My only experience with this is building and designing guitar amps, which often have 80dB of gain or more, a.k.a., a pain in the ass amount of gain to deal with. It's not something on par with, say, radio astronomy, but it's still a lot of gain to deal with.
Usually the main source of noise will be a 120Hz or 100Hz buzz, but with humbucking pickups and careful orientation of the guitar you can mostly eliminate that. The next source of noise will be a low-level white noise (sounds like a hiss), which is from the amplifier, and consists of a mixture of Johnson noise and shot noise.
In older amps you may hear a louder hiss/crackle which is from old carbon comp resistors, which is an inferior type of resistor that produces additional noise through a different mechanism.
If you're trying to record your guitar directly through a digital interface, you may run into clipping issues and have to enable the pad (a built-in attenuator). Unfortunately, my experience is that the pad often introduces an unacceptable amount of noise, and I believe that it's just plain Johnson noise from a resistive divider.
The experienced and mysterious audio engineer "NwAvGuy" [0] praised the virtue of using two gain stages and moving the volume control away from the first input to reduce Johnson noise in audio amplifier designs [1]. It's a good example of how the basic principle applies both to mundane audio and cutting-edge science: the system noise is dominated by the first amplifier stage. Adding some noise before the first stage significantly degrades signal-to-noise ratio, but adding the same noise after the first stage is often acceptable since the signal is much stronger now. To reduce noise, you move the noise-generating resistor away in an audio amp, or cryogenically cool the resistor in a radio telescope front-end.
> One of the big claims for many audiophile op amps is lower noise. The chip manufactures make a big deal about it and audiophiles, not surprisingly, have jumped on the bandwagon. But, in reality, it’s often the Johnson Noise that limits the noise performance of a headphone amp, not the op amps. Johnson Noise is, literally, self generated noise that’s present in any resistor. The larger the resistor value, the more noise you get. Many DIY headphone amp designs have the volume control at the input to the gain stage. And it’s, at the lowest, usually 10,000 ohms. By comparison the O2 has 274 ohms in series with the input. That’s a huge difference in Johnson Noise. The way volume controls work, the noise is typically worst at half volume where you have 5000 ohms in series with the source and 5000 ohms to ground. So, at typical volume settings, you get a fair amount of Johnson Noise from the volume control that’s amplified by whatever gain your amp has. That noise typically exceeds the op amp’s internal noise. If you put the volume control after the gain stage its Johnson Noise is no longer amplified. And, as a bonus, the volume control at lower settings now attenuates noise from the gain stage. For more, see O2 Circuit Description and Circuit Design.
> To put these numbers in perspective, referenced to the old 400 mV they’re –105.3 dBr and –108.2 dBr. On the exact same test, at half volume, the Mini3 had nearly 11 dB more noise and measured –94.5 and –97.5 dB. Noise of –113 dB below 1 volt is under 3 microvolts.
Bingo. In any piece of music gear that is after the guitar/mic preamp, where it is working with line level signal (a higher voltage than consumer audio line level, by the way), it hardly matters where you put the volume knob. If you design it halfway well, it will be quiet as a mouse.
> the system noise is dominated by the first amplifier stage.
In radio receiver design you have an LNA, low noise amplifier, as the first stage. It's designed for low noise and to be linear. Idea is take the energy from the antenna and amplify it with as little noise and cross modulation as possible[1].
[1] If the amp is non linear you end up folding out of band signals into your band of interest.
Has anyone worked out what happened to NwAvGuy yet? Afaik he never posted anything about taking a break or going away for a while. Given his pseudonym was totally anonymous I can only speculate - he could be dead or in prison or something...
It was also popular in the 80s, 70s, 60s, and yes, the 50s. Everything old is new. The real question is, "Why did people switch to single stage amps in the 1990s and 2000s?" The answer is that a bunch of chips appeared on the market around that time which could do everything.
I'd say a higher end DAC/amp would consider it. My Benchmark devices (which nwavguy uses as a reference to build his O2 and ODAC) does it the right way.
I was messing about with contact microphones last year and very much akin area to guitar amps as high-impedance, so very much the same issues.
If you run on batteries you will find it works best, as with anything mains, you will want a good ground.
What I did find was that if you use peizo's back to back you can effect a balanced signal and that in itself helps immensely in eliminating much of the noise. You can also use a contact material sandwich in-between the piezo discs and effect how it works tone wise as well as become more zoned in the pick-up area.
But impedance matching is, as with guitars, very much key for pre-amps.
