In an optimally biased class AB amp, the gm of the still conducting tube, when crossing into the class B region, should equal the sum of gm's in the idle (class A) condition. It then increases further as the 3/2 power law increases gm with more current, until the saturation region is approached, where gain stagnates then begins to fall. So one should see expansion until stagnation and compression set in at max signal. (for optimal biasing)
An under-biased (too high idle current) class Ab amp would show compression when one tube cuts off. At least until the 3/2 power law catches up at even higher current.
A fully class A amp will show greater gm at idle and less gm toward max signal. That's because the gm curve is SQRT of current for each tube, so makes for a gm bulge in the center in that case.
https://frank.pocnet.net/sheets/084/e/E55L.pdf (page 12 for gm versus current)
Draw the gm curve out on paper, and another complementary gm curve on clear plastic. By changing the amount of overlap, can see the effect of biasing on the sum of gm's. An upward bulge sum for class A, changing to a W form for class AB with the ends of the W bending over and down again in the saturation region. (saturation region at higher current not shown on the graph there)
An under-biased (too high idle current) class Ab amp would show compression when one tube cuts off. At least until the 3/2 power law catches up at even higher current.
A fully class A amp will show greater gm at idle and less gm toward max signal. That's because the gm curve is SQRT of current for each tube, so makes for a gm bulge in the center in that case.
https://frank.pocnet.net/sheets/084/e/E55L.pdf (page 12 for gm versus current)
Draw the gm curve out on paper, and another complementary gm curve on clear plastic. By changing the amount of overlap, can see the effect of biasing on the sum of gm's. An upward bulge sum for class A, changing to a W form for class AB with the ends of the W bending over and down again in the saturation region. (saturation region at higher current not shown on the graph there)
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You will find this is wrong.
If the A-A load is say 4K5, the load from the CT to ONE anode is most certainly NOT half the A-A load.
The GM of the valve is strongly affected by the real anode (the screen grid), while the virtual anode dips below the screen voltage.
That is why the GM is not constant, and why ultralinear operation introduces highly undesirable compression. (People don't want to admit this).
I noted the very interesting page 11 on the E55L
Also:- the waveform from stringed instruments is anything but a sine wave.
The pitch also varies with amplitude. (changes in tension take over).
The purer sine wave functions are invariably created by linear bore wind instruments such as flutes and organs.
I notice this thread getting more and more interesting.
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I am very interested in this theory which explains a lot about the way PP valve amplifiers react and sound when under moderate to high loads.
It particularly well explains what I loosely term the "magical" sound region using ultra high gain valves in the 20-25m/a/V range, such as the super low impedance, high current EL520.
These do, as you suggest do tend,-
I would suggest with the EL84 it's quite possible partially true, but becomes much more true if you double or treble the gm, as you showed in your quite unusual E55L example.
(At the end of the valve era, lots of interesting things were going on with ultra high gain frame grid valves).
The PPP with high quality "golden age" OPT scenario I think is even more interesting, because the saturation region becomes substantially different with a wider linear gm region. (gm is multiplied by 2 in PPP).
As I just mentioned, the problem with U/L is the non linear behaviour of the tapped screen.
This goes through a sort of "S" shaped curve, where as the load increases the screen voltage drops. This radically changes the gm of the valve, so as it goes out of class A into B, it hits a small region of expansion then heavy compression sets in.
If you add large amounts of NFB, it's quite understandable why some amps sound dreadful, sterile and dead.
I don't think it's got much to do with the distortion sig, lots to do with dynamic compression, sounding quite evil, despite ultra low THD and quite possibly good IMD on paper.
I've heard lots of those things, and eg. would never want to own a MAC or a Dynaco.
They make good door stops.
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6vheater,
Perhaps I did not write my earlier post very clearly. Let me make it clear:
Start with a push pull transformer that has a 4k plate to plate primary, and with the 8 Ohm secondary tap loaded with 8 Ohms.
Drive the complete primary winding, from plate to plate, you get 4k.
Check the impedance, or build a push pull amp to test this.
