"Reprint" What is a decibel?

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Everyone is a master of music with computer ... Well, that classmate! Don't be nervous ~ See you excited, Master actually also nothing great ... Don't believe me? Let me ask you a few questions, you can answer it, you are great! When we use the computer to make music, we often come into contact with a variety of tables, whether it is the measurement of the table, they are inseparable from a unit-decibel (db), my problem is related to it, listen to:
1. What is the difference between 20dB and 60dB? (Don't Answer me 60-20=40 (DB), I smoke you! You tell me how loud 40dB is, do you use your fingers to measure distances on the peak meter? ）
2. How loud does 72dB and 66dB sound fit together? Stop Look at your lips, I know--138db, right? Come on, this is the equivalent of a jet fighter flying a mile from your side. Is you nuts? And I'm talking about two numbers that are equivalent to a drummer playing with a guitarist, do you think a band performance is as noisy as a fighter plane in an airbase? ）
3. Often hear people say some equipment indicators, -10DBV and +4dbu, this is very familiar with it? They say that +4dbu's equipment belongs to "professional grade", -10DBV belongs to "civil grade", do you know why this is?
4. Why do some articles say that digital devices do not exceed 0dB, while analog devices can be exceeded?
5. What is the dynamic range of 16bit digital audio? What about 24bit? If you want to say 21bit, can you say it?
6. How much can a 100-watt guitar speaker ring than a 50-watt guitar speaker?
The above questions if you think it is a small thing for you, then you can not read this article, you are the real tall man! If you pull your scalp hard ... Come on, you need at least a scientific calculator to get your scalp out of the question! What, do you still think it's easy?

I know that everyone can use the computer to make the song, but thanks to the advanced technology and the operation of the Fool, if you put in the 30 's, you think that you can do what you know to do today? I have seen a lot of "master" is so, they may not even know how the decibel is how the situation! Of course, some people are also opposed and think that it is the outcome, not the process, that matters. The truth doesn't matter, can make it. What I'm trying to say is that the real recording engineers don't think so, because they really know the art of recording--not just pulling a bunch of buttons--if you want to create an unprecedented sound, you have to understand all the mysteries. So I said, those who just satisfied with the imitation, and even the imitation of the nondescript "master" is actually nothing great.

I am glad that you can insist on seeing here, it means that you are not an easy to meet the guy, your head is full of endless desire for knowledge. Perhaps you will read the instructions and help documents for all the equipment you can find, and you will often see nouns such as DBSPL, DBu, DBV, DBm, DBVU, DBFS, etc., and decibels. Unfortunately, there is little detail in this, and you often confused: who are they? What exactly is their relationship? Don't blame the vendors for not explaining these guys in the instructions, because they just want you to be the "master" I just said, so that you can buy their products/software from generation to generation, and if you understand them slowly, maybe you won't. ^^ Of course, these are really not easy to understand, because they are involved in mathematics, physics and other related expertise. (I also say that, in fact, not so exaggerated, as long as you can pass the copy transcripts, you can understand) below let's see what is the decibel is what?
Decibel: A unit that typically represents the relative difference in power or intensity of two sound signals or power signals, which is equivalent to 10 times times the ratio of two levels of a common logarithm. "

This is a general definition of the science of decibels that I found in a professional dictionary. That's what the decibel is! "But ... Wait a minute! ' Relative difference ... Two levels of ratio ... Commonly used logarithm ... ' this .... What's this all about? I can't read it! "Oh, don't worry, I certainly will not let you look at a long time to get such a conclusion, please listen to me slowly."
First of all, according to the above definition, find the subject, predicate and object, the other parts of the first omitted, we can get "decibel is a unit", this conclusion is clear? Our common sense tells us that units are used to measure, with a certain instrument or a formula, we can get the specific value of this unit. So what does the decibel measure? The practice tells us that the peak table and so on can measure it, but we do not know what the measured data means to us, even if it is an abstract meaning can ah! So we need math to help us with this problem. The scientists chose to use logarithms.