As for input levels and clipping - the rise of 32bit float has made a huge difference and means you can not worry about mic input levels at the ADC stage as much and normalise everything in post, sorting the levels out then without any fear of clipping at all.
Though those just unbalanced input designs, alas I'm not aware of any balanced contact mic's on the market - but can easily make them yourself using the above approach.
One common solution for piezo pickups / contact mics is to put an amplifier or buffer near the pickups, powered by a 9V battery or 48V phantom power.
The piezo pickup is not balanced but it's not necessary, you can make the output of the amplifier balanced. This is the same way that condenser mics work. The microphone capsule itself is not balanced, but it doesn't need to be... the output of the amplifier or buffer is balanced and that's all you need.
Not exactly - Zoom stuff does a clever trick of using 2 ADCs at different gain levels (essentially the same way that HDR photography works), but ultimately it's still using fixed-point ADCs.
This isn't actually a new idea - I know Line 6 has been using it in guitar pedals since at least 2006. Of course, ADCs have gotten better since then - I doubt they were getting even 24 ENOB back then.
I was surprised to find that after replacing most of the op-amps in a ADA MP-1 pre-amp, most of that orientation-sensitive remaining buzz that you still get with humbucking pickups was seriously reduced.
When I'm playing at a low volume, I can just mute the strings and put the guitar on a stand to get it to be quiet. On a high-gain program using the tube board and all.
The reason for some of the buzz is that the circuits are amplifying common mode. The op-amps are operated in feedback meaning that the - and + inputs are at nearly the same voltage. However, the incoming common mode noise moves that entire voltage; and it's possible for the common movement of +/- to itself be amplified.
So that is to say, suppose you have this representative single-ended stage:
The guitar cable's shield is connected to GND. Now suppose that GND is oscillating at 60 Hz due to the cable shield picking up EMI. (The cable shield is a big area of copper bathed in noisy electric fields, with nothing shielding it, and is galvanically connected to your amp!)
This means that the (+) node of the OP amp is seeing this fluctutation, and due to the feedback the (-) node is following.
An ideal op-amp will not amplify any voltage offset that equally affects (+) and (-). But real op-amps do. The degree to which they do not is the CMRR (common mode rejection ratio) which is a data sheet parameter that is better in some parts than others.
I remember seeing an interesting Audio Engineering Society's presentation (2005) [0] on a similar problem in balanced audio interfaces. Interestingly, an old-school audio transformer is more robust, it has higher CMRR in the real world when there's some common-mode impedance imbalance in the system, on the other hand the CMRR of an opamp seriously degrades. Designs which naively rely on the opamp CMRR were responsible for many noise problems in balanced audio.
> Where Did We Go Wrong? TRANSFORMERS were essential elements of EVERY balanced interface 50 years ago ... High noise rejection was taken for granted but very few engineers understood why it worked. Differential amplifiers, cheap and simple, began replacing audio transformers by 1970. Equipment specs promised high CMRR, but noise problems in real-world systems became more widespread than ever before ...Reputation of balanced interfaces began to tarnish and “pin 1” problems also started to appear!
> Why Transformers are Better. Typical “active” input stage common-mode impedances are 5 kΩ to 50 kΩ at 60 Hz. Widely used SSM-2141 IC loses 25 dB of CMRR with a source imbalance of only 1 Ω. Typical transformer input common-mode impedances are about 50 MΩ @ 60 Hz. Makes them 1,000 times more tolerant of source imbalances – full CMRR with any real-world source.
> CMRR and Testing. Noise rejection in a real interface depends on how driver, cable, and receiver interact. Traditional CMRR measurements ignore the effects of driver and cable impedances! Like most such tests, the previous IEC version “tweaked” driver impedances to zero imbalance. IEC recognized in 1999 that the results of this test did not correlate to performance in real systems... My realistic method became “IEC Standard 60268-3, Sound System Equipment - Part 3: Amplifiers” in 2000. The latest generation Audio Precision analyzers, APx520/521/525/526, support this CMRR test!
Shot noise was originally attributed to electrons hitting the anodes of vacuum tubes, but transistors turned out to make the same kind of noise so it applies to them too.
And it is current-dependent so sometimes you can be quieter at idle by biasing lower.
For resistor noise, nothing wrong with a megohm referencing input to ground since there's not any significant current flowing there.
But in a tube preamp the typical 100K anode resistor will conduct a bit and can get hot. These should be carefully auditioned. Plus higher wattage rating parts give less noise in this service than they put in most commercial amps.
