Talk:Noise figure

Noise figure in attenuators

"Attenuators have a noise factor F equal to their attenuation ratio L" I just can't see how this can be correct, for example an attenuator made of capacitors (voltage divider) will not introduce any new noise so the SNRin and SNRout will be the same, therfore the noise figure of such an attenuator will be zero, I am sure that there are many other examples where the NF is zero or irrelevant. A resistive attenuator's NF would be a function of the resistors used not the level of attenuation. — Preceding unsigned comment added by 114.34.217.17 (talk) 04:31, 27 March 2014 (UTC)

The signal gets attenuated by L but the thermal noise stays at the same level; consequently, the NF gets worse by the attenuation factor. Glrx (talk) 03:35, 22 December 2015 (UTC)

I think "attenuator" implies that the excess power is absorbed. In other words, input and output are matched. The reactive circuit you describe does not really attenuate; it reflects the excess power (it presents a mismatch). In a matched attenuator it does not matter what the internal resistors are, only the system impedance matters when calculating noise. And you will find that the statement that F=attenuation is correct in that case. Mayrayday (talk) 17:05, 8 February 2024 (UTC)

Satellite communication systems

The article currently says:

...in the case of satellite communications systems, where the antenna is pointed out into cold space, the antenna effective temperature is often colder than 290 K. In these cases a 2 dB improvement in receiver noise figure will result in more than a 2 dB improvement in the output signal to noise ratio.

From the definition of NF, I don't see how this can be true:

$\mathrm {SNR_{out,dB}} =\mathrm {SNR_{in,dB}} -NF$

The receiver doesn't know anything about the signal source. What am I missing? GyroMagician (talk) 10:29, 19 March 2010 (UTC)

External Links

Hello MrOllie. I'm curious - why did you remove the external links to Analog? I'm not saying you were right or wrong, just curious to know your reasoning. GyroMagician (talk) 17:30, 11 August 2011 (UTC)

I was thinning links to analog.com out (especially the ones that include fluff pieces on Analog employees and/or products) because I recently noticed that they have been systematically added by a single purpose editor for a fairly long period of time. - MrOllie (talk) 17:47, 11 August 2011 (UTC)

I agree with the removal of the ADC Noise Ref; it doesn't extend the article. I don't know about the log amp one; I can see reasons to keep or delete. I'm not sure a discussion of log amps belongs in this article. Glrx (talk) 03:44, 12 August 2011 (UTC)

Yes, that seems fair. I asked because I met an editor a while ago who was convinced that all company design guides, etc, were advertising (I think it related to an Agilent document describing S-parameters). Anyway, I'm happy to find you're more sensible MrO ;-) The log amp article seems useful, but I'd agree this is the wrong place for it. GyroMagician (talk) 18:35, 15 August 2011 (UTC)

For reference, the log amp link: http://www.analog.com/library/analogDialogue/archives/42-06/noise_figure.html Glrx (talk) 15:00, 16 August 2011 (UTC)

Amplifiers

The equation and description here seem to refer to receivers and electronics. Can anyone add similar information for optical amplifiers? Madgenberyl (talk) 16:15, 11 July 2012 (UTC)

I'm not certain, but as the calculation is entirely in terms of the amplifier input and output SNR (with no attempt to model the noise source), I would imagine it would also apply to optical amplifiers (or mechanical, or any other mode, for that matter). GyroMagician (talk) 17:38, 11 July 2012 (UTC)

Many of the WP noise articles are RF-centric with the side-effect that impedance issues are ignored (many RF systems use a standard impedance such as 50 ohms). More sophisticated models include noise currents and noise voltages and illustrate tradeoffs between noise matching and gain matching. Glrx (talk) 18:31, 11 July 2012 (UTC)

In general I'd agree (and not just on WP) - but as NF is defined in terms of power, Z doesn't make any difference here, does it? GyroMagician (talk) 22:43, 11 July 2012 (UTC)

This article says what NF is, suggests how it might be measured, and how to calculate cascades if I know the stage NF. It doesn't describe how to compute a stage NF given a source impedance and the amplifier noise parameters. It does not suggest design tradeoffs.

Impedance matters. If a stage has a high noise current and a low noise voltage, then a lower impedance source may be attractive. If the noise current contribution i_nR_s >> noise voltage e_n, then reducing the source impedance by a factor of 4 reduces the i_n contribution by a factor of 4 while the source's thermal noise voltage declines by factor of 2 (ideal transformer with 2:1 turns ratio gives the 4:1 Z ratio); SNR improves by 6 dB.

But there's another issue. Decreasing the source impedance may increase the stage mismatch loss and wreck the SNR another way.

Setting different bias conditions also impacts noise, gain, and noise figure.

Glrx (talk) 23:57, 11 July 2012 (UTC)

It's true that Z matters for amplifier design. Even in the RF world, low noise amplifiers are typically noise-matched rather than reflection matched (i.e. the input match stage is set to minimize the NF rather than reflection). But this is all about amplifier design, not NF itself. Maybe we do need a section describing how to calculate NF under different Z, talking about i_n and e_n, but I can't help feeling this would belong more on the low noise amplifier page than here (and that page could really do with some work).

