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In Reply to: Re: That's what I was thinking.... posted by Scott Frankland on May 08, 2003 at 14:41:13:
Hi,I'd like to see a device that has no high order harmonics,
and then apply feedback and watch the harmonic multiplication
occur. I think I'll see if I can find a decent model for Cheevers
example that used a TY55N20. Otherwise if any suggestions for
devices that could show this effect are welcome.I like doing this kind of stuff!
Follow Ups:
Why not try Cheever's preferred device, the 45 triode?
Hi Scott,Cheever didn't have much data on the 45. I'll look around
for a 45 model though.I tried the TY55N20 (which is really a MTY55N20) since Cheever
shows data for this. Also figured out how to get SPICE into
hi-rez so that small levels of harmonics could be seen.Ran the device at 3amps with a RL of 10 ohms. Investigated small
changes in feedback..With no feedback, Fundamental was 16.25V. 2nd was 1.19V, a
small amount of 3rd at 1.2mV. 4-6th at 12nV. 7th was 8nV.
The 11th and 13th increased to 250nV. There were higher
harmonics but these were due to Spice step size. Since they
were below 250nV, call it ok. Gain was 85.5.With a 1 Meg feedback resistor, adjusted the bias to get
same voltage swing on output. Gain went down to 84.8.
2nd didn't change much.
3rd went to 1.47mV.
4th/5th increased to 2.2uV/146nV.
6th went down to 97nV.
7th went up to 134nV. Also saw harmonics way out there 1.4K
showing up at levels around 10uV. A spurious tone at
380Hz/430Hz at 29.2uV/99.9uVWith a 200K feedback resistor, adjusted the bias to get
same voltage swing on output. Gain went down to 81.8.
2nd went down to 1.143V.
3rd went up to 6.86mv.
4th/5th increased to 51.4uV/47.8uV.
6th went up to 151nV. 7th stayed at 133nV. Saw some
spurious tones at 330,380,430Hz at 391nV/28.2uV/101uV.With a 20K feedback resistor, adjusted the bias to get
same voltage swing on output. Gain went down to 59.1.
2nd went down to .858v.
3rd went up to 38.0mv.
4th/5th increased to 194mV/131uV.
6th went up to 8.76uV. 7th went up to 624nV. Spurious
tones were similiar.So I'm convinced that small amounts of feedback cause
problems.
Nice work! Just bear in mind that multiplication due to feedback cannot occur unless there is finite open-loop distortion present within the device or circuit. As Baxandall demonstrates in his Dec '78 WW article, feedback acts to recirculate the inherent harmonic products present within the open-loop amplifier. Each circulation intermodulates with the inherent products to produce higher-order products.We know, however, that a linear device produces zero harmonic distortion products (this by definition); a linear device therefore contains no inherent products to modulate; thus feedback around a linear device produces no multiplication. In short, feedback is not the root problem--the root problem is device nonlinearity.
Hello,OK, got it. But then one advantage of feedback isn't really
an advantage (reduces distortion), cause it really is doing a
good job on the 2nd, but not the other harmonics. To get *real*
reduction, you have to apply lots of feedback. Otherwise you are
stuck on top of that hump that Cheever shows in his Fig 2-15.Doesn't using a lot of feedback open a different can of worms -
like phase problems?One side question, is there a link somewhere where I can
order copies of the articles you refer to in WW, like the
Baxandall article.Thanks Scott
Feedback-related phase problems are not necessarily insoluble. In the meantime you might consider an alternative solution: linearize your stages and circuits as much as possible prior to applying feedback. Just be sure to use more than 13dB of feedback!I don't know where to get WW issues except at the University library. Your local public library can order copies through their IL service for a buck or two. You can order AES articles at $5 each from www.aes.org.
Hi Scott,One thing that has me confused is that Hiraga talks about feedback
like small amounts *reduce* higher order distortion. We have seen in
this thread that small amounts of feedback *increase* higher order
distortion.The reprint in the March 2002 audioExpress article, Figure 13(B)
says:"...but to which has been applied a rate of negative feedback of
6db, which is, in effect, very little. Although the distortion
rate has decreased, and although the bandwidth is slightly
widened, one notes an apparent 'compression' of the sound, a
lack of aeration, of refinement (in the high notes). Note that
the harmonics of high order have disappeared, absorbed by the
feedback loop."Now 6db is sitting on the right side of the hump in Cheevers
figure 2-15 which plainly shows that 6db should increase distortion
of high order.How is this contradiction resolved?