If you increase gain using something like 150K, 220K, or even 330K there will be less current (through the resistor and the tube) but the increased amplification factor will equally multiply any noise which occurs before that gain stage.
Then with power you've got the ability to broadcast audio, naturally over extremely short distances (compared to radio frequencies which hopefully you are filtering out) but those are the distances inside your chassis where different parts of the wiring layout can interact beyond a cetain point as broadcast and receiving antennae, and either provide negative or positive feedback, stabilizing or destabilizing respectively parts of the circuit whether you intended it to happen or not.
On top of the expected acoustic mechanical feedback from the speaker at high volume, which reverses polarity based on distance, you've also got magnetic feedback. Once a very high-power output transformer goes wild it can reach out a lot further and touch your pickups directly from a few feet away.
At this point the noise at idle is usually as loud as as ten pounds of bacon frying and I hate that.
So get out the soldering iron and fix it so you can only tell it's on if you put your ear close to the speaker, when it's actually set loud enough to play with a heavy drummer.
While not exactly for guitar, Phil’s Lab on youtube recently posted a low noise headphone amplifier design that's both over-kill in some ways and interesting and cheap to make.
> In fact, a remarkably common response to a diagnosis of resistor noise is to seek a source of "good" resistors, with "good" being defined as without thermal noise. This is impossible.
It's impossible to make a totally noiseless resistor, but it's also important to understand that all resistors are not created equal.
Most resistors have noise levels that are orders of magnitude above the Johnson limit. Potentiometers are especially bad.
If you want "good" resistors for noise-critical applications, I recommend metal thin-film resistors. They hardly cost any extra anyway.
Also, in cases where resistors are used to set DC signals such as offsets and biases, you can add capacitors to filter the heck out of those lines to decrease their noise contribution.
Electrical engineer here. Thermal noise is the same for all resistors with a given R, regardless of their method of manufacture. You cannot have thermal noise either less or more than this, so it's not a Johnson "limit" but rather a definite value. You are correct that there are other sources of noise such as 1/f noise. But more importantly, the manner in which noise manifests in the end result has to do with the circuit as a whole.
For noise critical applications you should do a noise analysis of the circuit as a whole rather than make ad hoc selections of components.
I think you "well actually"'d a bunch of things I specifically didn't say.
I use "Johnson limit" synonymously with "thermal noise limit" because they are the same, and it's the limit of how low noise can be after removing all other sources of noise.
Most people, if they even learn about resistor noise, will only learn about thermal noise. If they're lucky enough to identify a resistor as the noise troublemaker in a circuit, they might not have any idea that they can potentially cut the noise 1000x by changing the resistor from thick film to thin film, with no other design changes, at the cost of one cent. It's not common knowledge, as illustrated by the fact that an article like this, dedicated to the topic of resistor noise, doesn't even mention it. And instead laughs at someone even considering to look for a "good" resistor as though it were superstition.
In fact, thick film resistors are far more common, so if you're in the situation where you're reading this article because you have a noisy resistor in your circuit and don't already know about Johnson noise, you almost definitely don't know about current/flicker noise, and since you got here because of a noisy resistor in the first place, a "good" thin film resistor is overwhelmingly likely to be the cure.
I'm not advocating ad hoc selection of components to reduce noise any more than selecting ad hoc components to reduce cost. A noise analysis can help you find the problem but won't help you solve it if you think your only option is to change the resistor's value, rather than its type.
Yep. Any time I actually care about the value of a resistor (which is to say, for precision analog work, not power supplies or logic pull-ups or LEDs or ...), I'll pick a cheap thin-film part, even without doing analysis. This does several things for me:
1. I get a "pretty good" (i.e., >80% of best achievable performance for <<20% of the effort) resistor in my important location.
2. I get a separate BOM line item for that resistor, so it stands alone (or with similarly important parts) and is easy to single out to, say, ensure correct ordering.
3. The part will be physically distinctive, so I can also distinguish it on the circuit board. If I have space, I'll even go up one size, to make it impossible to swap out with the less critical parts. (It would work fine, if expensive, to put thin-films everywhere. The reverse is not true.) It also sends the "pay attention to this" signal to anyone down the line who only has the board to work from.
