Talk:Neper

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)

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

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)

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)

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)

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)

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)

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)

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

1Np = 1

I've added a 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)

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)

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)

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)

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)

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)

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)

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)

Definition seems to have a wrong wording

"The level a ratio of two signal amplitudes" ... "is given by", ...where,...and.

If it means "The level of a ratio", then what is "The level of a ratio"?

In my understanding "Neper" and "dB" are ratios

and you only have to write a small number because the number is interpreted differently.

Somehow the whole notation of writing

$somenumber{~Np}$

seems wrong to me. Because,...

if $somenumber=1$

and ${\frac {voltage_{1}}{voltage_{ref}}}=1{~Np}$ means

${\frac {voltage_{1}}{voltage_{ref}}}=e$

then one could conclude,

$1{~Np}=e$

and $2*1{~Np}=2*e$

and then,... is there a Rule that prevents me,...

from $2{~Np}=2*e$

Shouldn't it be notated like so ?

$2*{~Np(1)}=2*e$

Alex fdhsjrtfg82 (talk) 21:54, 12 April 2023 (UTC)