I would have pointed Madgenberyl to the LNA article if it were helpful; that's why I made the many of the WP noise articles comment. The topic should be covered somewhere; it can have a short summary and link in other articles. I'm in basic agreement, but NF is both an amplifier and a systems issue. Glrx (talk) 14:06, 12 July 2012 (UTC)

Definition

The whole part about noise temperature doesn't really make sense in my opinion. T_e and T₀ are both called "noise temperature", so it's not clear what's the difference between these is. — Preceding unsigned comment added by 2A02:908:F324:7780:F830:11A7:9F6D:DA19 (talk) 18:49, 6 June 2016 (UTC)

Yes, the article uses the term standard noise temperature, T₀ as short hand for standard temperature at which noise is specified, T₀. Noise temperature is just another way to specify noise power. Saying there is a standard noise temperature is saying that there is a standard noise power, which is nonsense. Constant314 (talk) 19:01, 6 June 2016 (UTC)

New writeup needed to coherently address that there are two definitions for noise figure, one from Friss, and the other from the IEEE.

I intend to submit a new write-up, similar to the one "undone", and want to seek out agreement on publishing it.

As far as background, please understand that I am a life member of the IEEE and have been asked several times by different industry groups to teach seminars on "noise-figure" as its understanding is flawed and particularly problematic in the systems that I work with, which must deal with a combination of very high noise temperatures, and very low noise temperatures.

In those seminars, I have been asked several times to "fix" the Wikipedia noise figure page, and finally decided to try to do so. My write up is intended to be a significant help to the radio engineering community.

While the current article is similar to other troubling literature, that does not make it correct. Indeed, my article is written to help an audience (like those attending my seminars) that has been exposed to similarly flawed literature. There are significant problems with the current Wiki Noise Figure article. If there weren't, I would not have bothered with this work. To help you recognize the problems with the current article and to help resolve any differences we have over what should be published, I would very respectfully like to suggest we agree on the following

1. What documents are primary authoritative source documents?

1.1. On the positive side – There are, in fact, are two primary authoritative source documents regarding the definition of noise-figure? One is the 1944 article from Friss who originated the term Noise-Figure, and the other an industry standard from the IRE which is the current IEEE standard.

Friis, H. T. (July 1944). "Noise Figures of Radio Receivers". Proceedings of the IRE. vol. 32, no. 7: 419–422.

Haus, H A et al, (1959). "IRE Standards on Methods of Measuring Noise in Linear Twoports". Proceeding of the IRE. 32: 60–68.

1.2. On the negative side—Can we agree that all other articles, book chapters, application notes, etc. are not primary documents, as they depend on a reference that points to one or both of the above primary documents?

I hope we can all easily agree here on both 1.1 and 1.2.

2. The definitions in these two primary documents are different.

2.1. Simply read the two source documents. You will find the definitions are in fact different. You will find that the two definitions are as I have described in my contributed article. I respectfully request that you thoroughly read my article describing Noise-Figure and check the primary sources, which will verify this truth. I welcome review that points out discrepancies between my article and the primary sources. I believe you will find none as several senior/authoritative engineers and professors reviewed the article I submitted prior to my submitting it.

After careful review, I hope we can all also easily agree on #2-- that the definitions for noise-figure in these two primary documents are different.

3. Since the primary documents have two different definitions for noise figure, can we agree that a Wikipedia article on Noise-Figure should clearly state (1) that there are two definitions, (2) what the two definitions are, and (3) how to use each one properly (including common errors to avoid).

Again, if there is agreement with #1 and #2, I hope this is a very easy agreement.

4. Assuming you agree that the noise-figure article should cover the above 3 points in #3, can we agree that the current article does not and major changes are required? Some examples are:

4.1. Neither primary reference is cited.

4.2. It not only does not address that there are two definitions, it treats them as one and confuses them throughout the article.

4.3. Sentence 1 gives the Friss definition, but sentence 3 confuses the Friss definition with the IEEE definition—since the Friss definition has no “standard noise temperature”.

4.4. In the Definition section, the formulas for F and NF are the Friss definitions, do not even have a temperature within them, and are required by mathematical language convention to be valid for all source temperatures. Indeed, these formulas are 100% correct under the Friss definition. But there is a sentence under them saying, “These formulae are only valid when the input termination is at standard noise temperature T0 = 290 K…” This statement has many problems. (1) The sentence is an attempt to make the IEEE definition operative, but it fails. (2) The sentence is incorrect under the Friss definition, where the formulas are correct. (3) This statement, by mathematical convention, makes the formulas presented invalid. This formula invalidity issue is addressed in my article in the section “Mathematical Language Rigor”. This section was included in the article specifically because this error is so common.

I hope, especially after the review requested in #2, there is easy agreement here.

5. Given agreement on #4, and the need for the article to cover the points in #3, can we agree that rather than trying to incrementally “fix” the current article, a perfectly reasonable approach to make the required major changes is to have a new, self-consistent article, that starts with the primary sources, and coherently acknowledges and teaches the two definitions and their appropriate usage?

I actually initially tried to edit the current article, but gave up. The two articles are so dramatically different, (e.g. the points in 4.3 and 4.4) there was no reasonable/timely way for me to get to the final result by editing the current version.

I hope we can all agree that a replacement is a perfectly reasonable way to make the major changes required.

