Talk:Decibel/Archive 7

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Proposal: the definition from the standards as the primary definition

For nearly all units, scales etc., Wikipedia articles use the definition from the standards as the primary definition. For the sake of neutrality, we should do the same for the decibel. For the sake of completeness, other definitions should be presented as well. For the sake of clarity, the separation should be kept explicit. As Dondervogel suggested, this can be done in text form.

Definition In the standards ISO 80000-3 and IEC 60027-3, the decibel (dB) is defined as one-tenth of a Bel, more specifically, 1 dB = 1 B/10 = (ln 10)/20, which is approximately 0.11513.

It is used for scaling level differences between power quantities or between field quantities. The level difference L(P/P') between power quantities P and P' is defined by L(P/P') = (1/2) ln (P/P'). Hence, expressed in decibel, L(P/P') = 10 lg (P/P') dB. Conversely, x dB = L(10^x/10), for instance, 1 dB = L(1.25893).

For field quantities F and F', level difference is defined by L'(F/F') = ln (F/F'), hence L'(F/F') = 20 lg (F/F') dB.

Taking for P' or F' be a reference value P_ref or F_ref allows expressing "absolute" levels.

Standard notations The IEC 60027-3 (page 19) writes L(P/P_ref) as L_P/Pref or as L_P (re P_ref). It also condones writing L_P = x dB (P_ref).

This is an initial example. Any comments? Boute (talk) 13:12, 6 September 2014 (UTC)

While the wording can be improved, I agree in principle. I suggest starting with "The decibel is a unit of level, defined as one tenth of a bel", before going on to explain how the bel is related to the neper. Dondervogel 2 (talk) 20:11, 6 September 2014 (UTC)

I don't care for it. The decibel has a long and useful history before the standards org tried to pin it down as just a unit of level. It's more widely used to represent gain and loss than level. Where our lead says "often" I wouldn't want to imply "usually" or "always" as Dondervogel does. The standard org's "level differences" is better. Dicklyon (talk) 20:18, 6 September 2014 (UTC)

And the statement In the standards ISO 80000-3 and IEC 60027-3, the decibel (dB) is defined as one-tenth of a Bel, more specifically, 1 dB = 1 B/10 = (ln 10)/20, which is approximately 0.11513, which makes the decibel just the nondimensional value 0.11513, gives no clue to what the decibel is, or is for. Dicklyon (talk) 20:24, 6 September 2014 (UTC)

@Dondervogel: Even the literature before the original definition and the "defining papers" by Martin and Hartley indicate that level difference is indeed more fundamental than level, which depends on a fixed reference value, irrelevant for gain and attenuation. The IEC 60027-3 implicitly recognizes this, but writes sloppy equations like Q_(F) = ln(F₁/F₂).

@Dick Lyon: Although the standards are notationally sloppy (but "all" textbooks using dB are even worse), at least they give a clear and unambiguous definition of the decibel. It is fully self-consistent, and the fact that it defines dB to be just the number (ln 10)/20 does not hamper understanding --- perhaps the contrary. It also helps understanding if definition is separated from use (which is also subject to evolution): if two issues can be explained separately, it is always simpler to do so. Anyway, the "normal use" is explained immediately in the very next sentence: "It is used for ...", so nobody will miss it.

Since you seem to prefer the original definition over the standards for historical reasons, here is a proposed summary. Stating the intended use from the very start is justified here, because that was the only purpose --- a single-mindedness that arguably is the source of most problems that still plague us today!

Definition In the original papers (Martin, Hartley), the decibel (dB) is defined under its early name Transmission unit (TU) as a unit for level difference between power quantities. The level difference L(P/P') between power quantities P and P' is defined by L(P/P') = log (P/P') where log is the logarithm with unspecified base. The decibel is a unit defined by dB = log 10^1/10. Hence L(P/P')/dB = (log(P/P'))/(log10^1/10) = 10 lg (P/P'). Equivalently, L(P/P') = 10 lg (P/P') dB. Conversely, x dB = L(10^x/10).

Note: log with unspecified base is formally handled just like log_b for arbitrary --- but consistently used --- base b, with b > 0 not equal to 1. Thus, log (P/P') is indeed a fundamental "quantity" and dB is truly a unit of measurement, as emphasized in Horton's 1954 paper. The neper (Np) would be defined as log e² and the bel (B) as log 10. There used to be a Wikipedia article about the indefinite logarithm, possibly by Michael Frank, but some "mathematicians" who clearly missed the point removed it.

Clearly there are enough possibilities to choose from (see the earlier table). If your own preference is not included, it would be most helpful if you stated it completely and unambiguously. Sloppy notation (if any) can always be cleaned up afterwards. Boute (talk) 04:28, 7 September 2014 (UTC)

The Martin 1929 and Harrison (NBS) 1931 papers don't say anything about level or level difference; those concepts were made up later. Not sure about Hartley, as I don't seem to have that one. Harrison has a pretty traditional definition: The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 10^{0.1} and any two amounts of power differ by N decibels when they are in the ratio of 10^N(0.1). The number of transmission units [decibels] expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio. I don't see any ambiguity there. Why not stick with it? Looking at your table, I'd note that Martin does include the neper, and I don't see what the distinction is between the "naive" and "original Martin/Hartley" definitions, or why you can the latter in terms of level difference when that concept wasn't there yet (or was it in Hartley?). Dicklyon (talk) 05:50, 7 September 2014 (UTC)

Let's consider these issues one at a time.

(a) It is not helpful denying existence on the basis of "not having seen". The term "power level" (as a logarithmic quantity) is used in the 1923 paper by Alva Clark "Telephone transmission over long cable circuits" (pages 79-80, with an illustration) and in Hartley's 1924 paper "The Transmission Unit" (page 37) (sent to you on request) in a manner indicating that it was already common terminology at that time.

(b) I appreciate it that you make a concrete proposal. Still, Harrison's statement has some serious flaws, enough reason for not sticking with it. First, since you mention ambiguity (I didn't!) Harrison's statement leaves "difference" between "amounts of power" and "decibel" undefined. If one formalizes his definition as "D(P,P') = N dB iff P/P' = 10^N/10", both D and dB are still undefined. In fact, the pair D(P,P') = log_b (P/P') and N dB = log_b 10^N/10 satisfies the statement for any base b (>0 and /=1). Moreover, even the pair D(P,P') = P/P' and N dB = 10^N/10 satisfies it (and arguably better reflects current practice)! Second, it perpetuates the bias towards power quantities. This is mathematically nonsensical, since a ratio of quantities of the same dimension is a pure number: (1.34102209 hp)/(1 kW) = (3.2808399 ft)/(1 m) = 1. Sound notational engineering means treating all dimensionless ratios on the same footing. Third, your earlier argument: in no way does Harrison's restriction to power quantities reflect current practice.

(c) The naïve usage just says: let's represent P/P' by the expression 10 lg(P/P') dB, without caring about what it means. The Martin/Hartley definition is quite precise.

(d) Even if the term level hadn't been there in 1924 (but it was), there is no problem in the table. In general, recasting old concepts in new terminology is rarely a problem in science; to the contrary: it helps unification, streamlining and clarification.

(e) Thanks for the "neper" remark. I found "neper" in Martin's 1929 paper, and will amend the table ASAP. Boute (talk) 10:46, 7 September 2014 (UTC)

The table has now been amended by adding Note 0. Boute (talk) 15:41, 7 September 2014 (UTC)

Clark is using "power level" more informally, though I see you're right that he does plot "Comparative transmission levels in miles of standard cable". Maybe from your collection of sources you can find when the use of "level" to mean explicitly a logarithmic quantification of power came in. I'd be interested in knowing. I think it was a retrospective rationalization of the informal concept of level as represented by decibels. Dicklyon (talk) 16:43, 7 September 2014 (UTC)

On Hartley 1924

Boute, thanks for the copy of the Hartley paper. I see you are right that he very explicitly talked about how to interpret the decibel or transmission unit as a unit for measuring the log of a ratio (he discussed both current ratios and power ratios, and the advantage of the latter, in various parts of the paper). He says:

... Here the quantity which the unit expresses is the logarithm of a current ratio. The number of units x is the logarithm of the ratio being measured divided by the unit, which is log b. Thus the nature of the unit is the logarithm of a current ratio. Its magnitude is the logarithm of that particular current ratio b which is chosen for defining it; in this case 1.115. It should be noted that (11) is true regardless of the base of the system of loga­rithms used. The numerical value of the unit will, of course, vary with the base chosen, but the number of units corresponding to the particular current ratio will not.

... we see that the TU is a unit for expressing the logarithm of the ratio of two amounts of power, and that it is numerically equal to the logarithm of a power ratio of 10^{0.1}. When common logarithms are used its value is 0.1 and the number of units corresponding to any power ratio is ten times the common logarithm of the ratio.

So, this is like what the modern standards do, except that they use base e for current ratios. What bothers me most about this approach is how arbitrary, technical, and non-useful it is, in the sense he that notes: the value of the unit doesn't matter; a decibel could have any value, depending on what log base you choose. The only possible reason to tie it to a value this way would be so that you can write the nice math to relate the decibel to the neper. But in my experience, nobody ever need to know that to work with decibel or nepers, or to convert between them. It's arbitrary and useless to try to pin down a value for the unit. As Hartley says, "The numerical value of the unit will, of course, vary with the base chosen, but the number of units corresponding to the particular current ratio will not."