Why do you use logarithms? Because they are lazy ... I'm not kidding! As you delve into the mysteries of decibels, you'll find that you need to deal with a whole bunch of troubling numbers, and scientists--a bit like an instrumental performer--are doing everything possible to make the problem easier. Let's see how complex and simple the decibel is (please, you've already seen this, give me some patience and support, and get to the point now):
The loudness of a sound is the sum of energy in an area of a specified size within a unit of time (this you know?). But I do not know that it is OK, hehe):
loudness = ENERGY/(time * area)
We know that energy and time ratio is power (this should always be known, right?) You don't know? Holy...... Really all back to my dear teacher), so:
loudness = Power/Area
The unit of power is Watt, the area we use square meters, then the loudness of the unit is: w/m ^ (forum is not good to write special symbols, I use ^ instead of square, the same below)
Now let's assume that you know the smallest sound loudness that ordinary people can hear. 000000000001 w/m ^, and the sound that starts to feel painful is 1 w/m ^, then between these two numbers we get a lot of values, like. 000792710162 w/m ^, and. 000006288415 w/m ^ et cetera, try to compare these two numbers quickly and figure out how bad they are! What, are you getting dizzy? Can you imagine our peak meter being expressed in this unit? Oh, my God......

Our lovely scientists are not going to do this stupid thing, so they write the formula:
Log (. 000792710162) = 3.1
Log (. 000006288415) = -5.2
That's a lot of bad, isn't it? It's 2.1. Ah? What did you say? What's This 2.1? is the volume of the poor Ah, smart you may suddenly remember what it called-yes, it is bale!
However, this is not a decibel, because the scientists after Bell inherited his tradition, and then to carry it forward (what tradition?) Lazy! ）...... This time, they don't even want to see the decimal point, so they multiply by 10 and become this:
Ten * log (. 000792710162) = 31
Ten * log (. 000006288415) = -52
The answer has changed from 2.1 to 21, and this "21" is our main character today-the decibel.

How are the scientists smart? Students, we have to learn their random use of various formulas of good way ... Uh, well, I mean: dare to explore! They're lazy too, aren't they? and more lazy! The logarithm has an attribute, it can divide subtraction into division, so we can be a little bit simpler:
Ten * log (x)-Ten * log (Y) = ten * log x/y
So, for the problem just now, we do not have to separate to forget, with a formula to solve the problem:
Ten * log (. 000792710162/. 000006288415) = DB
This is why we have to use the logarithm of the reason, with this simple method, we can finally have a more in-depth study of the decibel.

There is also a small problem, if we get the measurement data is not all in the acoustic level of the unit, then what to do? If the units of the two data are different, the formulas we get are not destroyed? Think about what we usually use to get the values of different units to be calculated and the results of the same units. In fact, we just need to find a fixed constant to bring this formula to solve the problem, we call this constant "reference number". What do you use to make reference numbers? Just now we seem to have mentioned the smallest sound the average person can hear. The loudness is. 000000000001 w/m ^, let's use this! (another number is the same, we are just for the unity Unit) we use the letter "N" to denote this constant, so:
(x/n)-Ten * log (y/n)
= ten * log [(x/n)/(y/n) ]
= ten * log (x/y)
on the safe side, let's check the formula for the problem, or just the example:
ten * log (. 000792710162/0.0000000000 ) = 000006288415/0.000000000001 db
Ten * log (.) = dB-68 db
(db = + db)
OK, you are done! This method allows us to compare the values of different units. (The two data units in this example are the same, so it seems that the "reference number" does not work)
The measured units used often have the sound power (Watt), the loudness of the sound (Watts/m ^), the sound pressure is (Pascal)--Hey! You have to pay attention to what I said next, which is the easiest place to confuse the decibel.