Drive 1/2 the secondary (plate to center tap), you get 1/2 the turns, and 1/4 the impedance, that is 1k. That is what happens when one tube turns off.
With the output tubes at quiescent, and then with small signal applied (still in class A push pull), each tubes plate 'sees' or benefits from the other tubes plate motion.
So, working together, each tube plate sees 2k Ohms.
Now, increase the signal level until one tube is completely off (the tube plates are no longer working together).
In that case, the one plate has to work harder (into a load of 1k).
Does that make sense?
If you need a test, then take a push pull transformer, and pull the laminations out.
Then re-install the laminations with all the E's on one side, and all the I's on the other side, and use a very small air gap between the set of E's and the set of I's.
Now, put an 8 Ohm load on the 8 Ohm tap, and measure the impedance of the 1/2 primary winding (from one plate lead to the center tap). This is a measurement test to prove the concept
Because the laminations are air gapped, you can build a SE output, and drive from one plate lead to the center tap. This is a working test to prove what happens when one tube in a push pull amp is off.
I have done these tests with a push pull transformer that has been modified (all the E's on one side, and all the I's on the other side, and air gapped).
You probably do not want to ruin a good push pull transformer, so you can use an impedance meter to measure the impedance of the 1/2 primary (plate to center tap), and with the 8 Ohm secondary terminated into 8 Ohms.
Perhaps I did not write my earlier post very clearly. Let me make it clear:
Start with a push pull transformer that has a 4k plate to plate primary, and with the 8 Ohm secondary tap loaded with 8 Ohms.
Drive the complete primary winding, from plate to plate, you get 4k.
Check the impedance, or build a push pull amp to test this.
Drive 1/2 the secondary (plate to center tap), you get 1/2 the turns, and 1/4 the impedance, that is 1k. That is what happens when one tube turns off.
With the output tubes at quiescent, and then with small signal applied (still in class A push pull), each tubes plate 'sees' or benefits from the other tubes plate motion.
So, working together, each tube plate sees 2k Ohms.
Now, increase the signal level until one tube is completely off (the tube plates are no longer working together).
In that case, the one plate has to work harder (into a load of 1k).
Does that make sense?
If you need a test, then take a push pull transformer, and pull the laminations out.
Then re-install the laminations with all the E's on one side, and all the I's on the other side, and use a very small air gap between the set of E's and the set of I's.
Now, put an 8 Ohm load on the 8 Ohm tap, and measure the impedance of the 1/2 primary winding (from one plate lead to the center tap). This is a measurement test to prove the concept
Because the laminations are air gapped, you can build a SE output, and drive from one plate lead to the center tap. This is a working test to prove what happens when one tube in a push pull amp is off.
I have done these tests with a push pull transformer that has been modified (all the E's on one side, and all the I's on the other side, and air gapped).
You probably do not want to ruin a good push pull transformer, so you can use an impedance meter to measure the impedance of the 1/2 primary (plate to center tap), and with the 8 Ohm secondary terminated into 8 Ohms.
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6vheater,
Good points about musical instruments, and the dynamic and changing nature of their musical tones.
There is lots to be said about musical instruments, and the resulting waveforms.
All of these complex waveforms can be separated into sine waves.
The sine waves can be constant, present, then missing, and constantly changing.
A study of musical instruments on a real time spectrum analyzer, with real time scrolling spectrogram (that can be recorded, and played back, frame to frame at any speed you want), can show a lot about these sine waves.
Amplitude variations over time will result in AM (amplitude modulation of these notes). And each fundamental and each harmonic can be amplitude modulated).
Frequency variations over time will result in FM (frequency modulation of these notes).
And each fundamental note, and each harmonic can be frequency modulated).
Then there is the case with both AM and FM at the same time.
Guess what, spectrum analysis shows the multiple sine waves that added together give us the complex voltage/time waveform.
A stringed instrument has sound resulting from the string (i.e. a violin). It also has sound resulting from the 'scraping' of the bow strings on the instrument string. (I do not know of a better word to use than scraping)
Each of those sounds can be broken up into individual sine waves.
