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In Reply to: Re: Hiraga on Feedback posted by Scott Frankland on May 12, 2003 at 16:45:27:
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?
Follow Ups:
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.
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