The official definition the decibel (dB) is defined as one-tenth of a Bel, more specifically, 1 dB = 1 B/10 = (ln 10)/20, which is approximately 0.11513 is of this sort. It defines the decibel to have a value—a valid that doesn't matter at all to what the decibel actually means—but the only clue to what that value measures would have to be traced down via the reference to the Bel, which would redirect to the Neper, which would still leave the answer very cryptic. As a definition, it's the sort only useful to a mathematician, perhaps, or to a standards committee.

As for "Level" as a logarithmic measure of power, that's not what Hartley says. He defines level more informally, suggesting it's just a power or a power ratio, but that it's convenient to display it logaritihmically (my bold):

... Corresponding to each point along the circuit is plotted the “level” at that point relative to some point, usually the entrance to the long distance line, which is taken as a reference level. The level at any point is determined by the ratio of the power passing that point to that passing the point of reference. The purpose of such a chart is to indicate on the one hand what power the various repeater tubes will be called upon to handle, since they are limited in this respect, and, on the other hand, what is the ratio of the power of the voice currents to that of the inter­ fering currents. This ratio is important because it determines the detrimental effect, of the inter­ference when it reaches the listener. These relative levels are most conveniently plotted in logarithmic units, so it was natural to use 800 cycle miles.

It was some time later that the practice of treating level logarithmically got turned around and level got defined as log of power. I haven't quite found where that happened. In 1933, Fletcher and Munson define level in terms of dB: "The intensity level of a sound is the number of db above the reference intensity," as opposed to taking dB as a unit of level; seems like it's not quite there yet. ... Reviweing a ton of papers from the 1930s and 1940s that use both "dB" and "level", I find none that suggest that level means log intensity or anything that. They all use level more informally, the way I always did, as just a way to high higher and lower, without implying how to quantify or measure it. So when did it become log power or log intensity? I can't find it. Dicklyon (talk) 23:20, 7 September 2014 (UTC)

I fully agree that the numerical value of the decibel as a unit for logarithmic ratios does not matter in practice. This is exactly what I meant by saying that Harrison's "definition", written symbolically as "D(P,P') = N dB iff P/P' = 10^N/10" (let's call this the "generic specification"), specifies an uncountable number of D, dB pairs where D(P,P') = log_b (P/P'), and the value of b remains "invisible" in usage. However, when writing down a "primary" definition for the matching decibel, one has to make a choice, and the choice in the standards is not really worse than any other. Arguably it is the most "neutral" from the Wikipedia viewpoint. Personally, of course, I prefer the (D, dB) solution that reflects actual practice: D(P,P') = P/P' and N dB = 10^N/10, where no such choice need be made.

As regards "level" as a log power, the earliest reference I found (without looking for anything earlier) is Clark's 1923 paper, Figure 7, where the vertical axis on the left is labeled as "Comparative transmission level in miles of standard cable at 800 cycles". This "800 cycle mile" (M) was a unit for the logarithm of a power ratio, and is the unit that was replaced in 1924 by the TU (1 TU $\scriptstyle \approx$ 1.057 M), in 1929 renamed dB. The vertical axis on the right is labeled by the power ratio, which Clark calls "comparative power".

Comparative level in M	-25	-20	-15	-10	-5	0	5	10
Comparative power	0.0043	0.013	0.04	0.11	0.33	1	3.0	8.9

This unambiguously defines "comparative level" (or level difference) as a "log power ratio" quantity. Clark seems to consider this usage as self-evident; probably it was common. Anyway, regardless of its origin, "level" is more succinct than "amount of power", which is also sometimes identified with the power quantity itself. Boute (talk) 06:46, 8 September 2014 (UTC)

I don't see it as unambiguous, but I'll grant you that it appears that even as early as 1922 the use of log power ratio or log current ratio as "level" was "in the air". I found a more explicit description in Espenshied's 1922 "Application to Radio of Wire Transmission Engineering", which says This necessity of having to keep the power of the received waves above the interference level may be visualized by reference to Fig. 4. Here we have what in wire practice is called a “ transmission level” diagram. Such a diagram is useful in showing what goes on in the system from the power and interference standpoints. The vertical scale is plotted in terms of the transmission level expressed as the logarithm of the current or field intensity ratios, and the horizontal scale represents progression along the system. It's still not unambiguous that is plotted in terms of the transmission level expressed as the logarithm of the current or field intensity ratios means that level is defined as the logarithm, as opposed to just being plotted as the logarithm, but eventually I grant you that's what happened. Perhaps never very explicitly, which is why I never learned it.

Anyway, I agree that if you want to pin down the definitions of things like dB most precisely, then picking a log base and defining the dB as a unit of logarithm is a way to go. Emphasizing the value of the unit before explaining what it means is not a good way to go, though, since the value is irrelevant. And I don't agree that it would be less neutral to pick log base 10 and power ratio and bel as starting points, instead of base e, current ration, and neper. Most of the world, with the exception of those standards bodies, does the former. We could do both. Dicklyon (talk) 23:17, 8 September 2014 (UTC)

But wait, I have found evidence against level meaning a log. In the 1959 BTL Transmission Systems for Communications vol. 1 p. 2-3 there's a section called "Level" that says

... To put this in the form of a defintion:

The transmission level at any point in a transmission system is the ratio of the power of a test signal at that point to the test signal power applied at some point in the system chosen as a reference point. This ratio is expressed in decibels. In toll systems, the transmitting tool switch-board is usually taken as the zero level or reference point."

So, it says level is a ratio; but it is expressed as log; the "zero level" means the 0 dB or 1:1 ratio. This is like what I've always thought: that the dB value represents the level or ratio via a log, not that the level is a log.

Checking more books, I find more:

Cooke 1942 Mathematics for Electricians and Radiomen clearly says level is a power, not a log: Because the decibel is an expression for a power ratio, it would be meaningless to say, for example, that an amplifier has an output of so many decibels unless that output is referred to some power level. Several zero-decibel levels are in use. For example, telephone engineers commonly use 0.006 watt as the reference, or zero, level.

Everitt's 1937 2nd ed. Communication Engineering defines the neper, bel, and decibel clearly as units of power ratio, not of level. For level, he does not use log (his axis label has "power in watts" with 10^{-2} and 10^{-5}), and notes that for a long transmission line's level plot If the ordinates are logarithmic, the decay curves will be linear as shown.

Frederick Emmons Terman's various books don't mention level but have a traditional simple non-rigorous definition of decibel.

Frankly, I don't find anyone defining level as a log, and decibel as a unit of level, until the modern standards committees. Dicklyon (talk) 23:56, 8 September 2014 (UTC)

I found a handful of papers that include "level is defined as the logarithm", going back to Fletcher 1935 with "loudness level is defined as the logarithm". And similarly few in books. It seems a rarity, though it may be expressed in different words; can anyone find? My friends in the speech business see it as I do: the level is not a log, but is often expressed in dB. Dicklyon (talk) 02:36, 9 September 2014 (UTC)

Of course, the term level has been used as sloppily as the decibel during the 90 years since its definition. Still, what ambiguity do you see in Clark's usage?

I don't like the standards any more than you do (although my criticisms have quite different grounds), but at least they made "level" precise, as distinct from "ratio". This is a useful distinction. Consider the original definition of TU (dB) mentioning "difference between amounts of power". In English, difference means a - b. If "amounts of power" is interpreted as the values of the power quantities, this would mean P - P', --- not what we want. The term "difference" suggests logarithms of the represented ratios.

Anyway, let's postpone choice of words until concepts are settled. Your suggestion to use base 10 rather than base e² would amount to 1 B = 1, an option considered in Mill's "tutorial" on the standards, so you have a reference. This choice is no problem in view of the "generic specification" I mentioned earlier, allowing to choose any base.

When making some final changes to the paper I mentioned, I realized that one of my examples illustrates that the value chosen by the standards is the "most natural" one, and that its numerical value does matter: if cable loss is expressed as N dB/m, then, with dB = (ln 10)/20, this is the correct coefficient b in e^-bx (for the voltage ratio at distance x). Epistemologically, I came to the conclusion that many useful aspects of the decibel remain unexploited because "everyone" says that they are unimportant, such as precise definitions, and as a result don't become common engineering knowledge: a vicious circle.

I'm off for a few days of vacation, without Wikipedia reading. Boute (talk) 15:06, 9 September 2014 (UTC)

It matters not what we like, but the empirical facts. I can't speak for other sciences, but I know that in acoustics, the term "level", as formally defined by ANSI since the 1960s, has been the logarithm of a ratio, and the decibel has been a unit of level, so that is what the article should say. I do not understand the arguments of those who resist that. Dondervogel 2 (talk) 15:09, 14 September 2014 (UTC)

Early definitions of "level", "bel" and "decibel"

The earliest formal definition of "level" I am aware of is from ANSI S1.1-1960 Acoustical Terminology. The following definitions are all from that (American National) Standard

Level: In acoustics, the level of a quantity is the logarithm of the ratio of that quantity to a reference quantity of the same kind. The base of the logarithm, the reference quantity, and the kind of level must be specified.

Bel: The bel is a unit of level when the base of the logarithm is 10. Use of the bel is restricted to levels of quantities proportional to power.

Decibel: The decibel is one tenth of a bel. Thus, the decibel is a unit of level when the base of the logarithm is the tenth root of ten, and the quantities concerned are proportional to power.