6. If we can agree on the above 5 points, I respectfully submit that my article is an accurate, organized, fully detailed description of the "Noise-Figure" definitions in common use today. One that coherently addresses (a) both definitions, (b) how to use both in practical examples, and (c) common errors that should be avoided. And one that represents a reasonable way to update the Wikipedia Noise Figure page.

Again, I welcome review that points out discrepancies between my article and the primary sources. I believe you will find none as several senior/authoritative engineers and professors reviewed the submission prior to my submitting it.

Given the problems with the current page, I believe it is important to publish the new material immediately and that styling/linkage improvements are of less immediate importance and can be made incrementally as time goes on.

7. Regarding styling improvement, I did take to heart some of your styling comments and have made edits to fix what you suggested, like having a table of contents, eliminating some unnecessary text, adding some links, and fixing some of the equation formatting.

--JohnM7190 (talk) 02:07, 6 January 2019 (UTC)

You have made a lot of comments here. I may misunderstand of miss part of your reasoning or simply have no response. But I will attempt to answer point by point.

1. Secondary sources are preferred of primary sources, especially old primary sources. Primary sources make mistakes and are often incomplete. Definitions change over time. So, we cannot disregard reliable secondary sources such as books, articles in trade journals and application notes.

2. Most of us do not have access to the primary documents. You need to tell us what they say and preferably the formulas.

3. When reliable sources disagree on a definition, the article can have both definitions with due weight given to each. Definitions from historic primary sources may be given less weight than contemporary secondary sources. This will ultimately require a consensus of the involved editors.

4. Primary sources are nice, but not required. I disagree that a major rewrite is needed.

4.4 Yes, there needs to need a little more explanation of how the Friis formula relates to the noise temperature formula.

5. No. I believe that incremental editing will cover the gap. I don’t think that you will get a consensus for a major rewrite.

6. Wikipedia has been burned by accepting appeals to authority. It doesn’t matter who you are or who has reviewed your work. That’s why there has to be a reliable source. If there is no acceptable source, then we leave it out, even if there is a hole in the article.

I haven’t properly immersed myself in the subject, but appears that the Friis definition is a system definition which includes the antenna, and the noise temperature definition is for the amplifier with the antenna assumed to be at standard temperature. Is that an over simplification or entirely incorrect?Constant314 (talk) 05:31, 6 January 2019 (UTC)

Thank you very much for all your help and putting the latest draft of my article here [1]

Regarding your last, no, sorry, not correct. :>) The Friss definition requires the amplifier's input to be connected to something (like an antenna) that is producing signal and noise, so that there exists and SNRin. But the source temperature Ts can be anything. An amplifier with an input noise temperature of 50K will hardly impact the SNR at all if the source has a temperature of 1000K, but will impact the SNR a lot if the source has a temperature of 5K. The only way to say how much the amplifier affects the SNR, is to know the actual source temperature Ts of the system the amplifier is connected to. Ts cannot be a fixed number.

The IEEE definition applies to an amplifier alone, without regard to what it is connected to. As such, it cannot measure an SNR reduction. It characterizes the noise temperature at a port, without regard of any other port. It just changes degrees-K to another number. It is a forward and inverse that transforms Te->F, and F->Te.

I hope that helps.

At the heart of things, we have

1. no disagreement that Friss teaches the first two equations given in the current article

2 I don't think we have any disagreement that Friss teaches F=1+Te/Ts (it's just not specifically stated in the current article. The pictorial derivation in my article shows how simple it is to derive this.)

3. no disagreement that the IEEE teaches F=1+Te/290K, which is what the current article has, though in a muddled way that needs to be fixed. We can address this later.

With all that agreement, how can we have a big problem? I think that is your question.

The heart of the problem I am pointing out and that needs fixing comes from muddling the two definitions and not keeping them distinct. Indeed, the previous topic "Satellite communication systems" above raises a question that is caused by the muddling. The formulas for the two different noise figures have different arguments and are fundamentally different. The terms have different meanings, and their values are not interchangeable. These facts need to be transparently clear in the article.

Let's just start with getting an initial paragraph. I believe the initial paragraph in the current draft is a concise statement that captures the essence. Is this an acceptable opening paragraph? If not, could you offer an alternative that respects the distinctiveness of the two definitions?

--JohnM7190 (talk) 21:08, 6 January 2019 (UTC)

So, it appears that you would agree that Friis' equation F=1+Te/Ts would be the same as the IEEE's F=1+Te/290K if Ts=290K? Constant314 (talk) 21:44, 6 January 2019 (UTC)

Friis NF paper is available as a scanned in image here [2]. Constant314 (talk)

Friis says, right after equation 7, "It is suggested that the noise figure be defined for a temperature of 290 degrees Kelvin." That would seem to be in agreement with the IEEE definition. Constant314 (talk) 22:21, 6 January 2019 (UTC)

Let me respond to each sentence in order.