I favor Susumu thin-film resistors, as they're generally cost-competitive, very high quality, available in very tight tolerances if needed, and visually easily identifiable as Susumu parts (though the series is not identifiable). This means they have to be thin-film, because Susumu doesn't make anything else. RR and RG series are the go-to parts here. If cost is a concern, Yageo RT is also excellent, but not as noticeable on the board. For analog work, I'll go no smaller than 0603 (1608M) to ensure values are printed on the parts. This pays for itself after only one gain resistor mixup on the bench....
Your comment looks like it disagrees, but actually you are both agreeing that thermal noise is not the only noise source and that other design factors matter.
For other readers: some resistors have much lower flicker noise[1] where “wire-wound resistors have the least amount of flicker noise. Since flicker noise is related to the level of DC, if the current is kept low, thermal noise will be the predominant effect in the resistor, and the type of resistor used may not affect noise levels, depending on the frequency window.”
I recommend measuring the noise. Systems guru Phil Hobbs said that you should know where every dB of noise comes from in your design. Of course a dB could be a little or a lot in your application, but the point is that you should perform a noise budget and then test your assumptions.
It's not necessarily easy, but recommended if possible. I was doing it with DIY equipment, so I don't claim traceable results.
In one case, I literally measured the noise of some resistors, and within the parameters of what I cared about, I found no measurable difference between metal film and carbon film. I was passing no DC current through the resistor. Some sources of "excess noise" are proportionate to DC current and can be corrected by appropriate filtering.
Fun fact: for the most demanding RF applications, namely, radio astronomy, the front-end low-noise amplifiers are indeed cooled to cryogenic temperature by liquid nitrogen. Here's how it's done at NASA for the Deep Space Network [0]. It's a long paper, see Chapter 4 Cryogenic Refrigeration Systems, PDF page 179 (text page 159). Also, nice photos in page 183 and 188.
The reverse problem is interesting. Consider Voyager 1- its high gain antenna is pointed essentially directly at the sun, a powerful wide-band noise source. How does it detect anything from earth? The DSN has to outshine the sun within the tiny S-band window that Voyager listens to: 20 kW and 62 dB antenna gain.
Since the amplifier has both voltage and current input noise sources, there is an optimum source impedance that provides a minimum noise figure, and it’s not an impedance match. This is called a minimum noise match, along with associated noise contours where noise is traded off with impedance match.
Also, the noise from an antenna is dependent on it’s efficiency and what it’s pointing at. Even if it’s input impedance is 50 Ohms, it can generate far less noise than the equivalent resistor.
The opening paragraph of Goodstein's "States of Matter":
"Ludwig Boltzmann, who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics."
One of my first jobs, which I got while I was still an undergrad (in the mid-80s), was designing amplifiers for fiber-optic sensors. I pretty much had no clue what I was doing so I just started futzing around with op-amps and realized very quickly that my signal-to-noise-ratio was much higher than was acceptable. I figured there was some hardware design trick that they hadn't taught me in my EE curriculum, but one day I decided to do the math on resistor noise and discovered that that was in fact my limiting factor and the only way were were going to get it to work was to either cool the first-stage resistor or to use a ridiculously high value because the gain goes up linearly with the resistor value but the noise only increases with the square root. We ended up with a ten gigaohm resistor, which was just enough to get the S/N ration we needed to make it work.
Depending on the voltage across a resistor like that, you may calculate less than one electron passing through the resisitor per second.
Without ceramic or teflon standoffs, the circuit board can often conduct better than the resistor, plus dust can also accumulate on the outside of the resistor and conduct better eventually, which is why they are often encased in glass, so they can be effectively cleaned during a maintenance cycle.
> Depending on the voltage across a resistor like that, you may calculate less than one electron passing through the resisitor per second.
If memory serves (this was a very long time ago) the output signal was a couple of millivolts, so it wasn't quite that bad. But one other thing that saved us was that we only needed a few hertz of bandwidth.
I usually put a single 470 ohm resistor in line with the gate of a discrete jfet in common collector mode as the first gain stage in my projects. Once you boost up the signal voltage it’s way easier to maintain a good signal to noise ratio.
The resistor is there to prevent the jfet from being burned out by over voltage on the gate, which is very sensitive to static electricity. But, I can easily hear the difference if I put a 10k resistor there instead. It’s really important to get that first gain stage really, really quiet, a discrete jfet has a better noise floor than an op amp or a regular transistor.
