Talk:Neper

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Implicit conversions from wave amplitude

All the sources claiming that the value in nepers is $\ln {\frac {a}{b}}$ are also saying that in decibels it is $20\log {\frac {x_{1}}{x_{2}}}$ which is patently incorrect, decibels are clearly defined such that it is $10\log {\frac {x_{1}}{x_{2}}}$ - assuming the ratio between decibels and nepers are correct it is ${\tfrac {1}{2}}\ln {\frac {x_{1}}{x_{2}}}$ as given in [1] [2] and [3]

http://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm gives a clue as to where the 20 came from, but it needs to be made clear that the version with 20 and without 1/2 is specifically for power ratios in terms of values given in terms of voltage or current, rather than for power ratios in terms of power or ratios of any other quantity given in terms of that quantity.

It looks like $20\log {\frac {x_{1}}{x_{2}}}$ is supposed to be $10\log {\frac {x_{1}^{2}}{x_{2}^{2}}}$ where $x^{2}$ is a quantity that varies as the square of the quantity whose ratio is being considered in nepers.

--Random832 (contribs) 17:54, 28 April 2008 (UTC)[reply]

I'm removing the dubious tag, as the disclaimer summarizes this concern. Potatoswatter (talk) 12:43, 6 July 2008 (UTC)[reply]

The problem is what you've replaced it with is original research. You'll need citations to back up that position. Xihr (talk) 20:54, 6 July 2008 (UTC)[reply]

What needs to be cited? In my experience textbooks take the identity for granted. Actually this is the first I've heard of either unit being "naturally" suited to one use. Potatoswatter (talk) 22:46, 6 July 2008 (UTC)[reply]

The OR problem was that you replaced it with text that suggested that using a single, unified unit would be preferable. Xihr (talk) 22:49, 6 July 2008 (UTC)[reply]

Sometimes it is. I wouldn't say "unified." Nepers are easier when working with exponential equations and decibels are easier when characterizing/specifying a filter. But mixing two equivalent units on the same page of calculations is always asking for a disaster. Potatoswatter (talk) 04:26, 7 July 2008 (UTC)[reply]

That's a completely reasonable point of view, but that's also what makes it original research and inappropriate for the article. Xihr (talk) 04:52, 7 July 2008 (UTC)[reply]

Still not sure what you object to, but is this more moderate phrasing OK? I think it's important to link the statement that each ratio has a different natural application to the introduction of Joule's Law. Potatoswatter (talk) 08:08, 7 July 2008 (UTC)[reply]

Yes, that's fine. Xihr (talk) 08:21, 7 July 2008 (UTC)[reply]

1Np = 1

I've added a ^{[citation needed]} for 1 Np = 1. I can't find a source for this after a few minutes' Google searching. I haven't paid for the ISO document. To me, it would make more sense if 0 Np = 1. --Doradus (talk) 11:51, 25 August 2016 (UTC)[reply]

I found some evidence for 0 Np = 1. The BIPF document says this:

The statement LA = n Np (where n is a number) is interpreted to mean that ln(A2/A1) = n. Thus when LA = 1 Np, A2/A1 = e. The symbol A is used here to denote the amplitude of a sinusoidal signal, and LA is then called the neperian logarithmic amplitude ratio, or the neperian amplitude level difference.

If 1 Np is e, then 0 Np would be 1. This quotation isn't exactly making a statement about the absolute value of 1 Np, though. --Doradus (talk) 12:01, 25 August 2016 (UTC)[reply]

It is not correct to say that 1 Np is e. A correct statement is ln(e) = 1 Np. Another is 1 Np = 1. I have added a reference. Dondervogel 2 (talk) 16:20, 25 August 2016 (UTC)[reply]

1 Np is ratio of e to 1, just as 1 dB is ratio of 1.258925412 to 1. None of them are ONE because of the defining equation. Logarithm of one is zero with any base. I am referring to power ratios. @Dondervogel 2 is quoting a discussion about status of SI units. This only brings confusion as it clashes with the equation on which neper is based. Morycm (talk) 16:52, 25 September 2024 (UTC)[reply]

I'd say that 1 Np represents an amplitude ratio of e to 1. That does not make it equal to that ratio.

Similarly, 1 dB represents a power ratio of approximately 1.26; it also represents a root-power ratio of approximately 1.11, but 1 dB is equal to neither 1.26 nor 1.11. Dondervogel 2 (talk) 17:24, 25 September 2024 (UTC)[reply]

I have seen your comment from 2024, but I'm replying to your 2016 comment in which you say 1 Np = 1 without truly motivating that statement, although you did add a citation. I think your citation may be emphasizing that 1 Np is unitless. Removing the units altogether, as in 1 Np = 1, doesn't actually make the two sides unequal, they might argue. It seems to me that 2 Np = 2 is equally true but more misleading. 0 Np = 1 is not really "helpful" as an equation either, it invites the reader to divide by zero, and it obscures the fact that Np is notation, not a unit, it is not being multiplied by the number preceding it. In conclusion, I think all of these equations are rather unhelpful and don't model good or useful behavior, nor do they teach us anything. That includes 1 Np = 1, although it appears in a reputable source, it is not helpful or informative. Fluoborate (talk) 04:37, 8 January 2025 (UTC)[reply]

Your are correct to point out that 2 Np = 2 is equally true, but the statement 0 Np = 1 cannot be correct because 0 Np = 0. None of these statements are misleading because they are all direct consequences of the definition of the neper. Do you think a clearer explanation would help? Dondervogel 2 (talk) 08:48, 8 January 2025 (UTC)[reply]