Dondervogel 2 (talk) 09:21, 15 September 2014 (UTC)

Prior to 1960, the American National Standard was ASA Z1.24-1951, which contains the following definitions of "bel" and "decibel" (none of level):

Bel: The bel is a dimensionless unit for expressing the ratio of two values of power, the number of bels being the logarithm to the base 10 of the power ratio.

Decibel: The decibel is one-tenth of a bel. The abbreviation "db" is commonly used for the term decibel.

It seems reasonable to conclude from this that the modern definition of level was introduced in 1960, and has been with us for more than half a century. Dondervogel 2 (talk) 09:29, 15 September 2014 (UTC)

Good find. Yet, though the standarrds committee defined it thus, I don't think it was ever taught that way; certainly not in my engineering education in the 1970s. Has such a definition ever been widely adoped in texts? I have no objection to putting the standards-based definitions in the article, and attributing them as such, but we should also put the more conventional or "informal" way that people have been taught, which avoid the funny ideas of the neper being equal to 1 and such. Dicklyon (talk) 13:15, 15 September 2014 (UTC)

In that case we are in complete agreement :) Dondervogel 2 (talk) 13:22, 15 September 2014 (UTC)

Good. I also find the definition in terms of level to be awkward to apply to the usual uses for dB for gains and losses, since those don't really involve any reference quantities. They presume linearity and treat ratios of output to input, not to reference. Dicklyon (talk) 15:38, 15 September 2014 (UTC)

The way the standards deal with gains and losses is by defining them as level differences where a "level difference" is just that, the difference between two levels. Dondervogel 2 (talk) 16:39, 15 September 2014 (UTC)

I understand. But it's a fiction, since the gain or loss in dB as a level difference doesn't involve any actual levels or references. And it gets ever further from the original "transmission unit" that was a gain or loss and had nothing to do with level. Dicklyon (talk) 05:14, 21 September 2014 (UTC)

Definitions evolve with time, usually for the better. If the intensity falls from 500 W/m^2 to 5 W/m^2, the level falls from 27 dB re 1 W/m^2 to 7 dB re 1 W/m^2. The ratio of the two intensities is 100 and the difference between the two levels is 20 dB. Where is the fiction? Dondervogel 2 (talk) 06:38, 21 September 2014 (UTC)

I deal a lot in s-parameters for passive RF circuits. For example, the coupling between two antenna-like structures may be described as -20 dB. Where is the level in that measure? Assuming electromagnetic coupling is linear (it should be), the coupling is independent of the input power - which is why EM coupling is usually given as a ratio. GyroMagician (talk) 15:52, 1 October 2014 (UTC)

If EM coupling is a ratio of power (or root-power) quantities, it does not make sense to express it in units of dB. It is only when such quantities are expressed in logarithmic form (as a level) that the dB makes sense. Dondervogel 2 (talk) 12:38, 4 October 2014 (UTC)

This is where we differ in opinion. I do not consider a dB to be a unit, in the sense that a volt or a meter is. I consider the (deci)bel to be a convenient way to represent a unitless ratio in logarithmic form. I did not invent this usage - it's standard practice, at least in the physical sciences and RF/MW engineering. One example would be the one I gave above, where EM coupling (or any other s-parameter measurement) is rarely quoted in anything other than dB. I chose this example because it demonstrates a case where there really are no units - the coupling itself is a unitless ratio - and the level has no meaning. To limit the measurement to a particular level is to ignore the generality of the result. As Dickylon says, the level is a fiction. GyroMagician (talk) 01:19, 2 November 2014 (UTC)

specific proposal

How about this to replace the opening sentence of the lede?

The decibel (dB) is a unit of level that is formally defined as one tenth of a bel. Historically, the bel is defined as a dimensionless unit for expressing the ratio of two values of power, the number of bels being the logarithm to the base 10 of the power ratio. Modern standards define the bel by linking it to the neper. The decibel is a logarithmic unit used ...

Dondervogel 2 (talk) 17:05, 17 September 2014 (UTC)

Sounds good. Dicklyon (talk) 01:49, 21 September 2014 (UTC)

I agree with the anon IP that the new version of the lede is unclear, so I re-reverted back to the old version. Think of someone coming to this page who does not know what a dB is (or who has forgotten). The lede is the single most important paragraph in the article, and should be clear and concise. Is the linking of the decibel to the neper really the most important fact about it? Then why should it appear in the lede? Similarly, anyone with a basic grounding in science or engineering (i.e. anyone who knows enough to care about units and dimensional analysis) will already understand that a ratio of two values of the same physical quantity is dimensionless - so it does not need discussing in the lede. These are details that belong further down in the article. Dondervogel2 - I also don't understand why you're so determined to state the the dB is historically dimensionless - it still is. GyroMagician (talk) 15:45, 1 October 2014 (UTC)

I still object to this sentence: "The bel is named in honor of Alexander Graham Bell, but is seldom used." Firstly it seems to be implying that we'd expect a unit named after such an illustrious person to be used rather a lot (in fact there's no need to link these two unconnected facts in one sentence). Secondly, it ought to be made clear that the decibel is not covered by "seldom used". W. P. Uzer (talk) 16:05, 1 October 2014 (UTC)

The present version of the lede now completely ignores the modern definition, and only mentions the historical definition. Are we writing a Wikipedia in the 21st Century or the 20th one? Dondervogel 2 (talk) 17:12, 1 October 2014 (UTC)

Sorry, I should not have supported putting "level" in the opening sentence. I've put that info at the end of the lead instead. Perhaps that's more appropriate? Dicklyon (talk) 17:30, 1 October 2014 (UTC)

I support DickLyon's solution. Good edit. Dondervogel 2 (talk) 19:25, 1 October 2014 (UTC)

No worries, I think we're getting a better lede now. For the 'level' and 'level difference' paragraph at the end of the lede, the linked SI document doesn't say anything about levels. What it does say (p127) is actually rather sensible (emphasis mine):

Table 8 also gives the units of logarithmic ratio quantities, the neper, bel, and decibel. These are dimensionless units that are somewhat different in their nature from other dimensionless units, and some scientists consider that they should not even be called units. They are used to convey information on the nature of the logarithmic ratio quantity concerned. The neper, Np, is used to express the values of quantities whose numerical values are based on the use of the neperian (or natural) logarithm, ln = log_e. The bel and the decibel, B and dB, where 1 dB = (1/10) B, are used to express the values of logarithmic ratio quantities whose numerical values are based on the decadic logarithm, lg = log_10. The way in which these units are interpreted is described in footnotes (g) and (h) of Table 8. The numerical values of these units are rarely required. The units neper, bel, and decibel have been accepted by the CIPM for use with the International System, but are not considered as SI units.

I guess I consider myself one of those scientists. In case you're wondering, table 8 lists a selection of non-SI 'units' that SI consider acceptable to use. GyroMagician (talk) 22:34, 3 October 2014 (UTC)

The edits to the lede were intended to reflect the definition of the International System of Quantities (ISQ), of which the SI is a part. In the ISQ, the decibel is defined as a unit of level. Your opinion has no bearing on that statement, and neither does mine. Dondervogel 2 (talk) 12:34, 4 October 2014 (UTC)

My opinion is of little importance, but the cited document is. The section I quoted was the only mention I could find of the decibel in said document, and it does not support what is written in the lede. This was, and is, my point.GyroMagician (talk) 21:21, 4 October 2014 (UTC)

Point taken. I agree the cited reference did not support the claim so I replaced it with a reference to the specific ISO standard that defines the decibel in this way. Dondervogel 2 (talk) 21:31, 4 October 2014 (UTC)

Bogus math

In the "Power quantities" section, what's the point of asserting "Lp = 0.5*ln(P/Po) = 10*Log(P/Po)" when it is true only for the degenerative case: P == Po? Also, why term "Po" as "reference power"? "P" & "Po" should be "P1" & "P2" (that is, any arbitrary power measurements). Likewise for the "Field quantities" section. --MarkFilipak (talk) 16:04, 14 May 2015 (UTC)

Looks OK to me. The equation serves to define the decibel and is valid for any value of P/Po. Dondervogel 2 (talk) 17:48, 14 May 2015 (UTC)

Looks OK to you, eh? ...valid for any value of P/Po, eh? Okay, how about the following?

Let P/Po = 2. Then

0.5*ln(P/Po) = 10*Log(P/Po) becomes

0.5*ln(2) = 10*Log(2) becomes

0.3466 = 3.0103

--MarkFilipak (talk) 21:46, 16 May 2015 (UTC)

You missed the factor of 1 dB, which is defined as 1 Np * (1/20)*ln(10). Further, 1 Np is defined as 1, from which it follows that 1 dB =~ 0.115. If you put the missing factor back in you will see that it works. Dondervogel 2 (talk) 22:03, 16 May 2015 (UTC)

Thanks Dondervogel 2, but what I missed on the 14th was that Fgnievinski would fix it on the 15th. Fgnievinski added "Np" to the first equation. --MarkFilipak (talk) 22:32, 16 May 2015 (UTC)

It's one thing for it to be correct though, but it should be clear as well. It confused you to start with, and might still be confusing to others. Does it require a better explanation? Dondervogel 2 (talk) 22:49, 16 May 2015 (UTC)

120 dB vs 20 Pa

In the article it is claimed that 120 dB SPL "may be clearer" than "a trillion times more intense than the threshold of hearing" or "20 pascals of sound pressure". Why would an obscure logarithmic quantity ever be considered clearer than a description of the physical quantity in clear physical units??? Dondervogel 2 (talk) 20:19, 12 April 2015 (UTC)

As a quantity description it probably isn't clearer (although in my opinion that isn't always true), but when comparing a large range of values of things that the human mind processes as linear but in fact is non-linear, it is immensely useful to be working in linear numbers - admittedly perhaps only if you truly understand the decibel. DRZ85 (talk) 13:24, 30 June 2015 (UTC)

Relationship between voltage and power

Why does the article say "A change in voltage by a factor of 10 results in a change in power by a factor of 100"?