Data measured in terms of power or loudness, we use the above formula can be very good calculation. Usually, however, when people speak of "decibels", they refer to the pressure. After all, it is the pressure of sound waves that oppress our eardrum so that we can tell how loud the sound is. So, the decibel we usually talk about should be DBSPL (sound pressure levels).
Pressure is the force acting on the unit area, the unit of force is Newton (see your violent nod, I really helpless ...) ), so the unit of pressure is the ox/m ^. Another commonly used unit is Pascal, 1 kpa equals 1 kn/m ^.
The relationship between sound (I) and acoustic pressure (P) can be expressed by the following formula:
I = p^/ρ
ρ is the Greek alphabet, read: "Meat", which represents the resistance of air, is a constant. This value depends on factors such as atmospheric pressure, air temperature, and so on. Typically, at room temperature, the value of air resistance is approximately 400. Thus, the smallest sound loudness that ordinary people can hear is converted into sound pressure:
.000000000001 w/m2 = (. 00002 Pa) ^/400

However, just the formula in the back of the P has a square, that is, the sound pressure doubled, the sound is doubled four times times, the sound pressure four times times, the sound 16 times times. So, when we use sound pressure as a unit of measurement, does the formula we get before have a problem?

Let's take a little calculation:
DB = ten * log (x/y)---at this time x, Y is a unit of measurement using sound, we will p^/ρ into the formula:
DBSPL = ten * log [(px^/ρ)/(py^/ρ)]
= ten * log (px^/py^)
= ten * log (px/py) ^
= * Log (px/py)
In this way, the problem is solved, and the previous formula is different, is multiplied by 20.

This is DBSPL's formula, when we talk about "decibels", 99% is what it says, and the db we see on various gauges is actually DBSPL, but no one is saying that it always takes a SPL three letters. (Some may be afraid of trouble, but most probably do not know, hey ...) But now you know.

So when we use sound pressure as a unit of measurement, the "number of references" we choose is. 00002, close to what we call the smallest sound loudness that ordinary people can hear, and bring in the formula we just got, let's see:
DBSPL = * (P/. 00002 Pa)
Because log1 = 0, so:
* LOG (. 00002 pa/. 00002 pa) = 0 DB SPL

Note that you should notice that if we take a value that is the same as the reference number, then we will always get "0dB", regardless of what type--dbm, DBu, DBV, DBFS ... It's all so! And, you may have doubts,. 00002 PA is not nearly audible? How is 0dB? Yes! 0 is not equal to no? Oh, I see what you mean, you often see in the computer that 0dB represents the highest value of the peak table? Ho Ho, that's because the digital circuit is different from what we're talking about now, don't worry, I'll talk about it later.

The strongest sound pressure we can tolerate is about 20 kpa, would you try a decibel representation? Should be as follows:
* LOG (PA/. 00002 pa) = + DB
What, you remember what the physics class said? More than 120 decibels, we can't stand it, that's the value.
Here, we should review, I believe a lot of formulas and calculations have made you dizzy? No way, in order to clarify, I can only do this, but you just need to see clearly, you need to remember that is the following two:
db = ten * log (x/y)----The formula for calculating the decibel as a unit of measurement, the unit should be w/m^
db = * LOG (x/y)----The formula for calculating the decibel when the sound pressure is measured in units of Pa

That's great, that's it, you already know what the decibel is, and yet our lesson today is not over, because we don't yet know the meaning of dbu, DBv, DBv, DBm, Dbvu, dBFS. But with the above basics, you understand that these little things are just a matter of time, let's start with the principle:
We have already understood the meaning of decibels and should pay special attention to the fact that the decibel represents the ratio of two data of the same type (the same type, which is important, you cannot compare watts and volts directly). In these two data, one of which we call the "reference number", we will be measured by the number of values and reference numbers into the formula to calculate the corresponding decibel value. For example, we have used sound pressure as a unit of measurement, which is the number of references we have chosen. 00002. We finally get the decibel value that we call "DBSPL". In other words, the different letters in the back of the DB indicate what we use as the unit of measure to reach this decibel value. With sound pressure, then it is SPL (acoustic pressure levels). Should this be a very clear explanation? If you understand, then I'll explain the other units that are related to db in one place.