Regarding your first sentence, more precision is required and a vital point is made. Yes I agree that if Te is the same, and Ts=290K, then of course the VALUE of F obtained by both formulas (or equations) is the same. However, you said "it appears that you would agree that Friis' EQUATION ..." and no, I don't, because the equation or function F=1+Te/Ts is not the same as the equation or function F=1+Te/290K. In the first, F is a function of two arbitrary variables which can take on any combo of values. In the second, F is a function of a single variable. This point regarding mathematical formulas is vital because when you move on to say F=(Sin/Nin)/(Sout/Nout), that formula will be true only for the function F=1+Te/Ts, because Nin is defined to be KTsB. By mathematical definition, Nin and Ts are consistent and locked together. But they are not locked together when you say F=(Sin/Nin)/(Sout/Nout)=1+Te/290K--which is simply and invalid wrong formula. In this later case, the mistake is that you cannot fix a parameter on the right side of the = sign without also fixing the same parameter on the left side of the = sign. Without keeping both sides of the formula matched, the formula becomes incorrect. Misapplying the IEEE formula allows Nin to be arbitrary on one side of the formula, and not matched to the 290K on the other side of the formula. The fact of the matter is that the F from the IEEE formuala cannot be guaranteed to be equal to SNRin/SNRout. In other words, it is simply not a valid formula.

You will note that this is the very problem in the topic near the top, Satellite communication systems, where he says,

"From the definition of NF, I don't see how this can be true: ${\mathrm {SNR_{out,dB}} =\mathrm {SNR_{in,dB}} -NF}$"

The problem is he is trying to use the IEEE's definition for his NF term, but Friss's definition with an arbitrary SNRin, where, in fact, the noise in SNRin is not the IEEE's 290K. It is exactly the common mistake of not recognizing that there are two definitions, and they must be kept straight.

Regarding your second sentence, yes I've seen that one before. You will like the much cleaner copies of both papers at the Links (to IEEE) I give in the references.

Regarding the last sentence and what Friis says right after equation 7, he says, "All the terms in (4), (5), (6), and (7) have been defined, but a value for the temperature T of the generator terminal impedance must still be chosen before the noise figure is definite." Note the final, "before the noise figure is definite." What he is doing here is going through all the variables and completing an illustration of the use of his formula by filling in all the variables with numbers. At this sentence he has defined all of them but one, his T variable. Making all the variables specific numbers is what is required "before the noise figure definite." The fact that he chose 290K has nothing to do with the IEEE definition, which did not come until 15 years later. It is merely a number he used to illustrate the operation of his formula. He did not change his general formula for F to include 290K.

Hope that helps. This takes us back to getting an agreeable first paragraph. The latest draft article is here [3]. I think what I have concisely captures the essence of what the Friss and IEEE formulas for noise-figure mean. I am open to alternatives that respect the distinctiveness of the two definitions. Thank you for engaging on this. --JohnM7190 (talk) 05:11, 10 January 2019 (UTC)

If a manufacturer sold microwave amplifiers, they would have no idea as to the source temperature that was going to be used with the amplifier. In that case it makes sense to specify the noise figure with a source temperature of 290K. It will be close enough for terrestrial purposes. If a radio astronomer or an engineer designing a satellite down-link wants to use the amplifier, he can work backward from noise figure at 290K to the noise temperature of his amplifier and then plug that number into the Friis formula, using the actual noise temperature of his antenna. Doesn’t this cover the issue? Constant314 (talk) 00:00, 13 January 2019 (UTC)

Thank you again for writing back. What an excellent example! You say, "If a manufacturer sold microwave amplifiers, they would have no idea as to the source temperature that was going to be used with the amplifier". Yes, that is exactly right. Bingo! They absolutely cannot specify a Friis noise-figure. They can, however, specify its effective input noise temperature--which is the only information the IEEE's "noise-figure" carries. So, on the one hand, they CANNOT specify a Friis noise-figure, but on the other hand, they CAN specify an IEEE noise-figure. Hmmm. Does that mean an IEEE noise figure is not the same as a Friis noise figure? Yes! They are in fact, fundamentally different. Exactly as illustrated by the case you have stated.

Regarding the radio astronomer or engineer, yes, of course they can convert the IEEE noise figure back to a temperature. Indeed, the rules I give in my article to maintain consistency with each definition say to do exactly what you wrote. My hat is off to you. You would have written the same rules I wrote :>) Did you read my rules?

I'm not suggesting we are dealing with rocket science here. The rules are quite simple. I am also not suggesting that the IEEE's noise-figure cannot be used. Of course it can.

Getting back to the main issue, the article needs to be mathematically rigorous and recognize and teach that the two terms are fundamentally different, as your examples have just proven. The current article is not mathematically rigorous and it does not teach that the two terms are fundamentally different.

I think you will find that the introductory paragraph in my article captures the essence of the Friss and IEEE noise-figure definitions. I believe this paragraph would lead readers to appreciate why the steps/rules to keep them straight include (1) Only use IEEE's noise-figure to go back and forth to a temperature, never use it as if it is an general SNR metric, and (2) Use Friis's formulas (using Ts and Te temperatures) to make all SNR reduction (i.e. Friis's noise-figure) calculations.

Can we agree on changing the first paragraph in the article to the one in my article?

When you say, "Doesn’t this cover the issue?" In my mind, the "issue" or "problem" is that the current article does not just fail to make clear that the two noise-figures are fundamentally different, worse, it adds to the confusion between them. If you mean by your question, does what you have written eliminate this problem, the answer is no. If just the reverse, by "cover" in this question, you mean does what you have written illustrate the heart of the problem, that there are two definitions, then yes, it does, as I have further described.

