RCA Engineers Test Telefunken 12AX7 Tubes against Their 12AX7

[gadget73]

So is this what I'm hearing in tubes that produce that "windy day at the beach" sort of noise? I've got a set of Amperex 12ax7's that do that.

 

[Tinkerbelle]

So is this what I'm hearing in tubes that produce that "windy day at the beach" sort of noise? I've got a set of Amperex 12ax7's that do that.

The above discussion seems to indicate that flicker noise would effectively not be audible for our purposes. Maybe the windy day at the beach is more from the other tube related noises, shot noise, gas pressure, or... await comments from the physicists.

 

[Retrovert]

So is this what I'm hearing in tubes that produce that "windy day at the beach" sort of noise? I've got a set of Amperex 12ax7's that do that.

Many, many sources of noise exist and these combine.

1/f noise is minor except in high-gain, low-frequency circuits.

What you are hearing, however, is not 1/f noise, but a bad tube.

 

[wyn palmer]

Thanks for the kind words, Dave. I'm never entirely sure anyone actually reads this stuff or cares.

The space cloud is typically—and notably inaccurately—described and depicted, using a water tank or capacitor analogy, as some sort of reservoir or buffer from which electrons are smoothly leaked across the tube at a rate dependent upon the grid's potential. The British name "valve" even suggests this behavior. But that's not exactly how it works. Here's what I worked out by reading through a lot of the ancient tomes and cogitating upon how it works. No guarantees, and a lot of it is handwavy since I'm not a quantum mechanic, only the regular kind that does the electronic equivalent of oil changes, brake pads, and tire rotation.

The space cloud is not a giant tank of noise-free electrons, stored to the point they are permitted to exit through gaps in the grid and transit across the tube, much like a water tank having a spigot at the bottom which releases water at a steady rate. (Even that analogy instantly breaks down, spigot would have issues of laminar vs. turbulent flow because of surface tension, plus other interactions of water molecules with each other, impurities, and the interior surface of the pipe.) If the space cloud were a tank, one might think the electron properties somehow ended up being averaged or muted, analogous to how a capacitor purportedly functions as a shock absorber, absorbing charge in fits and starts but releasing it at a constant rate. (That analogy, too, breaks down, as the capacitor has frequency-dependent behavior, particularly electrolytics, and voltage-dependent behavior, particularly ceramics, and electrons become trapped in the dielectric only to be released over time.) The pool analogy clearly ignores the noise issue. It may help to consider how electrons acquire noise and how it may be removed. Think of how a clean signal is modulated by a noise source, and once having been altered how the only way to make the excrement back into a cow is to extensively filter it and even that isn't perfect, as the filter may itself introduce noise in the pass-band because of ringing in the pass-band or stop-band.

The migrating electrons are modified, one might say "corrupted" since it is a negative outcome, by noise on their journey through the cathode's internal structure and then again as each escapes from the cathode's rough surface. Once emitted each electron—again, containing its own statistical component of the noise spectrum—would normally directly transit across the tube to the plate, except that the interposed grid (when in cutoff or semi-cutoff) forces all of them back into the space cloud, much like a holding pen. So the cloud is chock full of noisy electrons which are attracted to the plate (or screen) but which are not permitted to cross the tube. (The plate is essentially saying, "Give me your huddled noisy electrons yearning to be free, I lift my electro-positivity beside the golden grid", and the grid, decked out in a jet-black Hugo Boss uniform and mirror-polished boots, is saying, "Papers, please!".)

Thermal noise, Brownian noise, flicker noise, mains-frequency and power-line leakage noise from the heater; every possible type of noise is represented in the cloud's electrons. Once noisy the electrons can't become non-noisy without doing work to remove that noise, like using a filter. Even if some averaging could occur, the electrons in the aggregate are all picking up noise on their journey, so it's not like a noise-free source exists to average down the noise.

Shot noise (individual transit) and partition noise (electrons going to the screen instead of the plate, hence "partition"), are different types of noise, being statistical noise arising from how the electrons travel across the tube in randomized discrete units, so that's not the sort of cathode-induced noise we're herein discussing. Emission of electrons from a filament is random, so each electron is a statistically independent event, which is how noise diodes are made.

The cathode's space-charge doesn't have an infinite pool of electrons, which is why high spikes in current demand can damage the cathode as the emission moves from a steady replenishment of the cloud to lighting-bolt like emissions from the surface. The space charge essentially smooths out the electron emissions process, so the electron transit from cathode to plate isn't a random (statistical) process which adds more noise (cf. shot noise or partition noise) as electrons leap from the cathode to the plate, but the cloud does not and cannot smooth out the noise of individual electrons because no mechanism exists for that. A filter is needed. The cloud itself is full of noisy electrons which can't get rid of that noise because that would imply loss of information without some means to do that. It takes energy to move around information aka noise.

All of this becomes clearer, I think, when considering all of this from a different angle: electrons don't actually exist as particles jostling each other in that cloud. Instead, a wave function encodes the entirety of the electron's properties, including energy and noise, and the wave function collapses to actual particle behavior as needed. (Atoms, for that matter, also don't exist. They are just convenient abstractions and shorthand which explain the behavior of the software running on the computer we call the universe.) The aggregate of electrons has statistical noise properties but so do the individual electrons which retain their properties, just in a fragmented way since they're discrete entities. I don't know if this approach clarifies it or makes it worse.