dBm and Dbvu
We have discussed the method of using power measurements to get a decibel value, when we were talking about the power of the sound, in Watts. But we know that in addition to sound, there are many phenomena that can generate power, such as electricity.
long ago, in the "ancient" days when LEDs and LCDs were not yet born, engineers relied on a device called the VU meter to do their job. The VU meter looks like a speedometer in the cab, with a pointer indicating the current increment through the problem in a clockwise direction. Vu is the shorthand for "Volume unit", meaning: the volume measurement unit. The problem with the
Vu meter is that every vu meter is different! It was not until the late 30 that a group of engineers sat together and decided to unify the metering specifications of the VU meter to solve the problem. They determine the standard: when the current power is 1 MW (1 MW), the VU meter indicates 0dB. In other words: 0dBm = 0dBVU. The M on the back of the DB represents the Milli-watt. DBM is also measured in power, and the reference number is 1mW.
dbm = ten * log (Power/1mW)
This way, we can easily use dBm to represent changes in current power. Do you remember? is the DB value always 0 when the measured value and the reference are equal? So:
1 * log (1MW/1MW) = ten * log () = 0 dBm
When the VU meter pointer points to +3dbm, the power increases by one times, how is it calculated? This:
log (2MW/1MW) = ten * log (2) = 3 DBm----I said, at least you have to prepare a scientific calculator, the logarithm is not good mental arithmetic.
What if it points to -6dbm?
* log (. 25mw/1mw) = 6 dBm
dBu (also called DBV) [/color]
Recall High School Physical bar. The Power (p) can also be expressed by the relationship between voltage (V) and Resistance (R):
P = v^/R----resistance is in ohms (Ω)

When we talked about DBM, the reference number was 1mW. This standard was set up in the 30 's in the last century. At that time, the input impedance of all audio devices was 600 ohms, tape recorder, mixer, front power amplifier ... As long as there is a plug, then the resistance from the FireWire to the ground is 600 ohms.
So how much voltage does it take to generate 1mW of power when the resistance is 600 ohms? Calculate with the formula just now:
P = v^/R
.001 W = v^/600ω
V2 =. 001 W * 600ω
V = sqrt (. 001 W * 600ω)----sqrt is open squared, I don't know how to play this symbol.
v =. 775 v
The answer is 0.775 volts. So, when the input impedance of all devices is 600 ohms, the number of references used to calculate the dbu is. 775 V, that is, the DBU is calculated as a voltage measurement unit is the decibel value. But we also noticed that the voltage in the formula just now is squared. Based on the previous experience, we know how to deal with this problem:
dBu = * LOG (voltage measured/. 775 V)
If you are careful, you might find it strange: why dbu instead of DBV? In fact, long ago people are directly using DBV to express, but later people found that DBV and dBV too easy to confuse, so you use the lowercase letter "U" to replace the lowercase letter "V". If you can still see DBV, then it means the dbu--that we talked about today, unless someone who writes DBV can't figure out what he's trying to say!

So, what is the dbv of the confusion with DBV?

For a long time, the audio devices used by people are 600 ohms input impedance, and today we will meet some higher impedance devices, such as 10000ω. The higher the resistance, the less power the circuit consumes. (according to the formula above, we know that power and resistance are inversely proportional)
Remember that the number of references used by DBU is. 775V? Many engineers think this number is too troublesome, but since all the devices are fixed input impedances, using the. 775V as the reference number will be a logical one. The device does not improve, the reference number can not be changed, but for ease of use, a new reference number has been developed quickly-incidentally, the new decibel unit DBV. This reference number is 1V:
DBV = * LOG (voltage measured/1V)
In fact, DBV and dbu very similar, but the reference number is different.