What you just wrote (the mfg can use one but not the other) is spot on and clearly proves that the two definitions are fundamentally different. But just to be clear, do you agree that they are indeed fundamentally different?

May I ask you, have you thoroughly read my article [4]? --JohnM7190 (talk) 06:50, 14 January 2019 (UTC)

Can you please tell me the proper way to add images in my draft so they don't get deleted? Thanks, --JohnM7190 (talk) 20:17, 14 January 2019 (UTC)

I'm not sure why your images are being deleted. The best way to find out is to politely ask the editor that deleted them. Constant314 (talk) 20:41, 14 January 2019 (UTC)

• Comment. (e/c) I oppose including the first paragraph of Draft:Noise Figure in this article. The paragraph is far too detailed, so it does not convey the general notion noise figure or why people use noise figure. The paragraph focuses on the misuse or inconsistent use of the two equations, and that should not be the main topic of the article. I also have trouble with verbal equations such as "By the IEEE definition, $F$ and $NF$ are not SNR measures, but are measures that are nonlinearly proportional to the effective noise temperature of a port on a device." The text needs to serve the reader. Also, Wikipedia is not intended to be a tutorial on using noise figures. I have no problem with introducing the two notions of noise figure, and I have no problem with citing primary sources. Wikipedia needs secondary sources to support judgments about those notions. I have a huge problem with Wikipedia publishing a set of rules to live by. Wikipedia requires reliable secondary sources. The primary focus of the article should be what noise figure is and not how it is abused. Glrx (talk) 21:03, 14 January 2019 (UTC)

Could you please offer up an alternative that respects the distinctiveness of the two definitions and that you would not oppose? Here is something shorter.

There are two widely used definitions. By the original definition from Friis, Noise figure ($NF$) and noise factor ($F$) are measures of degradation of the signal-to-noise ratio (SNR), between the input and output of a signal chain. $F$ is the ratio of input to output SNR. $NF$ is the number of dB that the SNR has dropped by. By the IEEE definition, $F$ and $NF$ are not SNR measures, but are measures that are nonlinearly proportional to an effective noise temperature and as such, are used to specify or characterize the noise made by an antenna, amplifier, or a radio receiver, which is equally specified using a noise temperature. The terms cannot be interchanged--the IEEE's $NF$ cannot be substituted into Friis's $NF=SNR_{in_{dB}}-SNR_{out_{dB}}$formula. --JohnM7190 (talk) 02:03, 15 January 2019 (UTC)

I think that I understand your objection. I think it can be accommodated in the second paragraph of the lead. I am not suggesting that the following change should be made, I am simply offering it as an example of how it could be changed. Change from:

“The noise factor is defined as the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination at standard noise temperature T0 (usually 290 K).”

to

“The noise factor is defined as the ratio of the output noise power of a device to the portion thereof attributable to thermal noise in the input termination. If the temperature of the input termination is not specified, it is assumed to be the standard noise temperature T0 (usually 290 K).”

You could then introduce Friis' formula down in the main body. Constant314 (talk) 02:47, 15 January 2019 (UTC)

This really helps. Thank you. There remains, however, problems. The example text implies there is an input. But the IEEE definition is used on 1-port devices. Also, the definition has an "if..., then..." that is problematic. Definitions don't "assume". The example text implies there is one definition--a singular "it"--with common units, meaning, and usage, regardless of which clause applies. But that is not the case.

May I suggest the original text quoted above could be changed

to

"Noise factor F is defined two different non-interchangeable ways. F is the ratio between the input SNR and output SNR (SNRin/SNRout) of a 2-port device, or F is the non-linear transformation (1+Te/290°K) of an effective noise temperature Te at a port on a device. In the first case, F=10 means the SNR has dropped by 10dB between an input and output port, in the other, F=10 means the noise temperature at a port is 2610°K." --

If that is too long, we could drop the last sentence, but I think it really helps make the meanings crystal clear. --JohnM7190 (talk) 01:12, 17 January 2019 (UTC)

Perhaps some other editors would express opinions.Constant314 (talk) 01:24, 17 January 2019 (UTC)

Wow. It has been a week+. Hearing no objections, I guess it is adopted by unanimous consent. :>)

Since the above only addresses Noise Factor, and never mentions the topic title, Noise Figure, I thought making it just a tiny bit longer could fix that. How about changing

to

"Noise factor $F$ is defined two different non-interchangeable ways. $F$ is the ratio between the input SNR and the output SNR of a 2-port device, or $F$ is the non-linear transformation $\left(1+T_{e}/290^{\circ }K\right)$ of an effective noise temperature $T_{e}$ at a port on a device. In the first case, $F=20$ means the SNR between an input and output port has dropped by a factor of $20$ (or $13\ {\text{dB}}$), in the other, $F=20$ means the noise temperature at a port is 5510°K. Noise figure $NF$ is the noise factor expressed in dB. For $F=20$, $NF=13\ {\text{dB}}$."