I've rewritten this a number of times and simplfiied the arguments, but it still isn't as clear as I'd like it to be. Time to throw it out into the world.

Really? I'm surprised that you're invoking wave functions and wave function collapse for this when really all we're talking about are statistical macro processes? The processes do have a QM origin (duh!) but it's the statistics that matter and I hardly see how this helps- in fact it adds a layer of "magic" to the whole thing which seems to be unnecessary.
In any case, what do you mean by encoding "energy and noise" in the wavefunction? Surely there is no "noise" encoding per se - there's just an energy operator acting upon the wavefunction to define the evolution of the quantum state over time. After all isn't it the randomness in the momentum of the particles (as defined by the evolving energy operator) that creates the "noise". Perhaps it's the time evolution of this operator that you are defining as "noise". Please explain. Are you also talking about the properties of the individual particles or some kind of collective state?
I also am confused about your claim that the cloud cannot smooth out the "noise" of individual electrons. Doesn't elastic scattering between electrons occur in the cloud, resulting in the exchange of momentum? Doesn't an effective thermalization occur? It's less direct than in semiconductors, I grant you, but why would it not occur?
Overall, I don't see that the fact that electrons are actually wavefunctions propagating in a field adds any insight into the issue. It certainly didn't add clarity in my mind and I have substantial knowledge of QM, something that I expect most of the readers lack.

http://www.keith-snook.info/Stuff-y...ise in Vacuum Tubes and Attached Circuits.pdf.
I was informed that the above paper is used for the development of tube noise in simulators. I've not investigated this claim in any detail- although I did read the paper. Perhaps you disagree. If so I would appreciate some insight. The paper is dated from 1980, so it's fairly recent.
Thermodynamics is, of course, involved, but as bulk properties (good old Boltzmann).

 

[wyn palmer]

I still don't get why flicker noise has a 1/f power spectrum characteristic. From the descriptions above, it seems it would be more "white" noise (equal power spectrum across the entire band, rather than pink type noise with a 1/f characteristic). Comparing flicker noise to something I can relate to, 1 KHz pink noise, what is the resonant or base frequency of flicker noise? Does this frequency change based on the type of material from which the flicker noise is emanating?

It's complicated,
https://core.ac.uk/download/pdf/25335995.pdf
and this is only a partial/incomplete explanation...

 

[Retrovert]

Really? I'm surprised that you're invoking wave functions and wave function collapse for this when really all we're talking about are statistical macro processes? The processes do have a QM origin (duh!) but it's the statistics that matter and I hardly see how this helps- in fact it adds a layer of "magic" to the whole thing which seems to be unnecessary.

Errr, I'm actually not adding magic, I'm removing it. (Which, as per the three laws, requires work.)

Electrons aren't billiard balls, they're little packets of information. The wave function is a shorthand way to look at the issue of how all these properties are encoded and transmitted, instead of as the conventional pool-hall model of physical electrons somehow being munged around like water molecules in a tank until the water emerges from a spigot at the base and the behavior is magically averaged and smoothed. It doesn't work like this. It's about information exchange, not about water in a tank. I was trying to combat that bit of misinformation using a different perspective.

Consider adding noise as an information-based process, such that added noise encodes additional information into the signal. Whenever information is added to a signal removing it requires energy, with a relationship between the energy required and the noise removed.

If, for example, the power supply noise is treated as information, which it is, then energy is required to move the ions around in the electrolyte present in an electrolytic capacitor to distribute charge across the plate's surface and thereby remove noise via filtering. The power supply is a low-pass filter (which, like other filters, has ringing and peculiar stop-band behavior) which alters the systems information content. The traditional view is that the power supply is just a tank (capacitor) which stores and releases energy in an idealized fashion, and the frequency-dependent aspects of the filter are completely ignored. That's why power supplies are often misunderstood, as are the associated issues of ringing and parasitic tanks. Another way to look at the same problem which avoids falling into the conventional rut.

Scads of papers in the 1950s developed separate theories on tube noise not arising from shot noise or partition noise, each purporting to explain how a specific type of electron beam transited the tube, and the model which worked for one type didn't work for another. Reading those was about the point I gave up, lost interest, declared victory, and moved on to more interesting—to me, at any rate, no value judgement for the interests of others intended to be expressed or implied by that statement—aspects of noise in HiFi. My conclusion was to minimize resistor noise and capacitor noise, as those were under my control. and accept the rest of it as axiomatic from the rules. Done.

Diodes, BTW, have no grid or space cloud but do have shot noise, statistical and random, which is why shot noise may be used to make a noise source, aka noise diode.

In any case, what do you mean by encoding "energy and noise" in the wavefunction? Surely there is no "noise" encoding per se - there's just an energy operator acting upon the wavefunction to define the evolution of the quantum state over time. After all isn't it the randomness in the momentum of the particles (as defined by the evolving energy operator) that creates the "noise". Perhaps it's the time evolution of this operator that you are defining as "noise". Please explain. Are you also talking about the properties of the individual particles or some kind of collective state?

Self-organized critical systems encode state and time, being an expression of the underlying cellular automata, where each particle talks to its neighbors in a "think local, act local, cause global" behavior process. Cf. Wolfram, the Bak/Tang/Wiesenfeld sandpile model, Olami/Feder/Christensen earthquake model, etc. In the sand pile the dropping of a grain may result in a sandquake or it may result in absolutely nothing, except an increase in potential for action. Electrons may or may not cause bursts of noise as they worm their way through the cathode. Same thing.