Now, by the way, the difference between the so-called "professional" and "user-level" devices. You may have known, professional-grade equipment is +4dbu and user-level equipment is -10DBV, of course, this is actually very absurd, haha. We have just seen that both dbu and DBV are calculated by comparing the voltage to the decibel value, except for the reference number, they are not any different. The so-called professional grade, refers to the use of these devices are a number of "uncle" (because the standard early, the use of course most of the "qualifications" are also older). In fact, it is too arbitrary to determine the "level" of the device on the basis of these two parameters, which can be done well in any situation where both specifications are required. I think, in this respect, we should play a lot of human initiative. The hard difference between the devices we have a better idea, but how to use our knowledge to let your hands of the equipment to play the greatest potential is the realm we should pursue. Equipment bad is a problem of money, with a good equipment to do bad music that is the problem of people, money can be solved, the problem of people is not good to solve it! Across our channel there is a small island, although not many people, but a lot of music, we admit that their music development is good, but also on behalf of their music people are very high level, where they have a bird forum, there are some birds on the "professional" and "user" equipment differences Big Dog- What's the gas! Let me the other side of the channel rookie (by the way, there are a lot of people who think that people on this side of the strait are far worse than they are) have a little to see. This is the same root born ah ~ But who let the present is such a situation? In order to make this side of the channel comrades do not look like them as "professional", in fact, very "fucked", so I wrote this paragraph-should say, led me to write this article, there are a lot of reasons for this!

Well, the topic is far away, let's see what the difference between +4dbu and -10DBV:
+ 4 DBu = * LOG (voltage measured/. 775 V)
Voltage measured = 1.228 V
-DBV = * LOG (voltage measured/1 V)
Voltage measured = 0.3162 V
* Log (1.228 v/0.3162 V) = 11.79 DB
If you have both devices, you can do a test: Connect the output of the -10DBV to the +4DBU input, and then read the +4dbu vu meter, is it 11.79dBVU?

DBFS
Finally, let's take a look at the DBFS that we've contacted most closely. The full name of the DBFS is "decibels-scale"-a decibel-value representation for digital audio devices.
This guy is not the same as several other brothers, its reference number is not the smallest one, nor is it the middle one, but the largest one! That means "0 DBFS" is the highest level of loudness a digital device can reach. In addition, all values are less than this value--negative. That's why the highest scale of the peak table we see on the computer is "0", and the pointer never reads a higher number.
But why is that? To explain this problem, let's briefly talk about the principle of how digital audio is stored. We use 16bit digital audio as an example: "16bit" means that the sampled signal is stored in 16-bit binary digits. The binary number is two: "0" and "1". So, the maximum value is 1111 1111 1111 1111 (binary, converted to decimal is 65536), so the formula for calculating DBFS is:
dBFS = * LOG (sample signal/1111 1111 1111 1111)
This makes it easy to explain why you cannot exceed "0" because the DBFS reference number is the maximum value, so:
$ * log (1111 1111 1111 1111/1111 1111 1111 1111) = 0 DBF S
So the smallest? In addition to 0, the 16-bit binary smallest number is: 0000 0000 0000 0001, then:
* log (0000 0000 0000 0001/1111 1111 1111 1111) = -96 dbfs
Know why you see the peak table from 0 db to -96 DB? Next, you can figure out the dynamic range of the 24bit,32bit digital audio yourself, and I'll tell you one, the dynamic range of 24bit digital audio is 144dB. Why don't you try it yourself? (Don't forget to convert binary to decimal first, I don't use binary to calculate the logarithm!) ^^)

At this point, the content of this article is almost all finished, the time is hasty, there is an omission unavoidable, you are welcome to correct me ... However, I went back to look at the previous content, I always feel that there are some things to write, but can not be too hasty. Admittedly, this article is not very good to read, but I hope you can take a little thought to read, I dare assure you: there is no harm! If you think you have read, trouble you put the first few questions in the article to try to solve, if everyone can solve it, that I write it fairly clear, then I do not have to explain more, if there are many problems, then my concern is reasonable, I will write another article on the decibel, to solve these problems, Even if it is an addendum. (What is the problem, I do not say, lest everyone lazy, do not find their own problems, quack)