Now take a violin and a flute an put them in front of a microphone, and check the much more complex volt/time waveform.
Of course, this can be broken up into sine waves (but many many more of them).
As good as the best real time spectrum analyzers are, there is one way that works better:
The ear plus the brain.
Good points about musical instruments, and the dynamic and changing nature of their musical tones.
There is lots to be said about musical instruments, and the resulting waveforms.
All of these complex waveforms can be separated into sine waves.
The sine waves can be constant, present, then missing, and constantly changing.
A study of musical instruments on a real time spectrum analyzer, with real time scrolling spectrogram (that can be recorded, and played back, frame to frame at any speed you want), can show a lot about these sine waves.
Amplitude variations over time will result in AM (amplitude modulation of these notes). And each fundamental and each harmonic can be amplitude modulated).
Frequency variations over time will result in FM (frequency modulation of these notes).
And each fundamental note, and each harmonic can be frequency modulated).
Then there is the case with both AM and FM at the same time.
Guess what, spectrum analysis shows the multiple sine waves that added together give us the complex voltage/time waveform.
A stringed instrument has sound resulting from the string (i.e. a violin). It also has sound resulting from the 'scraping' of the bow strings on the instrument string. (I do not know of a better word to use than scraping)
Each of those sounds can be broken up into individual sine waves.
Now take a violin and a flute an put them in front of a microphone, and check the much more complex volt/time waveform.
Of course, this can be broken up into sine waves (but many many more of them).
As good as the best real time spectrum analyzers are, there is one way that works better:
The ear plus the brain.
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That makes very good sense to me. A somewhat less useful way to say it is that with one valve shut off, the other is effectively a single-ended amplifier driving a 1K Ohm load. And signal current now flows through the B+ supply, unlike the push-pull Class A case.
Much thanks, as always,
Chris
This may be a little OT but nevertheless of interest.
Being as I am a violinist, I did some interesting studies with this instrument, including interest in writing a scientific paper about what makes one player sound so totally different from another.
Analysing the waveform and having long conversations with one of the best bow specialists in the world, we looked very carefully at the microstructure of horse hair especially when impregnated with rosin (there's even different rosins!).
A bowed stringed instrument creates a ragged waveform which is extremely rich in harmonics (I do a lot of high quality recordings of this instrument rather unsurprisingly!).
This ragged waveform in micro detail shows the string reaching a tension with the rosin particules dragging the string over to one side, then they reach a rupture force point and the string springs back.
As this happens typically 440x a second (eg. on the 2nd string), you can imagine the waveform is a sort of jagged triangular section, not even remotely like a sine (which you will get from a flute, which has a linear bore)
Another variable is, of course the louder you play, the more you have to flatten the pitch, because the higher string pressures increase the strong tension, raising the pitch. (all the best players know this!).
For our interest in recording & reproduction it becomes vital to validate a whole chain from recording, to editing to reproduction.
Clearly when we start to look at the whole distortion chain the 6V6 is merely a minor irritation in the chain, complicated by room reflections, proximity effects, microphone polar sensitivities, Op-amp performance right thru the studio, multiple A-D-D-A conversions, dither, speaker spectral response and losses in cables and parasitic noise generated by speaker cones and cabinet responses.
Also what the violinist hears is very radically different to what the audience hears, with a SPL often exceeding 100dB in the left ear, and a drastic inbalance L-R in the player's SPL, as well as transmission thru the Pinna.
Ahum!
Nothing is quite as simple as it seems!
Coming back on topic:-
Of course a PP amp IS 2 SE amps, which generate lots of SE distortion!
Why would it be any different?
The main advantage of course is not needing any air gap, and of course cancelling out all the dirty but "harmonious" even harmonic excess distortion.
The following is not a correct analysis of class A however.
You DON'T drive the complete winding, you can't, only in SE can you do that, but then requires an Air gap for the DC component to avoid core magnetisation problems.
As one valve is driven more negative the anode current drops, while on the valve driven positive the anode current increases.
It's class A, because the SUM of the 2 currents remains (should remain) constant, but the anodes are working in counter phase.