According to P=vi (one of the must fundamental equations in electrical engineering), for a constant current i, power is directly proportional to voltage. 199.46.200.232 (talk) 21:04, 27 May 2015 (UTC)

Because for constant resistance, R, current is also proportional to voltage: P = v^2/R. Dondervogel 2 (talk) 21:30, 27 May 2015 (UTC)

So we are both correct. The article should specify constant resistance -- not just assume it -- in order to spare other readers from mentally wandering down the same road that I did. 199.46.200.232 (talk) 00:58, 29 May 2015 (UTC)

Article has been fixed 75.163.204.203 (talk) 06:41, 12 July 2015 (UTC)

War, pestilence and decibels are all common, but are they also good?

The common use of the decibel has been added to the list of advantages. I guess it can stay if it can be backed up by a reference, but just because something is common does not make it a good thing. Also common are war, disease and spelling errors. Should we applaud those? Dondervogel 2 (talk) 17:10, 11 June 2015 (UTC)

i am not bad — Preceding unsigned comment added by 117.222.143.105 (talk) 03:45, 11 September 2015 (UTC)

dB as a "unit" of power/field quantities

Everywhere in this article, "unit" is to be understood as a logarithmic unit, not as in units of measurement. Since the former redirects to logarithmic scale -- article which does not even mention the word "unit" --, this shorthand is misleading in the present article. For example, decibel can be said to be a unit of power level, but it cannot be said to be a unit of power (perhaps saying it's a power scale is okay). In other words, decibels are rightly a unit of level-type derived quantities; but when referring to the primary power- or field-type quantities, decibel cannot be said to be directly a unit of the primary quantities themselves, only as a unit of the logarithmic ratio of such primary quantities. Therefore, I'd like to propose rephrasing "unit" as "level unit" or "scale" where appropriate. Fgnievinski (talk) 02:39, 15 May 2015 (UTC)

The best way of solving this problem is to state clearly, and early on in the lede, that the decibel is unit of level. Further down, by way of clarification, one could then explain the implications of this, including the fact that it is not a unit of power. Using the term "level unit" is OK to reinforce this (though not really needed all the way through IMHO), because that is literally what it is, but "scale" would not be correct. Dondervogel 2 (talk) 08:16, 15 May 2015 (UTC)

Are you saying that "scale" would be an incorrect shorthand for "logarithmic scale"? I assume you don't dispute the latter aptly describes the decibel, analogous to decade. Fgnievinski (talk) 03:24, 16 May 2015 (UTC)

I'm saying that a decibel is a unit of level, and a level is a logarithmic quantity. It is therefore correct to say that a decibel is a unit of a logarithmic quantity. A logarithmic scale is something else, implying some range of values in which logarithmic quantities are expressed (e.g., the scale of notes on a piano). So 'decibel' and 'logarithmic scale' are not synonyms. Dondervogel 2 (talk) 08:36, 16 May 2015 (UTC)

I am against the use of the word "unit". Unit means "one". When you have zero kg, zero meter or zero ampere, you have nothing, niet, nada. However, when you have 0 dB, you have a 1:1 ratio of power/voltage/current. Personnaly, i'd suggest "Logarithmic expression". Normand Martel 09:43, 02 December 2015 (UTC)

The decibel is a unit in log space. In the logarithmic world, a 1:1 ratio is precisely what you say: zilch = niets = niente = nada. Dondervogel 2 (talk) 14:01, 2 December 2015 (UTC)

Unintended mistake when interpreting 80000-3

Please comment and contribute:

Almost all formulas for calculations with levels that are expressed in decibel presume that the decibel has no dimension, and certainly not has a value. This is valid for most, if not all(!) formulas in ISO standards regarding acoustics, but also for formulas is many legal regulations and (educational) publications related to noise assessment.

If these formulas are applied with the notion that, according to ISO80000-3, a dB equals 0,115..., then huge mistakes will be made. This is a serious issue that has to be solved. As long as it is not solved this wiki-article should contain some kind of text addressing that. I like to prepare such a text but want to know what is concidered an appropriate location and heading.

Michiel van Eeden — Preceding unsigned comment added by Mvenl (talk • contribs) 15:29, 5 December 2015 (UTC)

Does "dB re" mean "decibels relative to" or "decibels with reference to"?

Does anyone know of a source that gives a definitive answer to the meaning of "re" in "dB re"? Dondervogel 2 (talk) 23:43, 13 November 2015 (UTC)

this is a common abbreviation of "with reference to" for example "dB re 20 µPa" for sound pressure level. It is not standardized by my knowledge. — Preceding unsigned comment added by Mvenl (talk • contribs) 19:57, 9 December 2015 (UTC)

@Mvenl Thank you for this explanation. Can you cite a source to back up "with reference to"? Dondervogel 2 (talk) 00:36, 10 December 2015 (UTC)

logarithmic mean

I'm sure I'm misunderstanding something, but could someone just check to see that using the equation in the logarithmic mean article actually gives you an answer of 87? I can get 87 by converting 90 and 70 dB out of dB, using the arithmetic mean and then converting back to dB. But using the equation in logarithmic mean, I get Mlm(90,70) = (90-70)/(ln(90)-ln(70)) = 79.5816. Additionally, in the Inequalities section, it says that the logarithmic mean is smaller than the arithmetic mean. How can this be the right equation if the result is supposed to be 87? If it's not the correct equation, there should be some clarification before direction to the logarithmic mean article. -Wongba (talk) 13:26, 8 January 2016 (UTC)

Lead rework

I have taken a second shot and improving the lead. My first shot did not correctly respect terminology and was reverted by Dicklyon. There was some discussion on my talk page about this. ~Kvng (talk) 16:34, 5 September 2016 (UTC)

Dicklyon was right to revert initially, for the reasons he gave on your page. Today's edits correctly respect the definition of 'level'. Dondervogel 2 (talk) 16:40, 5 September 2016 (UTC)

Accoustic math error?

There seems to be an error in the math in section 5.1 (Uses/Accoustics) "the base-10 logarithm of 10^12 is 12, which is expressed as a sound pressure level of 120 dB re 20 micropascals." Earlier in the same section it states the formula for amplitude ratios as dBspl = 20 Log (Prms/Pref), which would make 120 dBspl equal to a ratio of 10^6 not 10^12. I'm not an expert but this seemed like a error to me. I didn't edit it on the page because I don't feel like I know enough to definitively correct this incongruity.

Also, the reference to the "Trillion" ratio stated in section 5.1 "The ratio of the sound intensity that causes permanent damage during short exposure to the quietest sound that the ear can hear is greater than or equal to 1 trillion (10^12).[33]" actually states the level as 120 dB not "equal to or greater than 1 trillion". This induction based on aparent faulty math should probably be corrected as well. 131.137.245.208 (talk) 13:09, 4 February 2016 (UTC)Malcolm

Ratio of 10^6 in pressure, ratio of 10^12 in intensity. - David Biddulph (talk) 13:30, 4 February 2016 (UTC)

Yes it is confusing, but that is life. dB is always a power ratio, or in the case of some discussions, intensity. Power and intensity are the product of field quantities, such as voltage times current. If the impedance is constant, power is proportional to the square of voltage or current. See, for example, dBu. In the case of acoustics, assuming constant acoustic impedance, the intensity is proportional to the square of the amplitude of the sound pressure. As the voltage output of microphones is reasonably close to proportional to the amplitude of the sound pressure, it is convenient to measure that way. You have to remember if you are measuring an amplitude (field quantity) or intensity (power) level, and use 20 or 10, as appropriate. Gah4 (talk) 17:16, 10 October 2016 (UTC)

Video and digital imaging

This section isn't so easy to follow. In electro-optics, such as phototransistors, the current is proportional to the rate of photons coming in. For a given wavelength, photons are proportional to input power. With a known load resistor, output voltage is proportional to photocurrent. So, the output voltage from a CCD array is proportional to the optical power input, for a known wavelength. This is unlike some other systems where the output voltage is proportional to the square of the input power. Gah4 (talk) 17:23, 10 October 2016 (UTC)

dBμ

I was remembering either dBu or dBμ used for the sensitivity of FM tuners. (The former when greek fonts aren't available.) That is, dB relative to one microvolt. http://radio-timetraveller.blogspot.com/2015/02/the-db-versus-dbu-mystery-signal.html seem to indicate that they are used for microvolts/meter electric field strength, again related to radio signals. Just to make it more confusing. Gah4 (talk) 16:37, 12 October 2016 (UTC)

Reference impedance for telecom

which used to be the standard reference impedance in telephone circuits. What is the standard reference impedance now? Gah4 (talk) 15:28, 12 October 2016 (UTC)