I also am confused about your claim that the cloud cannot smooth out the "noise" of individual electrons. Doesn't elastic scattering between electrons occur in the cloud, resulting in the exchange of momentum? Doesn't an effective thermalization occur? It's less direct than in semiconductors, I grant you, but why would it not occur?

Thermalization is for non-equilibrium carriers in solid-state materials with band issues, right? I don't think it applies here since the tube doesn't work that way. (Disclaimer: it's been thirty years since I did any transistor work, and, besides, I only worked with saturated ones. If I wanted non-saturated behavior, i.e. building guitar effects, analog signal effects like VCOs, or lissajou oscillators, I used an opamp where someone like you at AD or BB had solved the problem for me and put a bow on it.)

The space cloud doesn't function as the equivalent to an infinite pool of water which averages behavior. The electrons are forced back by the grid, so each electron in the space cloud has whatever properties (a) it has when it transited off the cathode plus (b) whatever properties are acquired from inter-electron collisions which, again, are an exchange of information. So the properties would seem to depend upon the extent to which the tube is in cutoff or not.

The limit point of this condition would appear to be a free-flowing arc, which possesses no cloud, but which also has its own noise signature. (Cf. spark-gap transmitters.)

Overall, I don't see that the fact that electrons are actually wavefunctions propagating in a field adds any insight into the issue. It certainly didn't add clarity in my mind and I have substantial knowledge of QM, something that I expect most of the readers lack.

Because the analogy for noise always comes down to an analogy of aggregating molecules in a water tank and slowly releasing via a spigot. Capacitors and batteries, etc. That starts going down a path which has inherent assumptions which lead everyone astray. If we instead consider the electrons as information it all becomes less idealized, and more understandable, than a bucket with a hole in it with ideal (and magickal) properties.

http://www.keith-snook.info/Stuff-you-should-read/Frederick Britton Llewellyn - Noise in Vacuum Tubes and Attached Circuits.pdf. I was informed that the above paper is used for the development of tube noise in simulators. I've not investigated this claim in any detail- although I did read the paper. Perhaps you disagree. If so I would appreciate some insight. The paper is dated from 1980, so it's fairly recent.
Thermodynamics is, of course, involved, but as bulk properties (good old Boltzmann).

Ummm, Llewellyn's work actually dates to 1930. It's really, Really, REALLY ancient. Soooo old that when it was published people still believed in the communism, national socialism, and eugenics as the future. Plus flying cars and personal jet packs. Can't forget those.

It would only be "recent" in the scale of geological time, not physics publication time. 1930 was a time in physics when many things were not understood. To put that in context, circa 1927 that Schrödinger and Heisenberg (of crystal meth fame) had published, and Johnson and Nyquist published their back-to-back papers.

So all of this was still very new in 1930. Llewellyn specifically addressed Johnson-Nyquist noise and shot noise, but not 1/f noise. Much of the noise behavior was not understood until the later 1950s, then semiconductor physics explained a lot of it, and then it wasn't until the 1980s when self-organized criticality was worked out and simulation was possible. Computers in the 1950s and 1960s certainly couldn't do the necessary modeling. It was all slide rules and analog computers.

 

[Retrovert]

It's complicated,
https://core.ac.uk/download/pdf/25335995.pdf
and this is only a partial/incomplete explanation...

"The appearance of power laws in the theory of critical phenomena and above all the work of B. Mandelbrot on fractals in the 1970's [5], seemed to indicate that something deeper was hidden in those ubiquitous spectra."

Which is self-organized criticality. Interesting how the paper omits the mention the relationship between SOC and 1/f noise, particularly in the sandpile.

 

[wyn palmer]

Errr, I'm actually not adding magic, I'm removing it. (Which, as per the three laws, requires work.)

Electrons aren't billiard balls, they're little packets of information. The wave function is a shorthand way to look at the issue of how all these properties are encoded and transmitted, instead of as the conventional pool-hall model of physical electrons somehow being munged around like water molecules in a tank until the water emerges from a spigot at the base and the behavior is magically averaged and smoothed. It doesn't work like this. It's about information exchange, not about water in a tank. I was trying to combat that bit of misinformation using a different perspective.

Consider adding noise as an information-based process, such that added noise encodes additional information into the signal. Whenever information is added to a signal removing it requires energy, with a relationship between the energy required and the noise removed.

If, for example, the power supply noise is treated as information, which it is, then energy is required to move the ions around in the electrolyte present in an electrolytic capacitor to distribute charge across the plate's surface and thereby remove noise via filtering. The power supply is a low-pass filter (which, like other filters, has ringing and peculiar stop-band behavior) which alters the systems information content. The traditional view is that the power supply is just a tank (capacitor) which stores and releases energy in an idealized fashion, and the frequency-dependent aspects of the filter are completely ignored. That's why power supplies are often misunderstood, as are the associated issues of ringing and parasitic tanks. Another way to look at the same problem which avoids falling into the conventional rut.

Scads of papers in the 1950s developed separate theories on tube noise not arising from shot noise or partition noise, each purporting to explain how a specific type of electron beam transited the tube, and the model which worked for one type didn't work for another. Reading those was about the point I gave up, lost interest, declared victory, and moved on to more interesting—to me, at any rate, no value judgement for the interests of others intended to be expressed or implied by that statement—aspects of noise in HiFi. My conclusion was to minimize resistor noise and capacitor noise, as those were under my control. and accept the rest of it as axiomatic from the rules. Done.