In my PP or PPP amps I always run them closer to 80-85% quiescent, (rather than the recommended 70%) because this extends the class A area, and they demonstrably sound better.
(ie a typical 35W beam tetrode like 8417 is running at 26-28W at idle, rather the practically class B they used from the OEM amp factory, which of course sounded simply terrible).
This is the main difference with the SE example, because we are now using 2 components instead of 1.
In the PPP example we use 4 components instead of 1, thus doubling the transconductance, and halving the effective anode impedance.
However creating perfect quads never mind perfect matched pairs of valves is not a trivial task.
Those obsessed with damping factor take note.
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I wanted to make one further comment about this one.
* In practice the speaker driver is never 8 ohms.
It varies with frequency in a fairly random way.
The valve sees this varying reflected load and the load line jumps around from what can be "danger zone" to anything from perfect to way sub optimal.
It's true they do tolerate quite large variations in reflected impedance with relatively small variations in Power output, but the distortion spectra varies enormously with Freq & load.
So we have a non linear distortion amp too!
Nothing could be closer to this paradigm than eg. a QUAD ESL.
They vary across the entire spectrum from more or less optimal, no a near complete short circuit at anything over 10-15khz.
Some amps don't like that at all and will go as far as into shutdown.
FYI, this is why I use a multi tap/bi/tri wire array of optimised speakers with higher than normal impedance (typically 18-25ohms) across 2 seperate windings and 4 seperate taps.
The total impedance load is optimal but with the averaging out of the entire reflected load across multiple windings the A-A load in effect becomes far more linear, across the entire audio spectrum.
(most people advise doing completely the opposite of this!)
Those kind of transformers are very rare, (being PA/ audio dist originally) but nice.
Hint, one of the most beautiful is found in a thing called Xx60A.
It has an A-A load in my tests of roughly 6k2>6k9.
I have the ratios mapped 29.4:1, 20.8:1, & 8.7:1.
Rated at 50-60W, a pair sold on EBAY last week for 130USD. (they were claiming 100W duh!)
I haven't tried that one, but I think would be perfect for PPP 6V6 at about 30W.
** condition doesn't occur in reality.
***1k load in effect for the SE part of the PP amp is likely correct but again very much dependent on *.
As LF represent the highest energies, but usually speaker impedance trebles to quadruples at resonance or approaching it....
We then have an interesting condition where maximum power is demanded, but the valve/load line is so devastatingly inaccurate that only 1/3-1/2 the actual power is actually made available****, and in any case the majority of OPT are also approaching sporadic saturation, which can look as good as a short circuit to the output device.
You can get around this, by increasing bass cone area x 3 & distributing the drivers over several optimised cabinets to even out the FS peaks. (that's what I did).
As far as I am aware this was the theory**** behind the Quad "current dumping" strategy.
Using sand creates a number of very different scenarios, especially when large amounts of NFB are used.
I wouldn't mind suggesting this is one reason why sand or empty bottle based amps sound really quite different.
Sorry to mention Peter Walker's Huntingon based company so many times, but they made both types of amps, and were highly innovative in fixing many of the problems.
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6vheater,
Instruments:
Thanks for the wonderful and revealing discussion of violins. The sawtooth wave is dominant 2nd harmonic (dominant in no way means there are not lots of other string harmonics, not to mention the ‘ripping’ of the rosin).
As to what someone hears from a violin, the harmonics are rolled off for the listener who is 30 feet away from the stage (attenuation versus distance versus frequency), not at all what the player’s single ear hears, nor the other ear that is not ‘aimed’ at the violin.
There are also different violin sounds of steel strings, versus the other ‘ancient’ strings and instruments (i.e. Monica Huggett, I believe).
How about a clarinet with a #1 reed, versus a #2.5 reed? Or two different players?
No, instruments are not simple.
