[HN Gopher] Resistor Noise Can Be Deafening, and Hard to Reduce ...
       ___________________________________________________________________
        
       Resistor Noise Can Be Deafening, and Hard to Reduce (2007)
        
       Author : bcaa7f3a8bbc
       Score  : 217 points
       Date   : 2021-06-09 13:47 UTC (9 hours ago)
        
 (HTM) web link (www.analog.com)
 (TXT) w3m dump (www.analog.com)
        
       | buescher wrote:
       | And yet, there is such a thing as a low-noise resistor, because
       | thermal noise is not the only resistor noise. This application
       | note, also from Analog, explains:
       | https://www.analog.com/media/en/technical-documentation/appl...
        
       | ng55QPSK wrote:
       | At my workplace one R&D engineer had the last lines printed out
       | as poster (i guess the AD note is older than 2007)
        
       | cushychicken wrote:
       | 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.
        
       | jbay808 wrote:
       | > 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.
        
         | prpl wrote:
         | ... and overspec them everywhere reasonable
        
         | wellthereitis wrote:
         | Great tips, thank you!
        
         | xenocyon wrote:
         | 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.
        
           | jbay808 wrote:
           | 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.
        
             | ldarby wrote:
             | Elsewhere in this thread there's a link to
             | https://dcc.ligo.org/LIGO-T0900200/public, which backs up
             | what you're saying:
             | 
             | "Metal film or thin film resistors have little excess noise
             | in these tests and thick film resistors show large excess
             | noise"
        
           | robocat wrote:
           | 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."
           | 
           | https://en.wikipedia.org/wiki/Flicker_noise
        
           | colin_mccabe wrote:
           | Thanks for the comment... good to have some EEs drop in.
        
         | analog31 wrote:
         | 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.
        
       | Unklejoe wrote:
       | 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.
       | 
       | The interview is posted in this thread:
       | https://www.audiosciencereview.com/forum/index.php?threads/t...
        
       | FriendWithMoon wrote:
       | Similar to what having permanent tinnitus sounds like. Take care
       | of your ears!
        
       | pontifier wrote:
       | 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.
        
       | fallingfrog wrote:
       | 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.
        
         | klodolph wrote:
         | > ...a discrete jfet has a better noise floor than an op amp or
         | a regular transistor.
         | 
         | This used to be true, but you can get really good low-noise op
         | amps these days.
        
           | guenthert wrote:
           | 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).
        
             | klodolph wrote:
             | 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.
        
               | squarefoot wrote:
               | 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.
        
               | fallingfrog wrote:
               | 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.
        
           | adammunich wrote:
           | What is your favorite?
        
             | klodolph wrote:
             | 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.
        
       | [deleted]
        
       | ChuckMcM wrote:
       | 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.
        
       | peter_d_sherman wrote:
       | 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...
        
         | DiabloD3 wrote:
         | You overcomplicated it, and somehow badly described LVDS at the
         | same time.
        
         | h2odragon wrote:
         | Like the maths of trying to urinate silently on a tin roof.
        
       | lisper wrote:
       | 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.
        
         | analog31 wrote:
         | >>> I figured there was some hardware design trick that they
         | hadn't taught me in my EE curriculum
         | 
         | https://patents.google.com/patent/US4744105A
        
       | [deleted]
        
       | zihotki wrote:
       | The article, actually a single Q&A, is dated Sep 2007.
        
         | jeffbee wrote:
         | 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.
        
           | JamesBryant wrote:
           | You can find all the RAQ (Rarely Asked Questions) at:-
           | https://www.analog.com/en/analog-dialogue/raqs/raq-issue-
           | xxx...
           | 
           | 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.
        
             | OnlyOneCannolo wrote:
             | 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.
        
           | zihotki wrote:
           | And that's only the AD, if we add old articles for the last
           | century from other sources, the HN will be flooded over. But
           | would be they news?
        