I do have one question, what is the convention, use regular text for the inline equations in this initial paragraph, or use real equations with their associated fonts? --JohnM7190 (talk) 02:37, 25 January 2019 (UTC)

• Oppose Saying "is defined two different non-interchangeable ways" in the lede will just cause confusion. As far as this math in the lede, I think that it would be too technical.Constant314 (talk) 03:02, 25 January 2019 (UTC)

However, I have been reminded by an admin that Talk:Q factor that the article should presented in the same that it is presented in reliable sources. I have three books that would qualify as reliable secondary sources and they all start with the ratio of the input signal to noise ratio divided by the output signal to noise ratio. I think, then that you would be on solid ground to introduce that definition in the lede and defer any discussion of noise temperature to the main body. Constant314 (talk) 03:31, 25 January 2019 (UTC)

Thanks for your response. I, of course, what hoping for a different answer. But I need to know what your are thinking.

As we go back and forth, I would really appreciate it if we could all agree to offer up, with each iteration, edits of this paragraph that continue to respect the distinctiveness of the two definitions and that you would not oppose. That way, we can track exactly where each of us stands and close on an acceptable paragraph.

Let me share with you my thoughts on your three comments (the first sentence causing confusion, math in the lead, and being on solid ground).

(1) Regarding your statement about causing confusion, I believe just the reverse, since the term has multiple meanings in common use, stating that noise figure "is defined two different non-interchangeable ways" gives the reader two points that are "of the essence"—the most critical/early and vital information they must understand,. In so doing, it avoids and dispels confusion. Let me explain.

(a) The first "essence" that the paragraph declares is that there are two definitions. Seriously, if a term has more than one definition, the very first thing that a reader MUST understand, is this fact. A person who sees the term “noise figure” and goes to Wikipedia to find out what it means, must first and foremost be told there are two different definitions and meanings. They need to know that they will have to figure out which one is operative by the context of its use.

Given all our previous discussion over the last month, your suggestion to state only the Friis definition and ignore the IEEE definition, even though it is much more broadly used and its definition is completely different and not interchangeable, is quite shocking to me. Obviously, this suggestion fails at communicating this most critical and essential piece of information about the term – it is defined two different ways.

(b) As soon as one reads there are two definitions, the next "bottom line" or "essence" question is, are the different definitions interchangeable--do they mean the same thing and have the same units, even if they come about by a different process? Again, a person who sees the term “noise figure” and goes to Wikipedia to find out what it means and how it is used, needs to know if the terms can be interchanged—can one be substituted into an equation that describes the other. The answer, for the term “noise-figure” is NO. In order for this initial paragraph to not be confusing, this fact must be clearly communicated to the reader. At the overview or top level, before anything else, the reader must be informed on this matter so that they will know that they must be careful to keep the two terms distinct and careful to only use them in the equation that defines them. Inclusion of this vital and introductory information belongs in the initial sentence.

(c) Moreover, given the common, often ingrained, pre-existing confusion regarding the term "noise-figure", including these two points becomes all the more vital. In other words, the points being made by this first sentence are all the more vital because they address and "un confuse" an all too common set of confusions—namely, that the two terms are nominally or basically the same, mean the same thing, can be interchanged, and can be treated as if there is only one definition—all of which are false.

(d) It is a very concise statement of the truth. Math is math. There is no place for " close enough" or “usually close enough”, like your Jan 13 comment suggests. The definitions are precise, they are expressed in completely general mathematical formulas, where each is always and exactly true, precise, and not just "close enough". There are two very simple and distinct formulas, 1+Te/290 is a nonlinear transformation of a temperature on one port. It represents a temperature. 1+Te/Ts is a different formula. It is an SNR reduction across two ports. It does not represent a temperature. They do not mean the same thing and they are not interchangeable. Applied in general, as a general purpose formula, the two are different and unequal functions. The terms on a side of one formula cannot be swapped with a side of the other formula—the two different “noise-figure” terms cannot be interchanged, exactly as this first sentence so succinctly states.

For all these reasons, I believe it would be unacceptable and a disservice to Wikipedia readers, not to make this clear, short, and precise statement in the initial paragraph. The two points being made in this opening sentence could not be more vital. Even with the support of the sentences that follow, these opening points remain vital. Rather than leading to confusion, it brings the truth into sharp focus and dispels pre-existing common confusions by making the specific and clear declaration that the term "noise-figure" "is defined two different non-interchangeable ways".

(2) Regarding your statement that, "math in the lede ... would be too technical", I would say that in this particular case, your assertion, while debatable, perhaps does not hold. I would concur that the (1+Te/290K) "math" could be removed but I personally think doing so would be a step backward. I personally do not think it is "too technical", and actually think its obvious simplicity brings significant clarity and transparency--a lot of value for a very few characters. Don’t you think the “math” makes the meaning of “a non linear transformation” crystal clear—much more clear to a high school reader— and a lot less abstract? If you still think this "math" should go, please remove it in a paragraph you would suggest. But I personally think the paragraph is a lot better with it.

(3) Regarding your last comment and being on solid ground…

The ground my article and this initial paragraph stand on, #1, is open to inspection, #2, is simple enough for the majority of high school entrants to understand (seriously, 1+Te/290 and 1+Te/Ts, you cannot get much simpler), and therefore very easy to thoroughly inspect and validate, and #3 has not been disputed—in my entire article not a single equation, not a single assertion in the text, has been shown to be false. Regarding this initial paragraph, I do not know how to express what these two very simple formulas mean, any more accurately or succinctly.