I used to design telecom test equipment. We provided 600 ohm reference for audio (voice) band measurements and tone outputs. Older instruments had 900 ohms and even older (such as the long obsolete Wilcom T 105) also had 110 ohms. For higher frequency DSL, HDSL and ADSL we provided both 135 ohms and 100 ohms. Constant314 (talk) 17:10, 12 October 2016 (UTC)

So it isn't 600 ohms anymore? Gah4 (talk) 01:01, 13 October 2016 (UTC)

600 ohms out to 20kHz, then 135 ohms and 100 ohms for higher with 100 ohms at the highest. I don't recall where the switch fro 135 to 100 occurs. Constant314 (talk) 02:27, 13 October 2016 (UTC)

Hmmm. Seems you have to define what is a telephone circuit, and specifically whether it includes the DSL part of a telephone/DSL line. That is, only below 20kHz, or not? The actual reason for the question is the past tense of the above note. Gah4 (talk) 06:14, 13 October 2016 (UTC)

Dubious

There is a Dubious claim on the use of dBmV in cable television systems, and the use of 75 ohm cable. The use of 75 ohm cable for CATV systems is so widespread that I don't see anything dubious. In days past, it was not so unusual for TV antenna inputs to be balanced 300 ohm twin lead, that is rare. The impedance of a folded half-wave dipole antenna is close to 300 ohms, but CATV only uses coaxial cable. Gah4 (talk) 17:41, 10 October 2016 (UTC)

There is also Dubious related to nuclear hardness. I presume this is related to hardening of missile silos, and not a property of nuclear physics. I can't say much about the dubiousness in this case. Gah4 (talk) 17:41, 10 October 2016 (UTC)

OK, I removed: {{Dubious|date=March 2016|reason=if it's relative to a reference voltage, the impedance should be irrelevant. If it's a power measurement misnamed as a voltage measurement, this should be clearly specified.}} dB is always a relative power measurement, but voltmeters measure voltage. As TV cable is reliably 75 ohms, this isn't a problem. In other cases, it is much less obvious. It seems that audio uses a 600 ohm reference, as far as I know, even when it isn't actually 600 ohms. At audio frequencies, reflections aren't a big problem like they are at RF. If this is still a question, then somewhere else the article should make obvious the meaning of voltage vs. power measurements. Gah4 (talk) 06:29, 13 October 2016 (UTC)

The reference value is 1 V, not 1 V rms

In fact there is no such thing as 1 volt RMS. It's just one volt. Period. Dondervogel 2 (talk) 14:35, 26 November 2016 (UTC)

Not true, despite your "period".

Pros and Cons

The "cons" part is much longer than the "pros" part, and seems contain mostly complaints that people who don't understand decibels don't understand decibels. Logarithms are confusing to people who don't undersand logarithms. Long division is confusing to people that don't understand long division. Is any of this worthy of putting in an encyclopedia article? Sorry, ignorance of math does not score a point against math. — Preceding unsigned comment added by 139.68.134.1 (talk) 21:34, 19 January 2017 (UTC)

I agree. And the sources being cited don't really support the implication that they are "complaining" about how decibels work; they're just explaining. That's not a con. Dicklyon (talk) 23:11, 19 January 2017 (UTC)

The sources cited refer to confusion caused by use of the decibel. Explaining the confusion can be a benefit, but the confusion itself is not. Dondervogel 2 (talk) 00:15, 21 January 2017 (UTC)

I agree that confusion is not a benefit, but I mostly don't agree that the sources are referring to confusion caused by use of the decibel. The 1954 "bewildering" paper is proposing an alternative that didn't catch on; obviously COI there in criticizing what he's trying to replace. Some of the others assert confusion, but these primary sources don't represent any significant viewpoint. Dicklyon (talk) 05:11, 21 January 2017 (UTC)

Those primary sources are all we have. I witness the confusion almost every day of my working life, so I would not agree that those primary sources are somehow unrepresentative. Dondervogel 2 (talk) 08:34, 21 January 2017 (UTC)

"Those primary sources are all we have." And they are weak. If they're all you have, then maybe the material should be deleted. Multiplication is like addition; but repeated. That's so confusing! We should just use addition, because someone who couldn't finish sixth-grade math is confused by stuff that they can't understand. It's all a pretty pathetic excuse for a "criticism" section. Is Wikipedia supposed to be supporting lackwits and losers and their ignorance? — Preceding unsigned comment added by 108.49.176.208 (talk) 05:10, 25 January 2017 (UTC)

Greetings. Following the discussion with interest. Just wondering if Dondervogel 2 would elaborate on the confusion that he witnesses every day. Constant314 (talk) 05:20, 25 January 2017 (UTC)

I'd like to hear about that, too. Seems odd to me, as I've worked with people using decibels for decades, with no problems. And without secondary sources, I don't see how we can say that decibels cause confusion. Dicklyon (talk) 05:36, 25 January 2017 (UTC)

I'm not entirely sure of the relevance of my own experience. What matters are the sources. But seeing as you ask, my work involves interaction with people who use the decibel without an understanding of its meaning. These include regulators, administrators, and similar, and in general are not well versed in mathematics or engineering. For example, they read a sound power level of 120 dB and a sound pressure level of 100 dB and infer from that that the power level represents more noise (and therefore requires more of their attention) than the sound pressure level. Alternatively they might see an rms sound pressure level of 80 dB and a peak sound pressure level of 83 dB and imagine using similar reasoning that the peak sound pressure level is a bigger concern. I have also seen journalists make ridiculous claims that s source level of 190 dB is equivalent to this many nuclear explosions or that many billion Boeing 747s. The confusion is rampant. I can dig out the crappy journalism for you if that helps at all, but even thought the comparisons made are clearly nonsense, their interpretation as such would be OR in my view. In what sense are the multiple letters not secondary sources? Dondervogel 2 (talk) 07:58, 26 January 2017 (UTC)

Thanks for sharing. I see what you mean. Like Dicklyon, I have worked with telephone and CTV technicians for 40 years who use dBs daily. It was hard to see any confusion. Constant314 (talk) 08:13, 26 January 2017 (UTC)

DV, do you think people would be less confused to see sound pressure in pascals? Human hearing works well from about 0.000020 to 2.0 pascals, and rock concerts might go to 20 or more, and that 190 dB explosion/jet engine would be about 100000 pascals. Would that help anyone? Would they think that 2 pascals is twice as loud, or twice as much sound power, as 1 pascal (hint, it's neither). Sound power flux in watts per square meter might be more meaningful, but then the sizes of the numbers would be even more ridiculous. Of course, you could use scientific notation, with powers of ten, but then the power is essentially decibels, so it just makes an even more confusing mixed notation. Dicklyon (talk) 16:32, 26 January 2017 (UTC)

What I find causes most confusion is that the difference between power and intensity is at best hidden in the reference value and too often lost altogether because the reference value is not even stated. If I were to tell a journalist that the mass of my body (say 100 kg, using round numbers here) and that its height is 2 m, he or she would not imagine that my mass was 50 times greater than my height. Why? Because they learn at school that fings wot hav diffrant units are diffrant in naytshah. For the same reason, if I were to state (taking my first example) that the rms sound pressure were 0.1 Pa and the sound power was 1 W, no one would conclude that the power was 10 times the sound pressure. By expressing quantities in decibels we take unsuspecting journalists, sociologists, regulators and the like, including some scientists who should know better, too far from their comfort zone, and the result is confusion. Dondervogel 2 (talk) 16:36, 27 January 2017 (UTC)

OK, that could happen, but it's not usual, and is best avoided by using dB correctly with reference specified, such as dB SPL. And in cases where it's really just dB characterizing a ratio, they really can be added or compared. Like this cable has 10 dB loss and that one has 5 dB loss, which is half as much, so if it's the same cable type it must be half as long. Or if I use two 10 dB amplifiers I can get 20 dB of gain. Very useful and intuitive. Dicklyon (talk) 17:13, 27 January 2017 (UTC)

Yes, for some operations (especially multiplicative one like 10*1.5 W = 15 W) a logarithmic unit can help, for others (especially additive ones like 15 W = 10 W + 5 W) they do not. The bottom line is that neither your experience nor mine are relevant to this discussion. We just follow the sources. Dondervogel 2 (talk) 17:34, 27 January 2017 (UTC)

3 dB

Background: we're discussing the alternative phrasings for describing a factor of 2:

• More precisely, the change is ±3.0103 dB, but this is invariably rounded to "3 dB" in technical writing.
• More precisely, the change is ±3.0103 dB, but this is often rounded to "3 dB" in technical writing.

@Dondervogel 2: I don't mean to get into an edit war, but "often" is far too vague of a WP:WEASEL word. This is WP:OR, but I've been doing this for a lot of years, and the only places I've ever seen "3.01 dB" is in tutorials like this which are explaining the approximation, or student exercises where a teacher wants to forestall arguments. (Which is why I added the caveat "in technical writing".)

Go compare:

• https://www.google.com/search?q="3.01+dB" (35,900 results, which are essentially all textbooks, tutorials, and homework problems)
• https://www.google.com/search?q="3+dB" (10,700,000 results)

The exceptions where "3.01 dB" is written in technical writing like [1] and [2] are cases where the value occurs in a table with other values expressed to 2 decimal places.