Diodes, BTW, have no grid or space cloud but do have shot noise, statistical and random, which is why shot noise may be used to make a noise source, aka noise diode.



Self-organized critical systems encode state and time, being an expression of the underlying cellular automata, where each particle talks to its neighbors in a "think local, act local, cause global" behavior process. Cf. Wolfram, the Bak/Tang/Wiesenfeld sandpile model, Olami/Feder/Christensen earthquake model, etc. In the sand pile the dropping of a grain may result in a sandquake or it may result in absolutely nothing, except an increase in potential for action. Electrons may or may not cause bursts of noise as they worm their way through the cathode. Same thing.



Thermalization is for non-equilibrium carriers in solid-state materials with band issues, right? I don't think it applies here since the tube doesn't work that way. (Disclaimer: it's been thirty years since I did any transistor work, and, besides, I only worked with saturated ones. If I wanted non-saturated behavior, i.e. building guitar effects, analog signal effects like VCOs, or lissajou oscillators, I used an opamp where someone like you at AD or BB had solved the problem for me and put a bow on it.)

The space cloud doesn't function as the equivalent to an infinite pool of water which averages behavior. The electrons are forced back by the grid, so each electron in the space cloud has whatever properties (a) it has when it transited off the cathode plus (b) whatever properties are acquired from inter-electron collisions which, again, are an exchange of information. So the properties would seem to depend upon the extent to which the tube is in cutoff or not.

The limit point of this condition would appear to be a free-flowing arc, which possesses no cloud, but which also has its own noise signature. (Cf. spark-gap transmitters.)



Because the analogy for noise always comes down to an analogy of aggregating molecules in a water tank and slowly releasing via a spigot. Capacitors and batteries, etc. That starts going down a path which has inherent assumptions which lead everyone astray. If we instead consider the electrons as information it all becomes less idealized, and more understandable, than a bucket with a hole in it with ideal (and magickal) properties.



Ummm, Llewellyn's work actually dates to 1930. It's really, Really, REALLY ancient. Soooo old that when it was published people still believed in the communism, national socialism, and eugenics as the future. Plus flying cars and personal jet packs. Can't forget those.

It would only be "recent" in the scale of geological time, not physics publication time. 1930 was a time in physics when many things were not understood. To put that in context, circa 1927 that Schrödinger and Heisenberg (of crystal meth fame) had published, and Johnson and Nyquist published their back-to-back papers.

So all of this was still very new in 1930. Llewellyn specifically addressed Johnson-Nyquist noise and shot noise, but not 1/f noise. Much of the noise behavior was not understood until the later 1950s, then semiconductor physics explained a lot of it, and then it wasn't until the 1980s when self-organized criticality was worked out and simulation was possible. Computers in the 1950s and 1960s certainly couldn't do the necessary modeling. It was all slide rules and analog computers.

Ah, 1930. Thank you. I'm trying to learn as much background information as I can in what is a new area for me. Yes, I realized that he did not explicitly mention 1/f noise, but it was nevertheless an interesting analysis to a neophyte like me.
However, Electrons do in fact have elastic collisions where momentum is exchanged, so in that sense they can be viewed as "billiard balls" even if the momentum is exchanged by force particles in the electron field, and it results in an increase in entropy for the system. This is called thermalization, even in a bounded box, and is a central idea in Physics.
Information is not conserved, at least not in the sense that you seem to be suggesting it- my understanding is that Conservation of Information in Quantum Field Theory merely describes the ability to effectively trace the evolving quantum system back through time, not that the information in any particular particle is conserved. This ability becomes increasingly difficult as the interactions between particles proceed. In essence the system has to be unitary, and as the Hamiltonian evolves actually being able to trace the evolution back becomes impossible.
In fact, isn't conservation of information more generally understood as the conservation of Information + Entropy, so a system in which Entropy is increased at the expense of Information is still a valid one.
By the way, my graduate quantum mechanics courses date back to the 70's and the birth of QCD days, so my knowledge is a bit dated.

 

[Retrovert]

Ah, 1930. Thank you. I'm trying to learn as much background information as I can in what is a new area for me. Yes, I realized that he did not explicitly mention 1/f noise, but it was nevertheless an interesting analysis to a neophyte like me.

If you're digging out old papers, Schottky's paper is also interesting. So is Miller's paper on multiplication of capacitance. All those papers were exceptionally well written and understandable.

However, Electrons do in fact have elastic collisions where momentum is exchanged, so in that sense they can be viewed as "billiard balls" even if the momentum is exchanged by force particles in the electron field, and it results in an increase in entropy for the system. This is called thermalization, even in a bounded box, and is a central idea in Physics.

Yes, I'm aware of this. But, again, entropy (a measure of randomness) isn't what we are discussing. Flicker noise has a power spectral density which indicates correlation between the adjacent samples. It's not the same as random noise, like shot noise or partition noise. Flicker noise, again, is a self-organized criticality, which has certain statistical aspects, but it's not white noise.

Again, my goal was trying to understand the origins of noise in HiFi circuits, what predominated, and how to best reduce it. Thermal noise, current noise, resistor noise, etc. are fixable, but everything else is basically unfixable, unless I start making my own cathodes and blowing glass for vacuum tubes, which is a bit much. Particularly as I'm too busy and lazy to ferment my own kimchi, and that's way easier.