Regarding the "yardstick on Wikipedia" being to explain things the normal way other sources explain things... You will find that I do not explain Friis's equation any differently. I do not explain the IEEE's equation any differently. These two very simple formulas, 1+Te/290 and 1+Te/Ts , are the core facts, they are presented the same way as other sources, and they are treated consistently with precise mathematical rigor throughout. The first paragraph very succinctly and accurately express what these formula, which are expressed in voluminous literature, mean.

Regarding my article as a whole, I invite you, please, point out to me any equation or any assertion in my article, that you believe is false. I would truly be extremely grateful for you to do so. Moreover, if you have a reference that you think disputes an equation or assertion I have presented, please send me a .pdf scan of the key pages and what equations or assertions you think don't match between my article and theirs. I will see if I can clear up whatever you think does not match up.

I asked in my Jan 14 comment and will ask again, have you thoroughly read and understood my draft article? —now located here [5]

Would you say you follow, understand, and agree with the pictorial showing the derivation of Friis's formula? It is really quite simple. I am not aware of any reference that disputes this formula relating Noise Figure to SNR reduction between two ports.

Would you say you follow, understand, and agree with the walk thru of the IEEE Standard in Appendix-1? It also is quite simple. It also matches the result of many others. I am not aware of any reference that disputes this formula for the IEEE’s standard relating Noise Figure to the noise temperature of a port.

Would you say you follow, understand, and agree with the "Mathematical Language Rigor" section? I certainly hope this section makes sense to you and you agree with it. For most people I have dealt with, this section, has been instrumental in helping them resolve their misconceptions by causing them to be more careful when they read and analyzed application notes, book chapters, etc. The “In Practice, Does The Difference In Definitions Matter” section, and “Example Usage” section have also been helpful. Perhaps these will do the same for you. Perhaps the Mathematical Rigor section will clear up issues you had with the books you were referring to.

Would you say you follow, understand, and agree with the "In Practice, Does The Difference In Definitions Matter" section? I certainly hope this section makes sense to you and you agree with it.

Regarding the above questions, I am not asking you to do something difficult or that requires any college. The math understanding required to understand all three of these sections is known by most high school entrants. The math and concepts are not "rocket science". No other books should be necessary. I do not mean any disrespect and do not imagine this to be true of you, but if a person cannot read and think through these sections independently on their own, and prove to themselves or convince themselves whether or not each of these sections is correct with "pound fist on table" certainty, and identify errors with equal certainty, they really should not be a reviewer on this topic. The article was written with the intent of being easily read and understood by high schoolers and lay people. No college training or physics or engineering is necessary.

Would you please respond to each of these questions with a simple yes or no? And if no, would you please explain what you think is wrong?

I hope that in the process of reading my article and answering the above questions, you will become convinced that this first sentence, and the entire suggested initial paragraph is absolutely and totally correct, and consistent with other outside sources. Moreover, I hope that you will come to agree that my suggested first paragraph makes clear the points that a reader must minimally understand.

In your response, if you still oppose what I suggested, please offer up a paragraph that respects the distinctiveness of the two definitions, as mine did, and that you would not oppose. Thank you again for all your help with this.--JohnM7190 (talk) 20:10, 27 January 2019 (UTC)

I would oppose any change in the lede that says that there are two distict definitions. As I see it, there is one definition and some special cases.Constant314 (talk) 23:26, 27 January 2019 (UTC)

Let me see if I can precisely state our disagreement. When you say, "As I see it, there is one definition", you are saying the functions f(x)=1+x/a and g(x,y)=1+x/y are not two different distinct functions and therefore do not represent two distinct definitions. In other words, as you see it, both f(x) (which is the form of the IEEE definition) and g(x,y) (which is the form of Friis's definition) are one definition, not two. So you oppose a "lede that says that there are two distict definitions." I am saying just the reverse. I oppose stating there is one definition because I affirm that f(x) and g(x,y) are two different functions that produce different results, and mean different things. I assert that while they may produce the same numerical value in the special case where a=y, they remain two distinct definitions with different meanings. So I oppose a lead that does not tell readers there are two distinct definitions. Given the above, in short, you want a lead that says there is one definition, which I claim is false, and I want a lead the says that there are two definitions, which you claim is false. I think this paragraph is a succinct statement of our disagreement. Would you agree? --JohnM7190 (talk) 16:49, 28 January 2019 (UTC)

I'll second Constant314. Do you have a reliable secondary source for NF is defined in two incompatible ways? Without that source, the statement does not belong on Wikipedia. WP:V.

Also, I fail to see a fundamental conflict here. Friis and IEEE intend the same thing. That one may be more general does not make the two incompatible.

See also Noise temperature, Effective input noise temperature, Friis formulas for noise

Glrx (talk) 18:52, 28 January 2019 (UTC)

Your responses are sad to me. I really thought we were going to be able to work this out with sound logic and math. When the discussion started, I thought you would give me the courtesy of thoughtfully reading my draft article. When that did not happen, I thought you would at least be willing to do enough reading to answer the questions I raised specifically addressing the math and logic necessary to help us come to a mutual understanding. But that did not happen either.