The vast majority of the time, whether an author writing "3 dB" is actually measuring 3.00 or 3.01 dB is irrelevant. Link budgets are rarely computed to more than 0.1 dB of precision, so 0.01 dB is simply negligible. Real-word component tolerances (and temperature coefficients!) overwhelm that degree of resolution. I may be able to simulate a circuit made with ideal components where I can meaningfully distinguish the 3.00 and 3.01 dB corner frequencies, but the distinction vanishes as soon as I leave the simulation.

The issue arises in theoretical discussions, where there is an exact answer, and in those the half power point is essentially always referred to as "3 dB".

I'm happy to discuss alternative phrasing, but I'd like something considerably stronger than "often". I was trying to keep it brief, and I thought "invariably"'s connotation of "for practical purposes, always" was about right. It's not impossible to not round, but it is, to a first approximation, never done. I haven't yet found a word or phrase that's more precise without being awkward. "Almost always?" 71.41.210.146 (talk) 14:44, 25 March 2017 (UTC)

"Often" has the advantage of being correct. It can be stronger if you prefer but "invariably" is plain wrong. I can accept "almost universally". Dondervogel 2 (talk) 16:21, 25 March 2017 (UTC)

I always round to 3.01 dB. Constant314 (talk) 16:28, 25 March 2017 (UTC)

@Dondervogel 2: "almost universally" it is, thanks! As for "invariably" being incorrect, I understand that its literal meaning is "without exception", but as a literary term it is understood to mean almost that, to the point that exceptions are noteworthy, e.g. "Seattle is invariably cloudy" or "Parisians are invariably rude." Since that's what I was trying to convey, the usage seemed apt to me.

@Constant314: Interesting! What area do you work in that this is common? I use dB primarily in filter design, link budgets, noise analysis (dB rel. 1 nV²/Hz), voice coil transducers (lots of dynamic range!), and a little bit of RF, and I've only seen corner frequencies described as "3 dB". E.g. "The 3 dB point of an RC filter is the frequency at which R = 1/ωC = 1/2πfC". 71.41.210.146 (talk) 20:20, 25 March 2017 (UTC)

"Those primary sources are all we have"

This may be true for pure facts in the historical sense (see Charles McCabe's maxim about facts). For scientific topics, especially mathematical ones, we also have our brains. For the decibel, sticking exclusively to primary sources (which are poor, as someone else politely remarked) will never yield a decent account. WP:OR is all too often invoked as a pretext for reverting exactly those edits that might be most clarifying for the readers. A major problem is that, in the absence of a proper consensus among editors, the only appropriate main source in the narrow WP:OR sense would be the standards. However, edits to that effect (not made by me!) have regularly been reverted or diluted into nonexistence for various rather strange reasons. A good reason is that the accounts in the standards are far from clarifying to readers and overly restrictive to reflect the freedom required (and taken) in actual practice. But nothing better can be put in their place if WP:OR is systematically taken too narrowly. This is the conundrum for the decibel. The only solution is leaving room for a modicum of clear thinking and interpreting WP:OR wisely. Boute (talk) 18:08, 5 June 2017 (UTC)

Criticism

I recommend to convert the

• "Advantages and disadvantages / Supporting arguments" subsession into an "Advantages" session

• "Advantages and disadvantages / Criticism" subsession into an "Frequently asked questions" session

• and remove the remaining empty "Advantages and disadvantages" session

The reason is, that better if no editor blames him- or herself by supporting the silly "Criticism" subsession, what anyways blames the quality of the Wikipedia itself as well.

To understand the level of same I have to state, that I give frequently references to Wikipedia pages for my university students, but this case I disregaded giving rerence to this page, due to this silly "Criticism" subsession, I simply do not want to teach how some people do not understand the basic arithmetics of logarithmic scales.

prohlep (talk) 09:31, 22 March 2017 (UTC)

There's nothing silly about the criticism. If you are teaching only the advantages of using the decibel you are misleading your students. Dondervogel 2 (talk) 11:10, 24 March 2017 (UTC)

I think the Criticisms section needs work (especially the last paragraph) and I am not opposed to exploring options to rename sections or reorganize. I don't like Prohlep's "Frequently asked questions" suggestion. It may be possible to rework "Criticisms" into a "Misapplications" section. There's nothing wrong with a logarithmic scale, you just have to know when and when not to use it. ~Kvng (talk) 13:54, 9 June 2017 (UTC)

OK, let us put in this way: (1) everything has disadvantages if it is misused, and the "disadvantages / Criticism" is nothing else but report on uneducated misuses. (2) The "Advantages and disadvantages" suggest as if there was a debate on the advantages and disadvantages of using decibel. But there is no debate at all, but only uneducated users of decibel. prohlep (talk) 15:56, 12 June 2017 (UTC)

In what sense are the authors of refs 25-31 uneducated? Dondervogel 2 (talk) 16:12, 12 June 2017 (UTC)

Introduction is not introductory enough

As a rule of thumb, we ought to try to explain dB in layman's terms before launching into the nitty-gritty. There should be some sort of overview that gives the general sense of what dB does, why it is relevant, and why it is often misunderstood. I could write something like that, but I am not an expert in the field and do not know the proper sources to cite. For example, we might have:

Decibels (dB) are used as units in many fields, most commonly in acoustics for the loudness of sounds and in electrical engineering for the amount of power in a radio frequency transmission. Decibels are not, by themselves, a unit of measurement. Rather the decibel is a convenient way to specify a logarithmic scaling factor, similar to scientific notation, with reference to a known quantity (such as, 20 micropascals or 1 milliwatt). Decibels greater than zero represent an amount larger than the reference quantity. Zero decibels (0 dB) is exactly one unit, while negative decibels represents a smaller fraction of the reference amount. Decibels are often misunderstood for two reasons: the reference quantity is sometimes omitted (writing "dB" instead of "db_SPL" or "dBm") and the scaling formula depends on whether one is measuring a "field" or "power" level. (See below.)

Ben (talk) 01:49, 24 September 2017 (UTC)

A layman's introduction would indeed improve the article. How about this?

The decibel (dB) is a unit used in many fields of engineering to represent power, most commonly in acoustics for sound level and in electrical engineering for the power in a radio frequency transmission. However, a decibel is not a unit of linear power in the same sense as a watt. Instead it is a unit used on a logarithmic scale (level), often relative to an interationally agreed reference power such as one milliwatt (1 mW). A level relative to 1 mW greater (less) than zero implies a power greater (less) than 1 mW, while a level of 0 dB implies a power equal to 1 mW.

Dondervogel 2 (talk) 09:20, 24 September 2017 (UTC)

I still like my version better as it is clearer about the reference quantity and relates dB to something many people are familiar with (scientific notation), but if you have the proper sources to cite, we should go with what you've got. I suggest we also make it clear, even in the introduction, that dB is *not* a unit, it's a scaling factor. Ben (talk) 15:13, 27 September 2017 (UTC)

"Not a unit" is one opinion. The NIST says:

Table 8 also gives the units of logarithmic ratio quantities, the neper, bel, and decibel. These are dimensionless units that are somewhat different in their nature from other dimensionless units, and some scientists consider that they should not even be called units. They are used to convey information on the nature of the logarithmic ratio quantity concerned. The neper, Np, is used to express the values of quantities whose numerical values are based on the use of the Napierian (or natural) logarithm, ln = loge. The bel and the decibel, B and dB, where 1 dB = (1/10) B, are used to express the values of logarithmic ratio quantities whose numerical values are based on the decadic logarithm, lg = log10. The way in which these units are interpreted is described in footnotes (g) and (h) of Table 8. The numerical values of these units are rarely required. The units neper, bel, and decibel have been accepted by the CIPM for use with the International System, but are not considered as SI units.

Dicklyon (talk) 16:32, 27 September 2017 (UTC)

In the International System of Quantities the decibel is defined as a unit of level. A statement to the contrary would be controversial because it would conflict with international standards. Dondervogel 2 (talk) 16:50, 27 September 2017 (UTC)

@Dicklyon: I think the NIST quote that "some scientists consider that they should not even be called units" should be in the introduction. @Dondervogel, from my layman's eyes it appears the consistent with international standards to say that a 'decibel' is not actually a unit, but is used as one in different fields by multiplying it against an implied unit. I think the word "level" is the key here. Yes, a decibel is a "unit of level", but that's presuming you have known reference quantity for the level (e.g., 1mW). For example, ISO 2041:2009 can correctly use statements like "the bel is a unit of sound-pressure-squared level", because the "level" in this case implies multiplying by 20 micropascals. Ben (talk) 16:06, 30 September 2017 (UTC)

list of suffixes in alphabetical order

I found it difficult to find things with the suffixes sorted by subject, so I added a list in alphabetical order. Suggestions for improvement are welcome. Dondervogel 2 (talk) 10:33, 30 September 2017 (UTC)

Maybe it is time to try a sortable table. ~Kvng (talk) 17:31, 4 October 2017 (UTC)

Great idea. (wouldn't know how though - gladly leave implementation to a more competent editor!) Dondervogel 2 (talk) 18:39, 4 October 2017 (UTC)

Field quantity (again)

Previous editors have asked for a definition of "field quantity", maybe easier to answer would be: what are valid "field quantities" in the context of this article? Since the use of decibel is more or less determined by IEC recommendations and ISO standards, it must be possible to list all of them, why not include that list in the article? Or if there aren't any apart from the ones already mentioned in the article (voltage, current and (sound) pressure), that would be useful information as well. Prevalence 19:53, 3 January 2018 (UTC)

I just added a link to Field, power, and root-power quantities, which I think would be a better home for such a list, though it would be necessarily incomplete. Dondervogel 2 (talk) 22:14, 3 January 2018 (UTC)

Adding the old meaning of dB in the historical section (0db=6mW)

In the audio electronics of 1939, 0dB was equivalent to 6mW. I believe this should be included in the Decibel page for completeness and also because hobbyists doing research and encountering the older equipment often refer to Wikipedia first when trying to understand various standard terms.