Thanks
Don't get me started on that translation, Mike. :- I've noticed a few doozies in there, too. "Absorbed by the feedback"?? I think he means that the high-f's are being effaced by the feedback. Hard to say without comparing it to the French original.There is no question that Cheever's chart is typical. Read through Cheever's math (or should I say Baxandall's math?) and you can see the explanation there, too.
OK. I'll ignore Hiraga.I studied the data from both somewhat...
Took the data from Hiraga and the data from Cheevers graphs.
They do two different things.
If you take a look at the delta between harmonics for Hiraga, the
deltas between the harmonics *increase* with increasing harmonic.
I get:
0-2: 22db
2-3: 4db
3-4: 4db
4-5: 7db
5-6: 9dbIf you take the data from Fig 2-2 of Cheever, the deltas *decrease*
with increasing harmonic. Lifted data from Fig 2-2 I get:0-2: not shown
2-3: 17db
3-4: 14db
4-5: 12db
5-6: 10db
6-7: 11db
7-8: 7db
8-9: 6dbThis relationship is apparent from looking at the graph.
(A side note - at 100Hz the deltas appear uniform).Now, in looking at harmonic patterns due to an unbypassed cathode
(or source) resistor, the harmonics also compress with increasing
frequency like Cheevers data.Do you think that Cheever's Fig 2-2 data is legit? It seems to
resemble what a feedback system should behave like. Hiraga's
pattern OTOH (increase delta with increasing harmonic) may
not duplicate in the real world.
Hiraga's Fig 13b (AudioXpress, Mar 2002) shows the spectrum of a SET amp given simultaneous input signals. Hiraga doesn't say what the frequencies are, just that they are locked as to level and phase. Without more info about the machine he's using it's difficult to say why his results contradict Cheever's (and also Baxandall's and Crowhurst's).Baxandall's math (WW Dec '78) gives the explanation for a single sinewave input and this is the general case. When we increase the number of inputs any number of interactions can occur that will appear as "exceptions to the rule." OTOH I don't think Hiraga has at all proved that his method of testing for the effects of feedback on harmonics shows a general case. Yet on p. 52 he asserts this as fact. He does qualify this, however, when he states that the spectrum shown in for a "low" input level. Perhaps he means very much lower than Cheever's levels? We don't know because Hiraga doesn't tell.
But this is not what Hiraga is after in any case. He actually *wants* all of the high-order products generated by a SET to be fully present in the spectrum. He complains when they are reduced by feedback! The amp now lacks "sparkle and air". Hiraga thus anticipates Cheever's thesis (that an amplifier's spectrum must match the overload pattern of the human ear).
Cheever therefore is not presenting a new thesis so much as trying to *extend* Hiraga's thesis (by deriving a new mathematical criterion for testing amplifiers).
Sorry, I don't think I have it. My second explanation isn't
right either. Hiraga shows this complex tone going thru the
test amp and then he looks at the output.It looks like the setup needs to be as shown in Fig 14.
His claim is that feedback absorbs the high order components
of the *input* waveform???
Hi again,Now, I think I see what Hiraga was saying...
I think the point about his complex waveform generator is that,
he could simulate an entire amplifier with feedback, and he did this
by setting up his complex waveform generator to produce a sine wave
with all the harmonics except for the high order harmonics.This then allowed his conclusion that deliberately excluding high
order harmonics from an amp, makes "an apparent 'compression' of the
sound, a lack of aeration, of refinement". Sounds like wine tasting :)But I still don't understand why 6db of feedback causes less
distortion :(
Hi,Oh. I didn't read this carefully enough. Hiraga isn't talking
about a single pure sinewave, he is talking about a complex waveform
compose of pure seperately contollable parts. I'm glad you caught
that. He is somewhat confusing because his Fig 13(A) and (B) seem
to be showing a pure sinewave and the distortion that the amp
produced from it.I suppose that he must mean that a complex waveform run thru
a feedback loop absorbs high order harmonics of the *input* waveform?If so, this should be a mathematical relationship. We can test
this with Spice.I can create a complex waveform of a bunch of pure tones of various
levels and see if some of the tones get "absorbed". What sort of
complex signal do you think Hiraga is describing?
My guess is that Hiraga used the spectrum of his Fig 12 as the multitone input signal. This is the spectrum produced by the human ear (as revealed by classical masking experiments).On p. 51 Hiraga states that: "Figure 12 graphs the ideal spectrum of distortion, which goes undetected by the ear."
This clearly states that Hiraga believes an amplifier should produce this same spectrum. We ought to take him at his word. This is Cheever's thesis also (but Cheever adds: or no spectrum at all).