 

[wyn palmer]

If you're digging out old papers, Schottky's paper is also interesting. So is Miller's paper on multiplication of capacitance. All those papers were exceptionally well written and understandable.



Yes, I'm aware of this. But, again, entropy (a measure of randomness) isn't what we are discussing. Flicker noise has a power spectral density which indicates correlation between the adjacent samples. It's not the same as random noise, like shot noise or partition noise. Flicker noise, again, is a self-organized criticality, which has certain statistical aspects, but it's not white noise.

Again, my goal was trying to understand the origins of noise in HiFi circuits, what predominated, and how to best reduce it. Thermal noise, current noise, resistor noise, etc. are fixable, but everything else is basically unfixable, unless I start making my own cathodes and blowing glass for vacuum tubes, which is a bit much. Particularly as I'm too busy and lazy to ferment my own kimchi, and that's way easier.

Actually, I was unaware that the 1/f characteristic in this instance necessarily implied correlation between adjacent samples. I assumed that it was because the spectrum is an integrated E^2 form so the power is reduced by half each octave- that is a reduction of 3dB. What is the autocorrelation function of the spectrum like, is it stationary? Is this because, like shot noise, it can be considered to be an exponentially delayed electron release function? If so- how is it different from shot noise?

 

[wyn palmer]

If you're digging out old papers, Schottky's paper is also interesting. So is Miller's paper on multiplication of capacitance. All those papers were exceptionally well written and understandable..

By the way, the Miller effect was trivially obvious in the 70's when I first encountered it, and in areas like the design of matched receivers for cell phone transceivers it's extended to a more generalized impedance transformation to provide good RF, low noise, input matches (not just opamps after all...). Oh, and I DO make my own kimchi on occasion- I would like to say that I'm helping to preserve all of the disappearing variants that can barely be found in Korea these days, but no. I just like a particular kind...

Retirement= too much unused time on my hands...

 

[Retrovert]

By the way, the Miller effect was trivially obvious in the 70's when I first encountered it, and in areas like the design of matched receivers for cell phone transceivers it's extended to a more generalized impedance transformation to provide good RF, low noise, input matches (not just opamps after all...).

Well, you did benefit from fifty years worth of understanding so that was in the zeitgeist. Schottky's noise work, in retrospect, would also be obvious, oh, yeah, sure, quantized packets. But at the time it was a sweet piece of work. Miller did that work in 1920 when the three-element tube was not well understood.

So they get credit for doing the heavy lifting.

Oh, and I DO make my own kimchi on occasion- I would like to say that I'm helping to preserve all of the disappearing variants that can barely be found in Korea these days, but no. I just like a particular kind...

I actually do make kimchi, since it's pretty easy (hence my point) to make, but I've lately been too busy and it takes up a lot of space in the fridge once it's made. I've been spending my cooking time on prepwork for ten-hour shortrib and other low-and-slow braises, which I can't buy in the store, unlike pickled cabbage.

 

[Retrovert]

Actually, I was unaware that the 1/f characteristic in this instance necessarily implied correlation between adjacent samples. I assumed that it was because the spectrum is an integrated E^2 form so the power is reduced by half each octave- that is a reduction of 3dB. What is the autocorrelation function of the spectrum like, is it stationary? Is this because, like shot noise, it can be considered to be an exponentially delayed electron release function? If so- how is it different from shot noise?

Very different kinds of noise.

Shot noise (quantity variations) and Johnson-Nyquist/thermal noise (velocity variations) have constant power per unit bandwidth (frequency invariant) and are white noise. Shot noise is the statistical emission of an electron which acts like randomly-emitted ball bearings hitting the plate. Noise diode.

1/f noise does not have constant power per unit bandwidth (frequency dependent), so it is pink noise. It's actually something like 1/(f^α), where 0.5 ≤ α ≤ 2. But nobody much worries about the exponent.

The cause of 1/f is purportedly a combination of surface phenomena for thinner layers (electron scattering) and volume phenomena for thicker layers (electron encapsulation in states with catastrophic release). Which might explain why it varies with frequency. The lower frequencies don't change state so it's easier to build up the entrapment as energy is pumped into the system with slow and lumbering electrons, whereas high frequency electrons are harder to grab.

I'll ask a theoretical physicist next time I talk to him. The answer, however, will likely only apply to perfectly spherical vacuum tubes of uniform density. Telefunken made some of those pre-war, but the Japanese long ago bought all of them, so good luck finding one. The spherical tube sockets are really hard to find, too.

The takeaway, TL/DR, is that 1/f noise is not something we need to worry about because: (a) like the Laws of Thermodynamics we are stuck with it (unless the rules change next Thursday), (b) it's small enough that it doesn't matter for audio and even if it did we're stuck with it as per (a), and (c) other sources, which we CAN fix, dominate, so we should focus upon fixing those.

Such as removing carbon composite resistors, barium titanate, and electrolytics capacitors from the signal path.

 

[Pio1980]

Fwiw, tho' I am struggling thru some of the posts, this thread alone is worth more than my subscription.

 

[kward]

I agree, good thread. Thank you all for the expert level discussion.

 

[wyn palmer]

Very different kinds of noise.

Shot noise (quantity variations) and Johnson-Nyquist/thermal noise (velocity variations) have constant power per unit bandwidth (frequency invariant) and are white noise. Shot noise is the statistical emission of an electron which acts like randomly-emitted ball bearings hitting the plate. Noise diode.