Finally, I would like to thank the bird forum I just said, and some of the birds above, you have given me the impetus to write this text, but also to thank a certain effect device (forget, as if the PSP Vintage) of the documentation, because this document is not fully explained, I have the opportunity to read Lionel DuMond article (Everyone can go to Prorec search, e-text), and finally to thank (this is a real thanks)Lionel DuMond, without your good words, I will not know what is a decibel what things! Ho Ho ~ ~ ~
In writing this article, I refer to high school physics, acoustics physics, Advanced algebra and so on secondary school textbooks and extracurricular reading ... Comrades, Gentlemen! 12 years bided or useful, must not be lost AH ~ ~ ~ ~ ~ ~:p

continue to refine this post: [Share]gos, RSSI, eb/no, Eb/io, DB, DBi, dbm Concepts
Gos:grade of services (service level, quality of service) mainly refers to coverage probability, blocking rate and so on.
RSSI: Received signal strength refers to the power of the signal at the receiver.
Eb/no, Eb/io: Refers to the same concept, is the signal-to-noise ratio, which is a measure of the system demodulation capacity indicators. For the specific business, the lower the required SNR, the system capacity and coverage is better.
The DB is the result of the ratio of the power to the logarithm. (such as gain, inhibition degree ACPR)
DBI is an indicator of antenna directionality, and antenna gain is generally expressed in DBI or DBD. DBI refers to the ratio of the power energy density of an antenna to a non-directional antenna;
DBD refers to the ratio of the power energy density relative to the half-wave oscillator dipole, the gain of the half-wave oscillator is 2.15dBi, so the 0dbd=2.15dbi.
RF signal power is commonly used DBM,DBW, and its conversion relationship with MW,W is as follows
For example, if the signal power is XW, then the size is expressed in dbm:
e.g. 1w=30dbm, equal to 0dBW
1, DBm
DBM is an absolute value of the test power, calculated as: 10lgP (Power value/1MW).
[Example 1] if the transmit power P is 1mw, converted to dbm after 0dBm.
[Example 2] for 40W power, the value of the conversion in dbm units should be:
10LG (40W/1MW) =10LG (40000) =10lg4+10lg10+10lg1000=46dbm.
2. DBi and DBD
The DBI and DBD are the value of the test gain (power gain), both of which are a relative value, but the reference datum is not the same. The reference datum of DBI is omni-directional antenna, and the reference datum of dbd is dipole, so the two are slightly different. It is generally believed that the same gain, expressed in DBI, is 2 larger than that of DBD. 15.
[Example 3] for an antenna with a gain of 16dBd, its gain is converted to a unit of DBI, then 18.15dBi (generally ignore the decimal place, is 18dBi).
[Example 4] 0dbd=2.15dbi.
[Example 5] The GSM900 antenna gain can be 13dBd (15dBi) and the GSM1800 antenna gain can be 15dBd (17dBi).
3, DB
A DB is a value that represents a relative value, and when considering the power of a is compared to a large or small number of DB, the formula is calculated as follows: 10LG (a power/b power)
[Example 6] a power greater than B power one times, then 10LG (a power/b power) =10lg2=3db. In other words, the power of A is 3 DB larger than that of B.
[Example 7] 7/8 inch GSM900 feeder 100 m transmission loss is about 3.9dB.
[Example 8] If a power of 46dBm, B power of 40dBm, it can be said that a greater than B 6 DB.
[Example 9] If a antenna is 12dBd, b antenna is 14dBd, you can say a smaller than B 2 DB.
4. DBc
DBC is also sometimes seen, which is also a unit representing the relative value of the power, exactly as the DB is calculated. In general, DBc is relative to the carrier (Carrier) power, in many cases, to measure the relative value of the carrier power, such as to measure interference (same-frequency interference, intermodulation interference, intermodulation interference, out-of-band interference, etc.) as well as the relative magnitude of the coupling, spurious, etc. In principle, db substitution can be used where DBC is used.
5, Dbuv
According to the basic formula between power and level v^2=p*r, we know Dbuv=90+dbm+10*log (R), R is the resistance value.
The dbm=dbuv-107 should be correct in the PHS system, because its antenna impedance is 50 kohm.
6, DBUVEMF and DBUV
Emf:electromotive Force (EMF)
For a signal source, the DBUVEMF refers to the port voltage when open circuit, DBUV is the port voltage when the matching load is connected

"Reprint" What is a decibel?