There is another inconsistency in Hiraga's article. His Fig 13A shows the spectrum of a single PX4 triode, for which Marconi gives a 4.5W rating at a max rail of 300V. Hiraga's chart shows the spectrum of the PX4 putting out 5W (!) so this is evidently the clipping spectrum. If not, it is certainly at the threshold of clipping.Now, in his Fig 14 Hiraga states that "the majority of negative feedback loops has (sic) an unfortunate tendency to absorb the high harmonic orders, with a low level of applied audio signal." But the Fig 13A spectrum of the PX4 is clearly *not* operating at a low level so how are we to interpret Hiraga's statement? It causes me to question whether the signal level in his corresponding Fig 13B (his paradigm feedback case) is low or high?! Hiraga states that Fig 13B is for "the same amplifier" but he does not state whether it is for the same *level*.
It is well known that if you operate a triode at clipping with feedback you are going to get a spectrum that extends far beyond that shown in Fig 13A. This regardless of how many input signals you feed it in tandem. Although we can cancel harmonics we cannot prevent clipping, and the flattening of a waveform at clipping is *caused* by high-order harmonics.
My conclusion is that Hiraga fails in this particular article to account for the effect of negative feedback on the harmonic spectrum of amplifiers. OTOH, his thesis that the ear does not notice certain patterns of distortion that correspond to our innate hearing distortion is something I'm still investigating. If it's true that's a powerful argument in favor of SET amplifiers.
Hiraga also states (p. 50) that Wegel and Lane's measuring equipment does not extend beyond 2000Hz. This is incorrect, as can be verified in E.C. Wente, “A Condenser Transmitter as a Uniformly Sensitive Instrument for the Absolute Measurement of Sound Intensity,” Phys. Rev., 10:1, Jul 1917. But this is a minor historical point.
Hi,I've kind of dismissed Hiraga on feedback, I agree with you,
his points about thresholds are very worthwhile however.An AHA for me lately has been this. Accept that certain distortion
patterns are invisible to the ear for a moment.Now pick which pattern is invisible - either Cheevers or Hiragas
(although Hiraga doesn't really tell you what to do out beyond the
musically consonant 6th :(The theory that I'm starting to test is this: if the closed
loop distortion behavior of your device *with feedback* is below
the threshold of either of these patterns, then your device should
sound neutral.I know that both Cheever and Hiraga would say that you should try
and *match* their pattern. Cheevers original data - Fig 2.2
(wherever it comes from) and not Cheever, suggest that by staying
below the thresholds given in the diagram, you will be neutral.I hope this is the case - then all we have to do is remain below the
thresholds and not try to match them. That is a lot easier than
trying to curve fit a distortion pattern to one of the diagrams at
all frequencies and levels.This implies then that *open loop*, you need to have a device that
has a distortion pattern that falls off faster then what is indicated
by the Fig 2.2 data. This way when you close the feedback loop, the
resulting distortion pattern will be below the threshold and thus
below the threshold of audibility.If you use a device that has worse *open loop* performance then the
Fig 2.2 data, then you are already in trouble by the time you close
the feedback loop. Now you have need to spend your time disguising
your distortions other ways.Thoughts on this? Is it obvious to the most casual observer or
completely goofy?
Mfc wonders whether we can hear amplifier harmonics that are below the masking threshold of the ear's pattern of self-distortion. Clearly Cheever needs the amplifier spectrum to fit the ear's self-distortion pattern in order to justify his mathematical criterion, the TAD deviation. This leaves a huge gray area between zero harmonics and a perfect fit, which is where mfc's thesis comes in. If mfc is correct, then Cheever's criterion starts to look pretty sloppy: his criterion evidently cannot distinguish between an amplifier with a perfect fit and an amplifier with no harmonics at all.
Hi,Cheever's equation must break down for harmonics like the 8th
(3 octaves), the 10th (3 octaves + major 3rd), and the
12th (3 octave + 5th). These harmonics are very consonant and
also very much in tune (although the 10th is slightly out).His equation would state that leaving them out is best, but they
should introduce very little bad effects. I see them playing a
role in neutralizing their nearest odd neighbor. The even harmonics
should be given a different weighting then the odd harmonics.As you say, the whole equation doesn't seem right. In the limit,
as distortion goes to zero, I calculate a TAD figure of 19
(1+1+1...+1). However if the harmonics match the level given in
equation 2-1 (ear threshold), then the TAD figure is 0. This seems
a little off.
MFC, you are on a roll. You are actually contributing to the 'art' . Keep up the good work. Send me your e-mail address if you want anything from me on this subject, or others It is: j_curl@earthlink.net
Thanks for hanging out in this forum. I appreciate the
opportunity to chat with people like you and Scott. Please
see this link below. The depth of this thread was starting
to get me dizzy trying to find things.