1/f noise does not have constant power per unit bandwidth (frequency dependent), so it is pink noise. It's actually something like 1/(f^α), where 0.5 ≤ α ≤ 2. But nobody much worries about the exponent.

The cause of 1/f is purportedly a combination of surface phenomena for thinner layers (electron scattering) and volume phenomena for thicker layers (electron encapsulation in states with catastrophic release). Which might explain why it varies with frequency. The lower frequencies don't change state so it's easier to build up the entrapment as energy is pumped into the system with slow and lumbering electrons, whereas high frequency electrons are harder to grab.

I'll ask a theoretical physicist next time I talk to him. The answer, however, will likely only apply to perfectly spherical vacuum tubes of uniform density. Telefunken made some of those pre-war, but the Japanese long ago bought all of them, so good luck finding one. The spherical tube sockets are really hard to find, too.

The takeaway, TL/DR, is that 1/f noise is not something we need to worry about because: (a) like the Laws of Thermodynamics we are stuck with it (unless the rules change next Thursday), (b) it's small enough that it doesn't matter for audio and even if it did we're stuck with it as per (a), and (c) other sources, which we CAN fix, dominate, so we should focus upon fixing those.

Such as removing carbon composite resistors, barium titanate, and electrolytics capacitors from the signal path.

A major source of 1/f noise in semiconductor devices is often explicitly described as being due to "traps" in the lattice- due to imperfections, contaminants (like gold, iron, nickel, copper etc.) etc. These traps occur at different depths within the structure and act to capture and release carriers and approximate to the exponential release characteristic described for "shot noise" in the electron tube paper that I cited earlier. The characteristic of the 1/f noise is not, as you say, 1/f but 1/(f^0.5<=n<1.5 or so), and can actually have a variable rate depending on the release characteristics of the distributed traps. The nature and characteristic of these traps and the associated modelling has been a subject of great attention for a number of years.
As a result of this understanding Semiconductor processing, particularly for CMOS, has been improved over time to reduce these traps and the 1/f noise that is associated with them, greatly improving the analog performance of the technology. Advanced models for the devices embody these characteristics and include both variable rates and statistical properties for the corner frequencies, geometry aspects, etc. etc.

There are several sources of noise that are important in semiconductors,
Thermal noise- your usual noise associated with resistive elements (this ignores excess noise such as exists in carbon Rs in discrete resistors and thick film etc. Rs used in ICs.
Shot noise- which is a current flow that is constant versus frequency up until the inverse of the transit time and is also temperature independent (white noise). This is associated with the quantized nature of current flow through the potential barriers associated with semiconductors and is proportional to DC current flow.
Generation- Recombination noise. Describing this is way beyond the scope of this thread. Suffice it to say that it has a different spectrum from shot or 1/f- it's constant at frequencies below a certain point, but falls at 20dB/decade at frequencies above that point.
1/f noise is as described above. It also includes 1/f^2 noise except that this form is generally observed in the metal interconnections of ICs and has some interesting properties...
Burst noise- this occurs at low frequencies and is associated with 1/f noise- i.e. it's due to contaminants in the lattice (heavy metals) and lattice imperfections.

Electron tube understanding and modeling seems to be extremely primitive in comparison.

 

[Retrovert]

A major source of 1/f noise in semiconductor devices is often explicitly described as being due to "traps" in the lattice- due to imperfections, contaminants (like gold, iron, nickel, copper etc.) etc. These traps occur at different depths within the structure and act to capture and release carriers and approximate to the exponential release characteristic described for "shot noise" in the electron tube paper that I cited earlier.

Again, as I above explained,there's apparently two different effects depending up on the layer's thickness. Thin layers, which is how modern semiconductors are created because it's the only way to get very fast devices, are apparently a function of electron scattering, not a function of traps which occurs with thicker layers. This was worked out by some clever physicists.

The characteristic of the 1/f noise is not, as you say, 1/f but 1/(f^0.5<=n<1.5 or so), and can actually have a variable rate depending on the release characteristics of the distributed traps.

Burst noise- this occurs at low frequencies and is associated with 1/f noise- i.e. it's due to contaminants in the lattice (heavy metals) and lattice imperfections.

Ummmm, first, if by stating "is not, as you say" I'm not sure if you're concurring with what I wrote or contradicting it. I specifically pointed out (in No. 56) that:

It's actually something like 1/(f^α), where 0.5 ≤ α ≤ 2.​

What you are describing for electron traps is commonly called "burst noise", aka "popcorn noise", which is why I moved up your statement about it. Burst noise arises out of from the discrete transitions in energy levels in any film, so it is not necessarily the result impurities or imperfections which implies error. Even a perfect film with a handful of atoms is going to have such transitions between the layers as the electrons move between homogenous or hetereogenous atoms which were assembled for particular purpose, i.e. doped.

Thermal noise- your usual noise associated with resistive elements (this ignores excess noise such as exists in carbon Rs in discrete resistors and thick film etc. Rs used in ICs.

The common name for thermal noise is now Johnson-Nyquist noise. The reason is that Johnson first identified the noise and then Nyquist, who worked down the hall, explained it, and both papers were published back to back in 1926. Both worked at Bell Labs in the same area, so it was natural they'd discuss this. The vibration of the charge carriers varies with temperature, so higher temperatures create higher noise. Johnson-Nyquist noise also exists in capacitors because it is an effect of charge distribution on the plate. Thick-film networks have more noise than thin-film ones.