             | segfaultbuserr wrote:
             | > _if we add old articles for the last century from other
             | sources, the HN will be flooded over._
             | 
             | HN has been doing it for... I think a decade already? The
             | situation so far looks good to me.
             | 
             | * "Corn-Pone Opinions" by Mark Twain (1901)
             | 
             | https://news.ycombinator.com/item?id=10822133
             | 
             | 127 points, 56 comments
             | 
             | * Five Hundred and Seven Mechanical Movements (1908)
             | 
             | https://news.ycombinator.com/item?id=19968114
             | 
             | 798 points, 147 comments
             | 
             | * G.K. Chesterton: The fallacy of success (1909)
             | 
             | https://news.ycombinator.com/item?id=6512288
             | 
             | 198 points, 97 comments
             | 
             | * The Basic Problem of Democracy (1919)
             | 
             | https://news.ycombinator.com/item?id=21893486
             | 
             | 206 points, 189 comments
             | 
             | * Why I Quit Being So Accommodating (1922)
             | 
             | https://news.ycombinator.com/item?id=14418877
             | 
             | 866 points, 316 comments
             | 
             | * Why I Never Hire Brilliant Men (1924)
             | 
             | https://news.ycombinator.com/item?id=7437643
             | 
             | 387 points, 264 comments
             | 
             | * War Is a Racket (1933)
             | 
             | https://news.ycombinator.com/item?id=22012255
             | 
             | 336 points, 181 comments
             | 
             | * A Mathematical Theory of Communication (1948) [pdf]
             | 
             | https://news.ycombinator.com/item?id=23035107
             | 
             | 197 points, 39 comments
             | 
             | * Claude Shannon Demonstrates Machine Learning (1952)
             | 
             | https://news.ycombinator.com/item?id=25919006
             | 
             | 209 points, 51 comments
             | 
             | * Three-dimensional model of electricity consumption in
             | Manchester (1954)
             | 
             | https://news.ycombinator.com/item?id=25959571
             | 
             | 135 points, 31 comments
             | 
             | * Kurt Godel's Letter to John von Neumann (1956) [pdf]
             | 
             | https://news.ycombinator.com/item?id=19281633
             | 
             | 183 points, 85 comments
             | 
             | * An Algebraic Language for the Manipulation of Symbolic
             | Expressions (1958) [pdf]
             | 
             | https://news.ycombinator.com/item?id=14885779
             | 
             | 171 points, 12 comments
             | 
             | * America's Cult of Ignorance (1980) [pdf]
             | 
             | https://news.ycombinator.com/item?id=14778856
             | 
             | 169 points, 113 comments
             | 
             | * How does a gas pump know to shut itself off? (1981)
             | 
             | https://news.ycombinator.com/item?id=24741029
             | 
             | 384 points, 390 comments
             | 
             | * Will cable TV be invaded by commercials? (1981)
             | 
             | https://news.ycombinator.com/item?id=22977448
             | 
             | 288 points, 354 comments
             | 
             | * Have You Ever Tried to Sell a Diamond? (1982)
             | 
             | https://news.ycombinator.com/item?id=4535611
             | 
             | 273 points, 229 comments
        
         | Causality1 wrote:
         | 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.
        
           | zihotki wrote:
           | My comment was only in regards with adding the date to the
           | headline.
        
           | IgorPartola wrote:
           | I am old enough to remember when naked Wikipedia articles
           | were discouraged (or maybe even disallowed) on HN.
        
       | xbar wrote:
       | Thanks. I will be sure to pay my respects at Boltzmann's grave
       | the next time I am in Vienan.
        
       | sunjain wrote:
       | 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.
        
         | exmadscientist wrote:
         | 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.
        
           | sunjain wrote:
           | 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.
        
       | mattkrause wrote:
       | The last line got a good chuckle out of me!
        
         | ISL wrote:
         | 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.
         | 
         | The value is 1.380649x10^{-23} J/K, exactly.
        
           | JamesBryant wrote:
           | It was correct when I wrote the RAQ in 2007.
           | 
           | In fact I've been making the crack about 'not being able to
           | change it because he's dead' in my lectures for at least
           | forty years.
        
             | StavrosK wrote:
             | 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!
        
           | thaumasiotes wrote:
           | > k_B is now defined as a part of the redefinition of the SI
           | unit system in 2018.
           | 
           | > The value is 1.380649x10^{-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.
        
             | minitoar wrote:
             | Not in SI. Kelvin is defined in terms of k_B. Joule is
             | defined in several ways, eg force & distance.
        
             | fsh wrote:
             | 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).
        
       | carapace wrote:
       | Not really related (I think) but I was reading about "an
       | electrical resistor that has no residual mutual- or self-
       | inductance at high frequencies."
       | 
       | The trick is to twist it into a Mobius strip!
       | 
       | http://www.rexresearch.com/davis/davis.htm
        
       | Footkerchief wrote:
       | The underlying principle:
       | https://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise
        
       | klodolph wrote:
       | 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.
        
         | bcaa7f3a8bbc wrote:
         | 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.
         | 
         | [0] https://spectrum.ieee.org/tech-history/silicon-
         | revolution/nw...
         | 
         | [1] https://nwavguy.blogspot.com/2011/07/o2-headphone-amp.html
        
           | pvitz wrote:
           | I think I remember seeing this in "The Art of Electronics"
           | for actually amplifying shot noise for a hardware random
           | number generator.
        
           | Gibbon1 wrote:
           | > 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.
        
             | MegaDeKay wrote:
             | The former bit is illustrated by the Friis formula.
             | 
             | https://en.wikipedia.org/wiki/Friis_formulas_for_noise
        
           | sobriquet9 wrote:
           | It's relatively easy to make a headphone amp quiet because
           | its input is typically already quite strong.
           | 
           | Noise is more of a problem for microphone preamps, guitar
           | pickups, etc., where the input signal is weak.
        