Mike, you make a good point about the even-order harmonics. But you are merely perfecting Cheever's weighting system! :- I think Cheever is onto something interesting here, but I also think he is only half right (about which, more later).One of the things Cheever insists on is a perfect fit to the ear's self-distortion. He insists on this because: (1) "the aural harmonics do not fall off at the same slope either by harmonic number or linearly with decreasing sound pressure levels" (p. 41); and (2) the IM products will become audible. Cheever makes his criterion cover IM products when he states: "Therefore the same TAD figure of merit quantifies the audio reproductions devices' audible IM distortion." (pp. 49-52) So to correlate IM products with masking, curve-fitting is evidently mandatory.
That is a good point. If the ear is creating masking IM distortion, then the position of the IM tone may not make it more sensitive, except for 'triple-beats' which are IM distortion products that are twice the level of normal beat frequencies. Can you imagine a 'triple-beat' generated from a 7th harmonic related nonlinearity? There is so much to know and understand.
I would also like to point out that most distortion comes from the active devices. In this case, bipolar transistor are the worst, fet's are second, and tubes are the best (in general). Usually the harmonic series generated by the devices falls off at a predicted rate. I have found it almost impossible to make much more than 3'rd (maybe 5th) harmonic in a tube circuit. It is the same with the best fet based circuits. Transistors, however, make a whole range of harmonics, and you must take extreme care, if you want the higher order harmonics to be reduced to almost nothing.
I might throw this in: Music is composed of multiple tones that generate IM as well as harmonic distortion. These simple tone tests that use only ONE major tone will be incorrect in what level is actually masked, because the IM tones can be anywhere. However, before everyone gets excited, it should be noted that musical chords IM in tune with the other notes. How about that? This could provide a further argument that higher order odd harmonics could be heard, even below the so called 'masking level' because the IM byproducts would make them accessable to the the ear.
Hi,An example of what you mean by "it should be noted that musical
chords IM in tune with the other notes." I'm not following you.The reason you lost me is because IM is a beat frequency with a
string of harmonics. These harmonics are multiples of the beat
frequency. Since we have seen that harmonics of a fundamental are
out of tune with their nearest note neighbors, why would IM
harmonics be in tune with their note neighbors?
Yes, there is a whole lotta blending goin' on. I agree that the single-tone case lacks precision when applied to the multitone case, but in its favor the single-tone case allows us to get a grip on the fundamentals.Besides bringing out strident intervals it's also possible for musical IM to *mask* them. To quote myself again: "The blending effect can be easily tested with a guitar. For example, playing F (below open E) together with open E causes objectionable beating. Adding an A intermediate to the two tones smoothes out the subjective effect considerably. The interval of F with E is a major seventh (8:15). Adding the A, however, creates two new intervals: a major third (4:5) and a perfect fifth (2:3). The two consonant intervals then "swamp out" the one dissonant interval to create an overall composite consonance. The critical parameter for composite consonance is thus not masking, but blending."
I am saying here what you are saying, John, that even a slight out of tune or out of phase resonance or IM can throw off an otherwise consonant blend of sounds. The masking effect is a small part of this equation, which equation I think is far more complicated than Cheever makes it out to be. Consonance or dissonance are the result of the composite waveform as it strikes the ear, and this includes room effects.
There is a paper in the AES preprint 'INTERMODULATION DISTORTION IN TAPE RECORDING' Robert Z Langevin, Ampex Oct . 1962. This paper shows that the IM generated by the same non-linearity as that that produces either 2'nd or 3'rd harmonic distortion will still be coincident to the music being played. Basically, if the order of harmonic distortion is low, the IM products will generally be OK in the musical selection. It would seem to me that higher order IM products would be just as bad as higher order harmonic products, but even more obvious in many cases.
John, I think you are right. I'm just pointing out a counterinstance. Although it *is* possible to mask high-order distortion via specific modes of IM blending (as my guitar experiment will show), it is also more unlikely to happen during music program. Cheers.
Scott, or anyone else, if you want a copy of the Langevin IM paper, I can send it by e-mail. Just send me your e-mail address to: j_curl@earthlink.net Unfortunately, without a website, I can't link it here.
Mfc, don't take this stuff too literally. If we are talking about ONE idealized device, like a pretty darn good triode, then the question of local vs loop feedback can be important. However, almost all devices deviate from the ideal, and have inherent higher order distortion that will actually change with frequency. Also, multiple stages will multiply the distortion up as well. Negative feedback, either local or loop is often very useful to get the best result.