There are many articles that describe the Friis and IEEE noise figures, such as those referenced in the current page, plus Friis’s original article and the IEEE standard itself. They are all mathematical articles. Like all mathematical articles, it is the responsibility of the reader to understand all the equations collectively as a cohesive unified whole. Authors of mathematical articles, like these articles on noise figure, have no choice but to depend on the reader to apply basic math to correctly interpret what they wrote. In this case, they depend on the reader to know the most basic facts about formulas, or functions. They depend on the reader to know that if g(x,y) means a specific thing for arbitrary x and y, that they cannot simply substitute f(x) for g(x,y), and say f(x) means the same thing and equals the same value as g(x,y). None of these articles are self-consistent, nor are they understood correctly, if these basic mathematical principles are not followed. The mathematical articles that you already accept as authoritative, are sufficient. No additional article or reference is required to assert the above facts concerning f(x) and g(x,y) being two distinct and non-interchangeable functions. All that is required is to know some basic mathematical principles, and apply them. Doing so is the only way to come to an understanding where all these mathematical articles are consistent, not only with themselves, but with each other and all the other articles out there as well. All these articles tell the same mathematical story, which is the same mathematical story I am saying must be communicated in the Wikipedia article.

Since our quite lengthy discussion is clearly stalled and you still "fail to see a fundamental conflict" even in the light of all the discussion, I think at this point, I need to ask for arbitration. Being new to this, could you please help me with how I start this process? Thanks. --JohnM7190 (talk) 05:47, 30 January 2019 (UTC)

I've never taken anything to arbitration. When I'm outvoted, I find other articles to improve. There is always something to improve. Constant314 (talk) 16:50, 30 January 2019 (UTC)

Sorry for disappearing for a while. Before taking that last step, I took to heart your request for more references. My current draft has 22 references so that all key points are cited. I still have a few more things I wanted to make even more clear and cite before I was going to ask you for another round of trying to reach a consensus.JohnM7190 (talk) 06:04, 28 July 2019 (UTC)

I'm not able to put a lot of energy into this at the moment. If you present your proposed change and nobody else objects, then I won't either. But, this section of the talk page has gotten very long and I doubt that anyone will read all the way through it, so I suggest that you start a new section for your proposal. Constant314 (talk) 06:24, 28 July 2019 (UTC)

The draft at User:JohnM7190/John's Noise Figure Page has too many problems. Its focus is on two different formulas rather than what NF means. Its tone is poor; I'm still getting a huge sense of wanting to trash IEEE. Wikipedia is an encyclopedia; it is not a journal. The comments about T_ref being defined as a constant but confused as a variable are out of place. Reference values are expected to be constants. Glrx (talk) 22:40, 18 August 2019 (UTC)

Single-sided vs double-sided NF

Could someone better than I add a discussion of the concepts of single- and double-sided noise figure? Thanks, Marcas.oduinn (talk) 10:08, 28 June 2022 (UTC)

Confusion around Noise Figure

After spending some time trying to untangle the confusion around noise factor I have to say that I do not agree with the basic and often repeated statement that the Friis definition is F=SNRi/SNRo. This statement is incomplete. Look at equation (4) in the Friis paper, and the text right above it.

The noise figure F of the network is defined as the ratio of the available signal-to-noise ratio at the signal-generator terminals to the available signal to noise ratio at its output terminals. Thus F=(Sg/KTB)/(S/N) (4)

Unfortunately, Friis does not state it clearly in mathematical terms by itself, or in the text by itself, but it is clear from matching equation (4) up with the text just above it: Ng=kTB. Furthermore, T has been defined to be T₀=290K by IEEE (Friis suggested it, but did not require it). Hence the often re-printed statement of F=SNRi/SNRo is incomplete, we must also state Ni=kT₀B. And when we do that, F becomes a number that describes the residual noise source in the network (a power in watts), as stated by equation (7). The power of that output referred residual noise source is (F-1)GkT₀B watts. Equivalently, the input referred residual noise source is (F-1)kT₀B.

Here is how to determine F of a given network:

Apply a signal that has a noise component of kTB (e.g. a highly attenuated signal, where thermal noise of the matched input termination is dominant). Divide the measured (or known) SNR of that input signal with the measured SNR of the output signal.

Here is how to use F:

1) compute the residual (additive) output referred noise power N_oa=(F-1)GkTB

2) compute the impact that additive noise has on your signal. Here you can plug in your actual signal without restrictions. But you need to know actual power, SNR (a relative measure) is not sufficient. N_o=N_iG+N_oa

Note that G (the network power gain) can be substituted for S_o/S_i (or S/S_g in the Friis formula), and hence we really do not need a signal, only noise.

If, and only if the input signal of the circuit has a noise component of kT₀B, the noise factor can be directly used to determine the noise at the output, i.e. N_o=N_iF=kT₀BF.

A generalized form of the Friis equation can be derived, which allows for an arbitrary input noise N_i. Note that these equations reduce to the Friis equation when substituting Ni=kT₀B.

General form of Friis equation

It is unclear why Friis chose to represent an addition by a factor. We can speculate that the reason is two-fold: Friis' paper was about radio receivers, where the input signal is highly attenuated and hence the input noise is defined by kTB, and the convenience of using dB. An addition in linear terms (which additive noise is) has no equivalent operation in dB. An addition in dB is a multiplication in linear terms. However, an addition of two fixed summands can be represented by a factor (the two fixed summands being N_i=kT₀B and the network additive noise N_a). Alas, this leads to confusion for any application where the input noise is not kT₀B. Mayrayday (talk) 16:59, 15 March 2024 (UTC)