Shot noise- which is a current flow that is constant versus frequency up until the inverse of the transit time and is also temperature independent (white noise). This is associated with the quantized nature of current flow through the potential barriers associated with semiconductors and is proportional to DC current flow.

I think this explanation is confusing for the average reader. Here's a different, and hopefully more comprehensible, explanation.

Shot noise arises when the control of current is discontinuous. It happens in semiconductors and it happens in tubes where it was first identified in the 1920s by Schottky, the grand master of the diode.

Current moves in discrete packets (aka electrons), so at some level current flow transitions from a continuous movement of a stream to a discrete movement of individuals. When a high current is flowing the statistical nature of the discrete units is averaged over time, so the flow appears to be more or less continuous, with minor fluctuations. Lower variation in flow is lower noise, while higher variation in flow is higher noise. But as the flow of current slows the movement of charge becomes more and more discrete, happening in fits and starts, and it eventually becomes dominated by the movement of individual electrons.

So shot noise arises because at low current the tube's cathode randomly emits electrons so a low current moves in irregular amounts. Statistically the current is whatever it is, but it might be a burst of electrons, then nothing, or it might be a steady pulse of electrons. Since it's random there's no way to know.

Think of army ants flowing across a branch spanning a stream. At a high volume it looks like a continuous flow. But as the number of ants reduces we can eventually observe individual ants making the crossing. That's the shot noise, because it's like firearm's shot (ball bearings) moving as discrete particles.

Vacuum tube diodes can use the shot effect to create a noise source. A standard tungsten or thoriated tungsten filament has the plate voltage increased until the current peaks (saturation). The filament voltage has a lot to do with that point. But higher filament voltage is short lifespan. The tube gods giveth and the tube gods taketh away. So it isn't just PN junctions which may be used in that fashion, although they do last significantly longer..

Hopefully that clarified the issue.

It isn't just shot noise, which generally is a minor issue because it matters for small currents. Think phono stage.

Here's a brief, handwavy summary of a few other types of noise in PN junctions.

A reverse-biased diode cannot conduct current because of the junction's depletion layer lacks free charge carriers needed to move the electrons. But two mechanisms exists to create those carriers and permit charge to move.

Avalanche Noise. The PN junction has a high-potential gradient between the two sides. The electrons moving through the lattice are accelerated (gain momentum) and because of all that momentum impacting other charge carriers in the crystal lattice, leaving holes behind. Each electron knocks loose two additional carriers, hence the "avalanche" effect. The collapse is like the sandpile, because all of a sudden the current flows in an uneven burst. This is how an avalanche noise diode works. It's also how a sensitive photodetector works, because the system is doped to be at the edge of stability so a photon is able to trigger a burst of electrons, as an amplifier. The avalanche effect occurs at around 5.5 V or above, and it's different than the Zener effect below described.

Zener Noise. The Zener effect is different because it uses electron tunneling. The field across the PN junction is very high, but also very narrow, so the avalanche can't occur because enough collisions don't occur. Instead, the electrons just transit through the junction using a quantum effect. Noise is, again, the result. For this reason Zener diodes are generally a poor voltage regulator for analog systems. (Digital doesn't care as long as the noise is below the threshold required to flip a transistor between 0 and 1 or 1 and 0.) The solution to noisy high-voltage Zeners is using a stack of low-voltage Zeners. The Zener effect occurs at around 5.5 V or below, which is different than the avalanche effect above described.

The amount of doping controls the junction type.

Avalanche effects were used in photomultiplier tubes, where the work function of the cathode is such that the impact of a photo knocks loose a shower of electrons which, in turn, contact other plates for a cascading effect.

Generation- Recombination noise. Describing this is way beyond the scope of this thread. Suffice it to say that it has a different spectrum from shot or 1/f- it's constant at frequencies below a certain point, but falls at 20dB/decade at frequencies above that point.

Well, that mostly is used in photon detectors and isn't relevant to tubes.

Electron tube understanding and modeling seems to be extremely primitive in comparison.

Nuh-Uh!

Did you just disrespect the work of several generations of physicists and electrical engineers? Dude, you must so not keep doing that, it is so, so not cool. The world of electronics did not magickally spring into existence with silicon/germanium junctions.

All of the semiconductor understanding grew out of the vacuum tube work, and it's equally applicable. The work in thin/thick films explains the cathode's behavior. I don't know that anyone is specifically working on, say, orthosilicate behavior in hot alkali cathodes these days, of course, but physics is physics.

 

[wyn palmer]

Again, as I above explained,there's apparently two different effects depending up on the layer's thickness. Thin layers, which is how modern semiconductors are created because it's the only way to get very fast devices, are apparently a function of electron scattering, not a function of traps which occurs with thicker layers. This was worked out by some clever physicists.





Ummmm, first, if by stating "is not, as you say" I'm not sure if you're concurring with what I wrote or contradicting it. I specifically pointed out (in No. 56) that:

It's actually something like 1/(f^α), where 0.5 ≤ α ≤ 2.​

What you are describing for electron traps is commonly called "burst noise", aka "popcorn noise", which is why I moved up your statement about it. Burst noise arises out of from the discrete transitions in energy levels in any film, so it is not necessarily the result impurities or imperfections which implies error. Even a perfect film with a handful of atoms is going to have such transitions between the layers as the electrons move between homogenous or hetereogenous atoms which were assembled for particular purpose, i.e. doped.