I do not know who originally defined this but 'Radio Handbook' is a recognized industry standard book, and Bell Labs, is a strong suspect for the origin of this old standard.

The old 6mW power level as 0dB usually had its voltage level as 1.732V into 500 Ohms, rather than 0.7746V into 600 Ohm impedance used for 0dB in audio today.

A possible reference is "The Radio Handbook, 6th edition". This can be downloaded from see pages 233 and 542. - but I understand that the original is preferable.

Here is a quotation from the Handbook: "A formula for the calculation of db gain or loss is here given: DB = 10 X log10 P2/P1 Since power is equal to the product of voltage times current when the power factor is unity, db units can be used to express voltage gain. In this case the formula is : DB = 20 X log10 E1/E2 This provides a useful means for computing the overall voltage gain of a preamplifier and the speech amplifier. When adding the gain of several stages, the db units are added or subtracted, which greatly simplifies the calculations. For example: if a preamplifier has 35 db gain, and the speech amplifier has 65 db gain, the total gain is 35 + 65, equals 100 db. One hundred db corresponds to a voltage gain of 100,000 times. Thus, for example, if the microphone level is -100 db the speech amplifier output will be -100 db + 100 db, or zero db level. Zero level corresponds to a power level of 6 milliwatts."

In the "The Radio Manual", 2nd edition, 1928, by GEORGE E. STERLING, Radio Inspector, Radio Division, U. S. Department of Commerce, Member, Institute of Radio Engineers, on page 376, it is stated: "The term decibel, abbreviated DB, has recently been adopted by international agreement to designate the unit formerly known as the transmission unit." Going back much farther may be difficult due to non-survival of publications.

Opcom (talk) 01:13, 22 January 2018 (UTC)Opcom

References

Good find. I see the 1928 book has the ".006 watts" reference level already, but neither has any indication of voltage or impedance. Have you found more on that? Dicklyon (talk) 02:32, 22 January 2018 (UTC)

Actually, page 399 of the 1928 talks about the 500 ohms:

3. No. 203-B Panel - The No. 203-B Panel is fundamentally a peak voltmeter. It is so designed that when bridged across a 5o0 ohm line or across an amplifier output circuit which is terminated in 500 ohms, it gives an indication of the power level at the point where it is bridged. This panel gives readings in terms of a unit known as the " transmission unit " (abbreviated " TU ") which is used in telephone engineering to measure ratios of electrical power. The transmission unit has recently been named the "decibel" (ab- breviated " db ") by which name it is to be known in the future, so that in the discussion which follows it will be referred to as the decibel. The controls of the earlier No. 2o3 -B Panels are designated in " TU," while the controls of the later model are designated in " db." It should be borne in mind that the decibel is identical, except in name, with the " transmission unit."

Actually, that "1928" ref is actually the 1929 second edition. I picked up the 1928 first edition, too, and it has no mention of the 203-B Panel or decibels. It does talk about transmission units (TU), the old name for decibels, but I don't see anything about the 6 mW or 500 ohms. Dicklyon (talk) 05:57, 6 February 2018 (UTC)

For example, if the reference value is 1 volt

In the case of For example, if the reference value is 1 volt, there is often an implied impedance. Should this be mentioned? Gah4 (talk) 11:13, 5 March 2018 (UTC)

What is a "logarithmic unit"?

I don't know the answer to de Piep's question (see edit summary), but the answer to the related (and more relevant) question "what is a decibel?" is "a unit of level". When I inserted this (correct) definition I was reverted, and the present wording put in its place. Dondervogel 2 (talk) 01:20, 3 March 2018 (UTC)

I know dB wrt sound. It is a physical quantity for sure. But *not* a 'logarithmic unit'. - DePiep (talk) 02:01, 3 March 2018 (UTC)

I agree it is not a logarithmic unit. Or rather, I think the unit "logarithmic unit" is used for dumbing down the text so readers do not worry about what a decibel really is. Dondervogel 2 (talk) 11:32, 3 March 2018 (UTC)

Hmmm. I'd say: the level (this is where the solution is to be found indeed, good link) is a physical quantity, defined as a logarithmic value (in quantities, the value is the "number × unit" whole). So "20 dB SWL" is a logarithmic value, but the unit part itself is not. - DePiep (talk) 18:28, 4 March 2018 (UTC)

The wording in BIPM docs such as this one is "unit for expressing the values of logarithmic quantities"; or "units of logarithmic ratio quantities" in this one. There is no doubt that decibel is a unit. What is it a unit of? Certainly not any physical quantity. Here by "logarithmic quantity" they mean the logarithm of a dimensionless ratio of physical quantities, and the point is that you don't have to say what log base you mean, if you use the unit to measure it. A logarithmic quantity measured in decibels or in nepers gives different numbers for the same logarithmic quantity because you measure it with different units; but it's the same logarithmic quantity being measured. Or so you should hope. But as this note points out, we really have two very different types of dimensionless ratios that we want to measure; using decibels both for amplitude ratios and for power ratios doesn't make sense; it needs two different decibel units. And measuring amplitude ratios both by nepers and by decibels is discordant with how the SI system works in general. He proposes using decibels for power, energy, intensity, mean-square etc. logarithmic quantities, and nepers for field/amplitude type logarithmic ratios, which makes a lot of sense for various reasons. It's really hard to treat these things as units of logarithmic quantities when the quantities are ratios of such different things. Dicklyon (talk) 18:59, 4 March 2018 (UTC)

A lot of interesting reading in here.

First shots: good to note that you do not write "logarithmic unit". Next: What is it a unit of? Certainly not any physical quantity -- I disagree. It is of certain physical quantities. Any scientist can define a physical quantity as they think best, and that includes dB formulae. Even when complicated math is involved, and even when the unit is dimensionless. -DePiep (talk) 20:30, 4 March 2018 (UTC)

Just depends on what you think "physical" means then. You said above "I know dB wrt sound. It is a physical quantity for sure." and I'm at a loss to interpret what you mean by physical there, or how the application to sound pressure or power ratios has an effect on what the unit is. Dicklyon (talk) 00:34, 5 March 2018 (UTC)

The decibel is a unit of level and the article should start with a simple factual statement to that effect. If that statement needs clarification, fair enough, but like dePiep I do not understand what is meant by "logarithmic unit". Dondervogel 2 (talk) 20:50, 4 March 2018 (UTC)

It might not be the preferred way to say it, but it seems clear enough what it means; find explanation at Logarithmic scale#Logarithmic units. Or some of these sources. Formally, a "unit of level" is what the standards guys like to call it, but since few people who use decibels have any appreciation for what "level" means, that might not clarify much. Still, probably worth saying, with a link to the appropriate BIPM docs. Certainly at least fix the nonsense that says "ratio of the two power levels". Dicklyon (talk) 00:34, 5 March 2018 (UTC)

Actually, the NIST Guide for the Use of the International System of Units (SI) does use the term "logarithmic unit":

8.7 Logarithmic quantities and units: level, neper, bel

This section briefly introduces logarithmic quantities and units. It is based on Ref. [5: IEC 60027-3], which should be consulted for further details. Two of the most common logarithmic quantities are level-ofa-field-quantity, symbol LF, and level-of-a-power-quantity, symbol LP; and two of the most common logarithmic units are the units in which the values of these quantities are expressed: the neper, symbol Np,

or the bel, symbol B, and decimal multiples and submultiples of the neper and bel ...

That doc also says "When reporting values of LF and LP, one must always give the reference level", which seems to be using "level" incorrectly (or more like we engineers use it informally, not necessarily as a logarithmic quantity), like some uses that I just fixed in the article. Dicklyon (talk) 02:52, 5 March 2018 (UTC)

I am not so sure how to compare the popularity of unrelated units, but pH and the Richter scale (which doesn't seem to have a name for its unit) should be on the list somewhere. Optical absorption is commonly described in a log base 10 unit that is not dB related, though it would seem to make about as much sense to use dB for it. Gah4 (talk) 02:19, 5 March 2018 (UTC)

Yes, those are logarithmic quantities that might not use standard units. The absorbance or optical density is essentially in units of bels, if I understand correctly; pH, too, sort of. Dicklyon (talk) 02:52, 5 March 2018 (UTC)

Yes both absorbance and pH are log10, but also include a minus sign. Gah4 (talk) 11:09, 5 March 2018 (UTC)

Just like dB of attenuation (input power relative to output); depends on which quantity you take as the reference (denominator). Dicklyon (talk) 16:29, 5 March 2018 (UTC)

0 dB = +8 volts in audio electronics

@Dondervogel 2: I believe this is notable, even though it's obscure, because it serves to document the history of audio level interconnect standards in the industry. Can you take a look at the source and help me make the below description more clear? The drawing of the meter on page 42, and on page 43 is the statement "On the scale, 0 db was chosen to be 8 volts, so -6 db represents 4 volts." which is a further basis for claims below. Oops; I just spotted the +6 dB instead of -6 dB typo on my part.

dB

dB – a 1950s consumer audio measurement scheme used without a suffix, with dB 0 calibrated to be +8 Volts (with −6 dB representing 4 volts), with a range of −22 dB/0 volts to +2 dB/10 volts.