Hi,I should clarify the previous message. We want to use devices
that have a harmonic pattern that falls off more rapidly than what
the Cheever data or the Hiraga data would indicate is neccessary.
This allows some headroom so that when applying feedback, the
increase in high order harmonics are still below these thresholds.I didn't mean to imply that all devices automatically are linear
enough that open loop, their harmonics fall off rapidly.
Hi,I don't really think I've ever found any written material that
has explored these particular intricacies of feedback.
I've learned a lot about feedback since this thread started.
Let me give my explanation as to why feedback may be successfully
applied. I'll ignore other uses of feedback. Just two cases I'll
consider.First is the case of lots of feedback - more than 13 db. Here we
are on the left side of the hump in Cheevers Fig 2-15. Higher order
distortion is starting to go down. Need to be careful of stability
and make sure we have enough gain. Watch out for overload. Also
check the Cheever or Hiraga data to make sure we don't exceed the
masking thresholds of these harmonics.Second is the case of applying a small amount of feedback
- less than 13db. This acts to raise higher order distortion.
Can't be avoided, no purlely linear devices, and it is purely
mathmatics as to why this happens. Can it be bad? Depends. If the
resulting harmonic structure is above the masking effects of the
ear/brain, then yes it is bad. This is where a graph like the
Cheever data or the Hiraga data yields an explanatin as to
why this isn't such a bad thing.I got another AHA out of this: Open loop devices have harmonic
patterns which fall off much more rapidly then the Cheever or
Hiraga data would indicate is neccessary. This means that we can
tolerate small amounts of higher level distortion introduced by
small levels of feedback until it exceeds the masking level of
the ear/brain.
I'm not sure why Hiraga considers it a bad thing that the high-order products are reduced by feedback (which, according to his test procedure, they seem to be). Let me read over his article some.
I'm glad to note that we are discussing something useful to audio designers. In reality, we usually still have to use both local and loop feedback, but it is not as easy to decide which or how much, as some would think. ;-) For example, if you take mosfets, jfets and perhaps tubes, and then make a differential pair from them, you completely change the distortion. It goes from 2'nd with a little 3'rd (probably expansive) to almost pure compressive 3'rd. Is this good? Is this bad? Are the advantages of direct coupling, total distortion reduction, bias stability, etc, etc worth the change in the harmonic series? This is what real analog designers wrestle with every day, and why many tube designs stay single ended at the input stage.
WW is tough to get, but contact me first, if you need something. I might be able to help. The very BEST AES bargain is the CD rom collection of almost everything for about $400. I have it and love it, especially the stuff published 20 years ago and more.
Hi John,I can almost hear several violin or piano makers discussing this
subject 2 or 3 centuries ago. Not that they would be talking about
feedback, but they would have terms for 2nd, 3rds, overtones. They
would be discussing how sound changes from dull to bright, attacks
and decays, what produces rich tone and how to alter the tonal picture.Maybe your answer lies partly in looking way back, before electronics,
at how the designers back then plied their trade in making the best
sounding instruments they could.I can imagine today that these solutions would involve partly
electronic, partly mechanical (eliminate vibration???), and a lot
of subjective evaluations.I wonder about the first people who believed that a piano string
should be struck in a position giving the minimum amount of 7th
harmonic possible. If the makers of these fine instruments were
aware of this (without even knowing what it was), what other nuggets
lie waiting to be uncovered and applied to our latest technology.This reference shows a (perhaps) deeper look into the relationship
between the 7th and the fundamental and how it varies with frequency.
The way I read this is that more 7th can be tolerated at higher
frequencies.Also interesting is the reality that their is an initial pulse
down the string. How does an amp best capture these sorts of attacks,
since they are very important to the "pianoness" of the sound.You mention the 3rd harmonic as being compressive or expansive.
These aren't terms I'm familiar with. Care to elaborate?Thanks
Compressive third harmonic is when the 3 rd harmonic is phased to REDUCE the amplitude of the top of the sine wave. This is the normal third harmonic generated by analog tape compression, etc. Expansive third can actually cancel compressive 3'rd, so it is interesting for this reason. It is more difficult to generate. Thanks for the input on the piano, and good reading of that 2/3 of a century old book that I recommended. I think that you will like it.
Hi,I received the book from Amazon. That is one of the first "physics
of music" type books worth getting...and its less than $10 :)They even had subjectivist/objectivist debates back then. Page 181
discusses whether a tune played in the key of C major sounds any
brighter when played in the key of G. Great discussion! Lots of
them in this book.Thanks for the recommendation
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