In high school, we had a Shure bullet microphone and Dumont scope. We looked at a French Horn player’s note on the scope, it had the classical French Horn wave shape, with dominant 2nd harmonic (but because of phase and the other harmonics, it was a much different general shape, and much smoother than the sawtooth violin waveform). But the most revealing part of this study was the French Horn player was so skilled, he could change the timbre to be more like a pure sine wave, no visible distortion. Did not have a spectrum analyzer, nor an FFT then.
the horn player could also play pedal tones (low frequency notes that even most professional players could not).
Bach (oops, back) to amplifiers:
My push pull amplifiers do drive the complete primary. One tube increases by 10mA, while the other tube decreases by 10mA. Both halves of the primary are driven. Yes, it is different than
SE across the whole winding. But the delta 20mA x 1/2 turn(s) = delta 10mA x 1 turn(s).
The distortion is different, but the power is the same.
Larger signal changes complicate this, transconductance and plate resistance changes versus small signal. In push pull, the total change in current no longer unity.
For a push pull transformer, put a resistive load on the secondary. Then if you put a current source on one primary plate lead, and a tube on the other primary plate lead, the driving plate will drive an impedance that is 1/4 of the plate to plate impedance. That is what I was trying to illustrate when one tube cuts off (By cut off, I mean when one plate current is no longer changing, some tubes conduct a small current, but the grid no longer has effective control).
Agreed, loudspeakers are anything but constant impedance.
I have studied the harmonic distortion versus frequency of an amplifier when loaded by a loudspeaker. Yes, that is much different than the same test into a Non-Inductive Resistor load.
Then there is the difference of phase versus frequency. That changes when you use a loudspeaker load, instead of a Non-Inductive load resistor. I have tested that too.
How a push pull amplifier reacts to varying load, and even into a resistive load depends on many factors:
Output stages of pentode and beam power; ultra linear; triode; and triode wired pentodes and triode wired beam power tubes.
The tube curves of these various configurations.
Class A, AB, B.
Global negative feedback
Local negative feedback: cathode windings, UL taps, Schade, etc.
The original Quad electrostatic speaker had a transformer to step up the signal voltage (and a high voltage bias supply to prevent the doubling of every signal that would have otherwise occurred). A step up transformer . . . inductance, distributed capacitance, not to mention the reflected capacitance of the electrostatic panels, that capacitance is multiplied by the step up ratio (makes a tube miller capacitive effect look like a small time player).
The Quad tube amps I remember are classical circuits.
The Quad solid state amp I remember had a feed forward amp for the majority of the power, and a finessed error amp that cancelled (subtracted) the distortion of the feed forward amp.
I think many of us often simplify on this forum. Details often require a book, or even a life study.
I apologize for any oversimplified or misleading statements I may have made.
Instruments:
Thanks for the wonderful and revealing discussion of violins. The sawtooth wave is dominant 2nd harmonic (dominant in no way means there are not lots of other string harmonics, not to mention the ‘ripping’ of the rosin).
As to what someone hears from a violin, the harmonics are rolled off for the listener who is 30 feet away from the stage (attenuation versus distance versus frequency), not at all what the player’s single ear hears, nor the other ear that is not ‘aimed’ at the violin.
There are also different violin sounds of steel strings, versus the other ‘ancient’ strings and instruments (i.e. Monica Huggett, I believe).
How about a clarinet with a #1 reed, versus a #2.5 reed? Or two different players?
No, instruments are not simple.
In high school, we had a Shure bullet microphone and Dumont scope. We looked at a French Horn player’s note on the scope, it had the classical French Horn wave shape, with dominant 2nd harmonic (but because of phase and the other harmonics, it was a much different general shape, and much smoother than the sawtooth violin waveform). But the most revealing part of this study was the French Horn player was so skilled, he could change the timbre to be more like a pure sine wave, no visible distortion. Did not have a spectrum analyzer, nor an FFT then.
the horn player could also play pedal tones (low frequency notes that even most professional players could not).
Bach (oops, back) to amplifiers:
My push pull amplifiers do drive the complete primary. One tube increases by 10mA, while the other tube decreases by 10mA. Both halves of the primary are driven. Yes, it is different than
SE across the whole winding. But the delta 20mA x 1/2 turn(s) = delta 10mA x 1 turn(s).
The distortion is different, but the power is the same.