I would also like to point out why an expression like "1 Np = 1" jumps off the page. As an illustration, one way to correct this would be to replace with "1 Np = 1 Np" so that both sides of the equation have units. Similarly, you could have expressions that show how to convert to other logarithmic based units, like deciBels, etc. These kinds of units are used to express the ratios of two entities that, in turn, have the same units. The cited report (written by Thor) has unclear wording, and then it is the source of the quoted "1 Np = 1", but just citing it doesn't make it correct usage. After all, these are not really physical units, they are just shorthand notation that allows you to convey to the reader the base of the logarithm. And then, after the log has been taken, then the reference quantity in the denominator is now tacit. You'd have to check back into the calculations to ask "with reference to what?" So why don't we just remove this line "1 Np = 1" and let it fade away onto the wayback machine? ;-) ~2025-32218-08 (talk) 20:08, 9 November 2025 (UTC)[reply]

Like the radian, the neper is a dimensionless unit whose value happens to be equal to 1. See, e.g., ISO 80000-3:2006 for an explanation (I don't have the Thor 1994 article. I have requested a copy).
Would you argue we should remove the statement "1 rad = 1" from Radian?

Dondervogel 2 (talk) 20:51, 9 November 2025 (UTC)[reply]

I have now read the relevant parts of ISO 8000-3:2006 (page vii) and Thor 1994 (p521). Similar to the definition of the radian, both sources define the neper as a dimensionless unit equal to 1. If the unit neper is defined as 1, it is also equal to 1. Dondervogel 2 (talk) 19:54, 10 November 2025 (UTC)[reply]

I'm not sure why this is so interesting to discuss, but let me join you at your logic and take it a step further. If we say that "1 Np = 1", by definition, and "1 rad = 1", by definition, therefore we can next say that "1 Np = 1 rad" which is not true, and its not something we want to say. So yes, that's my argument against such expressions -- even if somebody else says it's true. A Neper should be permissible only as a shorthand suffix for the value that was calculated by taking the natural log of the ratio of the amplitude of two measured signals. Thanks for the quick reply! ~2025-33126-42 (talk) 17:07, 12 November 2025 (UTC)[reply]

Formally, from a strictly mathematically perspective, it is correct to write 1 Np = 1 rad, and if I were to perceive any insights derived from writing that expression I would not hesitate in doing so. But I see no such benefits and therefore refrain from writing the equality in this way. Dondervogel 2 (talk) 18:59, 12 November 2025 (UTC)[reply]

Thank you Dondervogel -- I think we're coming to the same conclusion, though from different sides. Here it is, plainly: While writing "1 Np = 1 rad" might be surprisingly true from a strictly mathematical perspective (ie. since "1 = 1") there are no benefits from writing such expressions. In fact, these expressions provide opportunity for confusion, and this has been a long problem with such shorthand symbols such at dB and Np. So we should not write, "1 Np = 1", instead we should write something like, "after applying 10 volts to the input of the network, 2 volts were measured at the output. Therefore, the attenuation was ln(2V/10V) = -1.6 Np. This value is worse than the previous attenuation which was -1.2 Np". And in the text, the author could then talk about other measurements that lead to values in nepers, because the *context* would make the references implicit. So, unfortunately, these shorthand notations were never meant to be the subject of pure mathematical scrutiny, because they are context-dependent (and therefore frustrating for philosophical and mathematical discussion). So, I'm on the side that say, let's avoid saying "1 Np = 1" (or 1 rad = 1 for that matter) Cheers and thanks. ~2025-33126-42 (talk) 17:13, 13 November 2025 (UTC)[reply]

So we agree on not writing "1 Np = 1 rad". While strictly correct, neither of us perceive any value in it.
Where we do not agree is on writing "1 Np = 1". Here I do see a value (it makes the definition explicit), while you do not.

Dondervogel 2 (talk) 18:49, 13 November 2025 (UTC)[reply]

SI interpretation

I note with interest that the Draft of the ninth SI Brochure says:

"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 = log₁₀. The statement L_X = m dB = (m/10) B (where m is a number) is interpreted to mean that m = 10 lg(X/X₀)."

This borders on being incompatible with this article and Level (logarithmic quantity) (and the ISO 80000-3 standard). Are there substantial examples (outside of a few standards and articles about them) where the Np is used in the sense of log_e² (as opposed to log_e)? I know usage of dB for both 10 log₁₀ and 20 log₁₀ is extensive (unfortunately). —Quondum 03:35, 13 November 2018 (UTC)[reply]

From searching articles the main use of nepers seems to be attenuation, where it's a root-power (field) quantity and the unit is Np/m. I couldn't find any uses of the power form with the factor of 1/2 or log_e², but I don't know any good keywords. But the IEC standard seems pretty clear that nepers are also subject to the power vs root power ambiguity, unfortunately. I think you have to use a non-standardized unit like log change, maybe written as "2 l.c." following percentage points, if you want to avoid the possibility of squaring. --Mathnerd314159 (talk) 02:33, 10 April 2022 (UTC)[reply]

Argument of ln() must be unitless

The initial equations in this article need repair. The Neper is defined as natural log of a ratio of powers. One can take the log of a dimensionless number. One can take the log of the ratio of two powers because that is dimensionless. One cannot equate the log of the ratio of two powers to the difference of the log of the numerator and log of the denominator, since these have dimensions and the log function argument must be dimensionless. Tedweverka (talk) 18:29, 25 October 2022 (UTC)[reply]