Uh, for a looong time already. The LT1028 was available in the eighties and afaik, still unsurpassed (in terms of voltage noise, it's unfortunately a sucker in terms of input current and current noise, so it's for low impedance applications only and it's fairly expensive). The cheaper OP-27 is also old and still available. The challenge is to find a low-noise OpAmp with high input impedance where earlier hybrids with discrete JFets fronting a low noise OpAmp were often used. These days its rather a challenge to find low-noise discrete JFet pairs and one has to use an integrated OpAmp instead (the causal chain might be reversed there).
Indeed the LT1028 datasheet shows a BF862 JFET at the front end of a photodiode preamp using the LT1018.
The reason why we're at a plateau of op amp noise performance is that the current crop of chips are operating very close to the theoretical limit for both bipolar and JFET input devices.
Ironically I use a LT1028 in a homemade circuit for measuring the noise of things that are more noisy.
Also, a lot of the newer low noise op amps want much better frequencies characteristics and more GBW as they're primary application is sensors. Take for example the ADA4817. It has very comparable noise characteristics but is quite a lot faster.
Yes, I built a guitar pedal that was designed around JFET gain stages and the JFETs had to be sourced from a specialist. I wonder if they're still being made. Most of the discrete JFETs I see available are for switching applications.
Low noise JFETS are hard to find today. Devices like the Toshiba 2SK369, 2SK117, 2SK170 etc. went out of production years ago for being mostly THT and possibly non ROHS devices, while purely functionally speaking they would still be great parts. They can be seen online on Ebay, Aliexpress, etc. but those are almost always relabeled fakes; real ones are hard to find and not cheap. Before learning about counterfeit components the hard way, I bought two bags of 2SK117 from two vendors on Ebay: they were identical, but when fit in a circuit, I had to recalculate the drain and source resistor with all the parts from one vendor because it clearly had different specs than a real 2SK117. Ugh! ...lesson learned.
Somebody suggested the use of the BF256 JFET in audio circuits, even in RIAA phono cartridge preamps. It is a RF part (the natural successor and direct equivalent of the venerable BF245) but it seems it is also a low noise part capable of working down to audio with no issues. It went out of production more recently than other models and some vendors still have stocks available. Probably not as quiet as the others though.
I bought 4000 J201’s when I saw they were becoming obsolete, I still have most of them. But, I think there are better choices out there anyhow, that’s just what I’m used to using. They’re really easy to bias.
I don't really have a favorite op amp. There are so many good ones. Some audiophiles like to swap out op amps and talk about how good different ones sound, but I think that's a bunch of hogwash. If you believe that choosing the right op amp for an audio project has an impact on the sound, I'm the wrong person to ask about it.
There are some exceptions, like if you need a microphone preamp with 60 or 80 dB gain, but I have no experience in that area.
For audio, it's hard to go wrong with the OPA1654 for DIY projects that are not cost sensitive. It draws a lot of current. For battery power I'm intrigued by the TLC2264 which, while having somewhat more noise, has very low operating current and rail-to-rail performance.
I was watching an interview with Tom Christiansen (he owns Neurochrome, a company that makes very high-end DIY amplifier designs/kits, with THDs of 0.0001%).
He mentioned something about how resistor noise can actually track with the low frequency portions of the audio signal due to the resistor literally heating up and cooling down as the current through it varies. I thought that was interesting. I knew that noise was proportional to heat, but I didn't realize the temperature could vary that quickly, but I guess it makes sense when you're dealing with tiny parts. There are probably also localized hot spots that have less thermal mass than the entire resistor as a whole.
Chapter 8 of The Art of Electronics, 3rd Edition is a great resource on electrical noise. The first section is almost exclusively about resistors and noise budgeting. Fun read. I should get back to it at some point.
Lots of great tricks on bootstrapped filters, capacitive multipliers, precision transistor noise measurements with some outboard circuits fed into a spectrum analyzer.
It is now partially incorrect, too. Now we can no longer change Boltzmann's constant not because he's dead (indeed, until recently, it was a measurable quantity), but because k_B is now defined as a part of the redefinition of the SI unit system in 2018.
It's correct now too, since we can no less change the value now than before the redefinition (we can't change it in either case, and not because Boltzmann is dead), so the joke works fine!
> k_B is now defined as a part of the redefinition of the SI unit system in 2018.
> The value is 1.380649×10^{−23} J/K, exactly.
Hmm. This is a trendy thing to do with SI units, indeed.
But this definition makes me wonder if there are also definitions of the Joule and the Kelvin. If there are, it seems like they could easily conflict with this definition of k_B.
And if that happened, we'd have to admit that k_B was a measurable quantity all along -- the only way to demonstrate a conflict in the definitions would be by measuring the quantity more accurately.