The common name for thermal noise is now Johnson-Nyquist noise. The reason is that Johnson first identified the noise and then Nyquist, who worked down the hall, explained it, and both papers were published back to back in 1926. Both worked at Bell Labs in the same area, so it was natural they'd discuss this. The vibration of the charge carriers varies with temperature, so higher temperatures create higher noise. Johnson-Nyquist noise also exists in capacitors because it is an effect of charge distribution on the plate. Thick-film networks have more noise than thin-film ones.



I think this explanation is confusing for the average reader. Here's a different, and hopefully more comprehensible, explanation.

Shot noise arises when the control of current is discontinuous. It happens in semiconductors and it happens in tubes where it was first identified in the 1920s by Schottky, the grand master of the diode.

Current moves in discrete packets (aka electrons), so at some level current flow transitions from a continuous movement of a stream to a discrete movement of individuals. When a high current is flowing the statistical nature of the discrete units is averaged over time, so the flow appears to be more or less continuous, with minor fluctuations. Lower variation in flow is lower noise, while higher variation in flow is higher noise. But as the flow of current slows the movement of charge becomes more and more discrete, happening in fits and starts, and it eventually becomes dominated by the movement of individual electrons.

So shot noise arises because at low current the tube's cathode randomly emits electrons so a low current moves in irregular amounts. Statistically the current is whatever it is, but it might be a burst of electrons, then nothing, or it might be a steady pulse of electrons. Since it's random there's no way to know.

Think of army ants flowing across a branch spanning a stream. At a high volume it looks like a continuous flow. But as the number of ants reduces we can eventually observe individual ants making the crossing. That's the shot noise, because it's like firearm's shot (ball bearings) moving as discrete particles.

Vacuum tube diodes can use the shot effect to create a noise source. A standard tungsten or thoriated tungsten filament has the plate voltage increased until the current peaks (saturation). The filament voltage has a lot to do with that point. But higher filament voltage is short lifespan. The tube gods giveth and the tube gods taketh away. So it isn't just PN junctions which may be used in that fashion, although they do last significantly longer..

Hopefully that clarified the issue.

It isn't just shot noise, which generally is a minor issue because it matters for small currents. Think phono stage.

Here's a brief, handwavy summary of a few other types of noise in PN junctions.

A reverse-biased diode cannot conduct current because of the junction's depletion layer lacks free charge carriers needed to move the electrons. But two mechanisms exists to create those carriers and permit charge to move.

Avalanche Noise. The PN junction has a high-potential gradient between the two sides. The electrons moving through the lattice are accelerated (gain momentum) and because of all that momentum impacting other charge carriers in the crystal lattice, leaving holes behind. Each electron knocks loose two additional carriers, hence the "avalanche" effect. The collapse is like the sandpile, because all of a sudden the current flows in an uneven burst. This is how an avalanche noise diode works. It's also how a sensitive photodetector works, because the system is doped to be at the edge of stability so a photon is able to trigger a burst of electrons, as an amplifier. The avalanche effect occurs at around 5.5 V or above, and it's different than the Zener effect below described.

Zener Noise. The Zener effect is different because it uses electron tunneling. The field across the PN junction is very high, but also very narrow, so the avalanche can't occur because enough collisions don't occur. Instead, the electrons just transit through the junction using a quantum effect. Noise is, again, the result. For this reason Zener diodes are generally a poor voltage regulator for analog systems. (Digital doesn't care as long as the noise is below the threshold required to flip a transistor between 0 and 1 or 1 and 0.) The solution to noisy high-voltage Zeners is using a stack of low-voltage Zeners. The Zener effect occurs at around 5.5 V or below, which is different than the avalanche effect above described.

The amount of doping controls the junction type.

Avalanche effects were used in photomultiplier tubes, where the work function of the cathode is such that the impact of a photo knocks loose a shower of electrons which, in turn, contact other plates for a cascading effect.



Well, that mostly is used in photon detectors and isn't relevant to tubes.



Nuh-Uh!

Did you just disrespect the work of several generations of physicists and electrical engineers? Dude, you must so not keep doing that, it is so, so not cool. The world of electronics did not magickally spring into existence with silicon/germanium junctions.

All of the semiconductor understanding grew out of the vacuum tube work, and it's equally applicable. The work in thin/thick films explains the cathode's behavior. I don't know that anyone is specifically working on, say, orthosilicate behavior in hot alkali cathodes these days, of course, but physics is physics.

Actually, I don't believe that your explanations produce any increase in clarity, so perhaps it's time to end this exchange. Thanks again for an interesting time.

 

[Pio1980]

I have to go back and re-read some of the posts, but, thinking of a mentor that used to work R&D at Varian/Eimac (R.I.P, Lane) , I'm intrigued by the coating/conductor cathode interface behavior vs a pure hot tungsten emitter, such as used in long life industrial vacuum electron valves. It seems, without the coating and interface issues, the simple hot emitter would be much easier to model and analyze.
Thoughts?

 

[Pio1980]

I recall discussing some aspects of early development with Lane years ago about ATT, concerning Dr. Hendryk van der Bijl ("Funderbail").
https://archive.org/details/thermionicvacuum00vandrich
Dr. van der Bijl doesn't much mention in these discussions. There's an IEEE pdf online on this part of his career.