             | kazinator wrote:
             | 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.
        
           | wishinghand wrote:
           | That's really interesting. Is that a common design in
           | headphone and other consumer amps?
        
             | DiabloD3 wrote:
             | It basically is now. He didn't invent the technique, but
             | popularized it in inexpensive devices.
             | 
             | The O2 has been surpassed by many great designs, but the O2
             | really did start that arms race.
        
               | klodolph wrote:
               | 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.
        
             | isatty wrote:
             | 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.
        
         | floxy wrote:
         | >I believe that it's just plain Johnson noise from a resistive
         | divider.
         | 
         | Any reason for guitar pads couldn't use a capacitive divider in
         | place of a resistive divider? (I have no idea what a guitar pad
         | is)
        
         | Zenst wrote:
         | 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.
         | 
         | Some nice low-noise preamp designs to check out here:
         | http://www.richardmudhar.com/piezo-contact-microphone-hi-z-a...
         | 
         | 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.
        
           | klodolph wrote:
           | 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.
        
           | michael1999 wrote:
           | Wait. We have ADCs that produce floats now? That's amazing.
        
             | ansgri wrote:
             | It seems we do not, not quite. A quick googling got quite a
             | few research papers and prototypes, but nothing mass-
             | produced.
        
             | Zenst wrote:
             | Yip - not looked into any IC's, though kit with that
             | functionality been trickling past couple of years and
             | slowly picking up pace. https://zoomcorp.com/en/us/field-
             | recorders/field-recorders/z... one example.
        
         | kazinator wrote:
         | 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:                                    |\       in
         | --)|---+------- |+\                 |        |  > ---+---  out
         | <     ,- |-/     |                 >     |  |/|     |
         | |     |    GND   |                GND    `----------'
         | 
         | 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.
        
           | bcaa7f3a8bbc wrote:
           | 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 kO to 50 kO at 60 Hz. Widely
           | used SSM-2141 IC loses 25 dB of CMRR with a source imbalance
           | of only 1 O. Typical transformer input common-mode impedances
           | are about 50 MO @ 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!
           | 
           | [0] https://www.aes-
           | media.org/sections/pnw/pnwrecaps/2005/whitlo...
        
       | dekhn wrote:
       | Yet another unexpected sighting of Boltzmann's tomb.
        
       | OnlyOneCannolo wrote:
       | They have a cool PDF cheat-sheet related to this which doesn't
       | seem to be linked from the page.
       | 
       | https://www.analog.com/media/en/selection-guides/Equation_Pu...
        
       | cryptonector wrote:
       | > And, of course, we can't change Boltzmann's Constant because
       | Professor Boltzmann is dead[3].
       | 
       | Worth the read just for that punch line.
        
         | pfdietz wrote:
         | 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."
        
           | Applejinx wrote:
           | "...for as long as we can"? D:
        
           | Workaccount2 wrote:
           | Ehrenfest didn't just die similarly, he took his (disabled)
           | son with him!
        
           | matthewdgreen wrote:
           | https://en.wikipedia.org/wiki/Breeds_There_a_Man...%3F
        
         | mgleason_3 wrote:
         | The pinnacle on a wonderful respite from the mire of politics
         | and opinions that often invades hacker news.
        
       | jeffrallen wrote:
       | If you did not read to the last sentence, go back an do so. It's
       | worth it.
        
       | kazinator wrote:
       | Should say "Now that he's long dead, we could easily get away
       | with changing Professor Boltzmann's constant, but it would be
       | disrespectful".
        
       | bcaa7f3a8bbc wrote:
       | 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.
       | 
       | [0]
       | https://descanso.jpl.nasa.gov/monograph/series10/Reid_DESCAN...
        
         | exmadscientist wrote:
         | I haven't crunched the numbers, but I seem to remember that
         | LIGO has the RF guys beat in terms of requirements.
         | 
         | Fortunately for the rest of us, that meant they had to make
         | some measurements, which they were kind enough to share:
         | https://dcc.ligo.org/LIGO-T0900200/public
        
           | tedd4u wrote:
           | Hew boy, don't click through to that site unless you have a
           | few hours to check out all the custom LIGO part drawings ...
           | 
           | Thanks for the link.
        
         | madengr wrote:
         | 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.
        
           | p_j_w wrote:
           | >This is called a minimum noise match, along with associated
           | noise contours where noise is traded off with impedance
           | match.
           | 
           | You also get to trade off your impedances with gain and
           | stability. RF design is fun!
        
             | hughrr wrote:
             | It's not which is why I now write software :)
        
         | jhallenworld wrote:
         | 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.
         | 
         | https://descanso.jpl.nasa.gov/DPSummary/Descanso4--Voyager_e...
         | 
         | https://ipnpr.jpl.nasa.gov/progress_report/42-175/175E.pdf
        
       | [deleted]
        
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