My purpose here is to find dB relationships to volts used in the audio industry that will lead to the modern defacto standard of -10 dBV as the reference level for consumer line-level audio. I'm currently reading every issue of Audiocraft in search of other relevant references.PetesGuide, K6WEB (talk) 19:12, 18 September 2018 (UTC)

Thank you, this helps. One thing that still puzzles me is the apparent claim that -22 dB corresponds to 0 V. Do you understand what that means? Dondervogel 2 (talk) 22:32, 18 September 2018 (UTC)

Oh, I see it now - the -22 dB correspondence is in the drawing. That seems dubious to me. Better to start from the stated 0 dB point (8 V) and work back to -6 dB (4 V), -12 dB (2 V) and -18 dB (1 V). But these values do not correspond to those in the drawing, so something is still not quite right.

Question: The voltage values are rms, right? (otherwise the formula for power does not make sense). Is there an implied value for the resistance?

Dondervogel 2 (talk) 10:35, 19 September 2018 (UTC)

Oh, very good catch. From a quick glance, I thought that −22 dB and 0 volts on the scale image were coincident, but they're not. 0 volts is somewhere lower than −22 dB, but I don't see a way to calculate it from the article or the meter image. I do believe the voltages are RMS. Can you describe how you equated -18 dB to 1V, when that doesn't agree with the drawing? I'm not fluent on decibel math.

But −16 d and 1 volt appear to be exactly coincident, so how about this?

dB

dB – a 1950s consumer audio measurement scheme used without a suffix, with dB 0 calibrated to be +8 Volts (with −6 dB representing 4 volts), with a range of 0 volts (lower than −22 dB) to 10 volts (+2 dB), with 1 volt being equal to −16 dB.

Oh, also, do you have access to any of the ISO or IEC documents that define dBV and other audio level standards?PetesGuide, K6WEB (talk) 14:54, 19 September 2018 (UTC)

On this scale, 1 V would correspond to -18 dB, not -16 dB (each factor of 2 change in rms voltage results in a 6 dB change in level). The near-coincidence of -16 dB on the meter scale is misleading.

With this in mind how about

dB

dB – a 1950s consumer audio measurement scheme used without a suffix, with 0 dB, -6 dB and -12 dB corresponding to an rms voltage of 8 V, 4 V and 2 V, respectively.

I don't think you'll find an ISO or IEC standard defining dBV because use of that notation is deprecated by IEC. In IEC-speak the unit is the decibel (symbol dB), regardless of the physical quantity being measured.

Dondervogel 2 (talk) 16:44, 19 September 2018 (UTC)

I like it, except for not including 1 V, which I think will help readers relate this usage to other definitions that are defined relative to 1 V. And should there be some note about the alignment/misalignment of the scale?

dB

dB – a 1950s consumer audio measurement scheme used without a suffix, with 0 dB, -6 dB, -12 dB, and -18 dB corresponding to an rms voltage of 8 V, 4 V, 2 V, and 1 V, respectively.

PetesGuide, K6WEB (talk) 16:55, 20 September 2018 (UTC)

Perfect. I suggest waiting for 24 hours to allow others to comment, and if no one does, to add your latest proposal. Dondervogel 2 (talk) 18:56, 20 September 2018 (UTC)

Reading it again, I wonder if it is just an example, and not an actual indication. It mentions that they do put dB scales on voltmeters. Note that you can use such a scale to compare two values, without knowing the actual reference value, as long as both are made with the same load impedance. Even more, note that most voltmeters have more than one voltage scale, sometimes with the user supplying the decimal point. (In the one shown, that might apply for an 8V, 80V, and 800V scale.) It does mention dBm in the article. As well as I know it, audio, more specifically telephony, now uses a 600 ohm load, but that might not have been done at the time. Gah4 (talk) 19:36, 20 September 2018 (UTC)

I'm pretty sure the article does not describe a device with a switch that can be set to either dB or Volts, but we should read more carefully to be sure. Also, modern audio no longer uses 600 ohms except in very specific conditions, and only the POTS telephone system still uses it consistently. dBm is 600 ohm specific, but dBu is not, and neither is dBV. Read up on impedance bridging for a deeper understanding of why. And in particular, I think the topic of this addition may be one of the links in how we got from using dBm/dBu for audio to using dBV. PetesGuide, K6WEB (talk) 01:40, 21 September 2018 (UTC)

References

gamma correction

Continuing the previous note, some video signals are gamma corrected. A CRT monitor does not generate a signal linear in the input voltage, but some power, called gamma, of the voltage. To make CRT televisions easier to build, video signals are adjusted at the source (once), instead of in each individual receiver. Should this be discussed here? Gah4 (talk) 02:43, 11 January 2019 (UTC)

No. Nothing to do with logarithms (decibels), and covered at gamma correction. Dicklyon (talk) 05:09, 11 January 2019 (UTC)

The question is, how do you quote power levels or gains of signals that have had gamma correction applied. Gah4 (talk) 10:39, 11 January 2019 (UTC)

The gain applied to a signal doesn't depend on what the signal represents. Dicklyon (talk) 15:56, 11 January 2019 (UTC)

optics

I believe that the distinction between amplitude and intensity, that is, square or not, in the case of optical signals needs more fixing. Since most of the time, one doens't measure the amplitude (of the electric or magnetic field) of an optical signal, but instead the power imparted to some system, often an output signal is a voltage proportional (maybe gamma corrected) to the power level. Gah4 (talk) 02:39, 11 January 2019 (UTC)

Yes, the application of decibels to images is usually quite fucked up, applied as if for a field value when the voltage really represents an optical power or energy as counted by collected photo-electrons. It's hard to find a source that admits that though. Actually, it's covered a bit in the next section, Decibel#Video_and_digital_imaging. Dicklyon (talk) 05:12, 11 January 2019 (UTC)

Maybe this is a bit tangential, but this is IMO a symptom of the messed up definition of the dB: to make it "simpler" (no factor when going from root-power to power), the unit has been ill-defined; if the factor of 2 had been included (so that e.g. the power level is the sum of the voltage level and current level), the level of any ratio would have been unambiguously defined. The optical case is a little muddy, but the quantity being measured needs to be specified, e.g. the sensor response (voltage), the intensity, etc. One weird one that is rooted in physics is pressure: is it a root-power or a power quantity? In acoustics, it is clearly treated as a root-power quantity, but in electromagnetism (as three components of the stress–energy tensor, it can only be a power quantity, since it is proportional to the square of EM field strength, a root-power quantity. —Quondum 19:04, 11 January 2019 (UTC)

re "missing something?"

With reference to this edit comment , I was alluding to that even in linear systems, there is no simple relationship P/P₀ = (F/F₀)². I was sensitized to this only recently by one of the references (probably the Mills paper in Metrologia that I have). It is only true if either of two conditions holds: the impedance is frequency-independent (excluding phase), or the waveform has the same power spectrum. Either of these can be described as "idealized". I am not happy with the word "idealized", but I was finding an interim way of not reverting the revert of my edit, and simultaneously prompting a discussion. —Quondum 16:16, 1 March 2019 (UTC)

In that case I think all that is needed is the addition of some words in the body of the article, explaining the above . Dondervogel 2 (talk) 17:48, 1 March 2019 (UTC)

Hickling

@Mark v1.0: In edit on 2019-06-14 you removed a section mentioning Hickling, without a reference to who he is. Doing a [WikiBlame] I found it was added complete with reference in edit on 2013-09-06.

I'm not sure what to do with this information though... There has been talk in this talkpage about the encyclopedic merit of arguments that Decibels are confusing... Heddmj (talk) 10:41, 18 June 2019 (UTC)

That is news to me. How else can we measure sound level volume/pressure?--Mark v1.0 (talk) 16:43, 19 July 2019 (UTC)

Sound pressure, sound power and sound intensity are most easily understand when present in pascals, watts, and watts per square metre. The use of the decibel is confusing because one first needs to divide these intuitive physical quantities by some arbitrarily chosen reference value and then take the logarithm. Doing so obscures the original meaning, especially when one conveniently "forgets" to mention the reference value. Dondervogel 2 (talk) 20:01, 19 July 2019 (UTC)

On the other hand, the numerical ranges typical of dB are so much easier to deal with that measurements expressed in dB become very easy for practitioners to deal with and visualize and compare. Their use is not confusing to those who use them. Dicklyon (talk) 05:24, 20 July 2019 (UTC)

I guess it's fair to say that when used correctly, they're not confusing to those who understand them. In my experience they are rarely used unambiguously and often used by individuals with no training in acoustical or electrical engineering. In those circumstances the result is confusion. In the end though it is not my opinion that matters, but the views expressed in the publications we are citing. Dondervogel 2 (talk) 07:54, 20 July 2019 (UTC)

dB is in fact a pseudo-unit

The page states that decibel (dB) is a unit. It is more correct to state that decibel is a pseudo-unit. It is not a real unit because it is always related to a reference. ISO also does not recognise dB as a unit. — Preceding unsigned comment added by Mvenl (talk • contribs) 19:50, 13 December 2019 (UTC)

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