB!! If the output of a console is sent to +4 dBm towards an input at -10 dBV we will be saturating from the input and the solution is to use an attenuator of 12 dB or at least one of 10 dB.

The correct understanding of the decibel will also allow us to interpret the data found in the technical specifications of the equipment and can avoid many headaches when interconnecting them.

The sensoriality of our ears is "logarithmic" and it is not gratuitous that the decibel as a logarithmic representation was conceived to simplify things and not to complicate them.

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