Larger signal changes complicate this, transconductance and plate resistance changes versus small signal. In push pull, the total change in current no longer unity.
For a push pull transformer, put a resistive load on the secondary. Then if you put a current source on one primary plate lead, and a tube on the other primary plate lead, the driving plate will drive an impedance that is 1/4 of the plate to plate impedance. That is what I was trying to illustrate when one tube cuts off (By cut off, I mean when one plate current is no longer changing, some tubes conduct a small current, but the grid no longer has effective control).
Agreed, loudspeakers are anything but constant impedance.
I have studied the harmonic distortion versus frequency of an amplifier when loaded by a loudspeaker. Yes, that is much different than the same test into a Non-Inductive Resistor load.
Then there is the difference of phase versus frequency. That changes when you use a loudspeaker load, instead of a Non-Inductive load resistor. I have tested that too.
How a push pull amplifier reacts to varying load, and even into a resistive load depends on many factors:
Output stages of pentode and beam power; ultra linear; triode; and triode wired pentodes and triode wired beam power tubes.
The tube curves of these various configurations.
Class A, AB, B.
Global negative feedback
Local negative feedback: cathode windings, UL taps, Schade, etc.
The original Quad electrostatic speaker had a transformer to step up the signal voltage (and a high voltage bias supply to prevent the doubling of every signal that would have otherwise occurred). A step up transformer . . . inductance, distributed capacitance, not to mention the reflected capacitance of the electrostatic panels, that capacitance is multiplied by the step up ratio (makes a tube miller capacitive effect look like a small time player).
The Quad tube amps I remember are classical circuits.
The Quad solid state amp I remember had a feed forward amp for the majority of the power, and a finessed error amp that cancelled (subtracted) the distortion of the feed forward amp.
I think many of us often simplify on this forum. Details often require a book, or even a life study.
I apologize for any oversimplified or misleading statements I may have made.
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I will pursue this a little further, because I have been lucky enough to record some of the great violinists of all time. I'm not interested in those "baroque loonies".
Sometimes we could discuss different aspects of how it works.(one is the oldest musicians in the world today!).
Most don't realise a lot of the sound of the violin is actually being conveyed by resonance of the wood of the bow itself, hence the mystic surrounding the great "french" violin bows and makers such as the Russian Kittel...
What is most interesting for us was the ability to recognise an individual player has largely disappeared.
This is more than a mere curiousity, it's quite a painful constat about tonal signatures and creativity, now, note perfect but now stunted and totally dry of almost all musical expression.
Before, we could instantly recognise in a matter of 1-2 bars of music, if it was, Ricci, Heifetz, Menuhin, Busch, Kogan, Szeryng, Neveu, Szigeti, Huberman, Enescu, Gitlis,Ysaye,Thibaud, Grumiaux, Francescatti, Stern, Oistrakh, Milstein, Kreisler, and that is not all...lots of them had radically different technique.
The astonishing thing, no matter how distorted or low-fi, even poor mono, or bad mp3 copy, we could still recognise them instantly.
It's a sign of the times, with high resolution audio and the narcissm of hi-end or audiophile audio we no longer can! They nearly all sound the same,- the Vengerovs Mutters, Changs all being pointless to listen to.
Having an ear for reproduction, it's true you can really "hear" some characteristic tonal signature of certain valves like the 6V6, when paired with typical output transformers from the "golden age".
Again, because of the way we do audio today, these characteristics have tended to disappear, to the point that a lot of the "hi end" stuff made today sounds boring or plain underwhelming. Note perfect in many cases, but deadly dull.
I'm very interested to read of our friend's experiences with guitars, & TV valves both "tubelab" and "smoking-amp" providing to my mind fascinating insights into possibly why stuff sounds like it does.
NB:-btw.
People often come to my little studio to listen to their recordings, just to see if in fact it was good or not.
Some stuff I could play back to them, makes their hair stand up!
It took me ages, messing about with different elements to get it all to sound as good as that.....as I like to listen to some of the most demanding stuff you can ever get....Cavaille Coll organ recordings.
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