The underlying reason is that we don't actually need a unit for temperature. The temperature of a substance is simply the mean kinetic energy of its molecules which can be given in Joule. The problem is that historically thermometers were calibrated using the triple point of water and not by measuring the kinetic energy of the molecules. This is how the Kelvin scale used to be defined. The Boltzmann constant was simply a measure of the triple point of water in energy units (which could be measured). One problem was that the isotopic composition of water influences the triple point and was not well defined in the old SI system. Nowadays, we can actually calibrate thermometers by measuring the kinetic energy of molecules, so we no longer need to use the triple point of water. This is why the Kelvin is now just a rescaling of the Joule with a fixed coefficient (the defined Boltzmann constant). So the Boltzmann constant can no longer be measured. On the other hand, it is now possible to measure the triple point of water in Kelvin (this used to be 273.16 K by definition in the old SI system).
I read it more like a whine "don't blame our opamps, they better than resistors" :-) But it is something I've become much more familiar with building RF frontends for software defined radios. You want as much gain as you can get to pull in weak signals but keeping the whole thing noise quiet is really really hard.
Excellent article! I feel like I understand so much more about analog signals than I did before.
It seems very obvious now, that if you want to have a high signal to noise ratio, you should get as much signal as possible, and keep your signal voltage as high as possible as long as possible before amplification.
This fundamental resistor noise is something that I'm probably going to start seeing everywhere when I look at any analog signals, and will have to take into account when designing things.
It is surreal that this article showed up now. I am going back and forth currently with our electric utility company. They upgraded capacitor pack on the pole by my house. And these new ones are generating so much of this kind of low buzz sound, it is unbearable. I was researching into what generates this noise, and found this article very timely. Only solution is to move these, as nothing else can be done about this sound. Which is turning into quite a project.
It is quite rare for capacitor banks to hum. Much more likely that you're hearing the magnetics (transformers), which indeed have reason to be where they are. Good luck.
Thanks. Indeed those are transformers, upon further digging(for some reason, I think of transformers as big, these are not big but boy they emit this low-buzz sound). And indeed it has been very challenging to have them moved, because as you said they probably picked this location based on a reason.
Usually it's inductor coils and transformers, occasionally it's ceramic capacitors (all grades other than NP0 are microphonic, SMD or not), both problems are common in switched-mode power supplies, for example, powering the calculator LCD. I've never seen a singing resistor, very unlikely.
I don't know how this one made it, but if there's an Analog Dialogue article on the front page of HN weekly for the next five years it will still barely scratch the surface of all the treasure that's buried in that archive.
Where xxx (or xx or x - no leading zeros) is the number. Highest is presently 190. I wrote all the first ones, then I shared slots, and after I retired I just wrote the occasional one.
I binge-read the RAQs a few months ago. So much great information. Thank you!
I also appreciated the consistent URL scheme because it let me easily scrape all the PDFs to read them offline. The one bummer is that the links at the end of the PDF versions seem to be broken now.
To the best of my knowledge time-independent articles don't need a date stamp. I never see one on Wikipedia articles even if the last edit was years ago.
There's a strange relationship between Resistance, Noise (audible and above the auditory spectrum, such as RF), and the concept of Impedance...
I'll put a wager that future (or perhaps even current!) scientists are able to engineer complex waveforms such that the complex waveform effectively negates the resistance/noise/impedance -- effectively turning the resistor into a conductor -- but only for that specific complex waveform -- which very possibly would change over time...
Also, future (and perhaps current!) scientists should be able to use an electrical signal of known characteristics -- to determine exactly what the complex impedance of the resistor/resistance element/impedance element -- in a circuit is, exactly...
In other words, given one of the above things (complex waveform, complex impedance) -- derive what the other one is, from it...
Usually the main source of noise will be a 120Hz or 100Hz buzz, but with humbucking pickups and careful orientation of the guitar you can mostly eliminate that. The next source of noise will be a low-level white noise (sounds like a hiss), which is from the amplifier, and consists of a mixture of Johnson noise and shot noise.
In older amps you may hear a louder hiss/crackle which is from old carbon comp resistors, which is an inferior type of resistor that produces additional noise through a different mechanism.
If you're trying to record your guitar directly through a digital interface, you may run into clipping issues and have to enable the pad (a built-in attenuator). Unfortunately, my experience is that the pad often introduces an unacceptable amount of noise, and I believe that it's just plain Johnson noise from a resistive divider.