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For the more technically inclined: Distortion spectrum of SET amplifiers (1 Viewer)

Saurav

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OK, in slightly more layman's terms, based on what I've understood of what's going on so far:
Someone came up with something called an "ideal distortion spectrum". This spectrum has the property of the 3rd harmonic cancelling out the 2nd, the 5th cancelling out the 4th, and so on. By 'cancelling', I believe this talks about a psychoacoustic cancellation, so that even though the final waveform looks pretty distorted on a scope, the human ear isn't able to hear any difference between the distorted waveform and the original pure sinewave tone. Apparently, this was tested at up to 8% distortion at about 400 Hz (I think), which I'm sure most people would agree should be audible.
To put it differently, it appears that it's possible to set up a distortion spectrum that to the human ear sounds like the original pure tone. It also appears that SET amps have a spectrum that is very similar to this "ideal distortion spectrum". So, there might be a scientific reason to what subjectivists have said for a long time, that SETs sound more like the "real thing". So, on the face of things SET amps have higher distortion numbers, but what's possibly more important here is the distribution of that distortion across the different harmonics, not just the total number.
Anyway, the bottomline is, the blanket statement that "tubes have more distortion and SETs have the most among the different tube amp types" is probably too simplistic. This is quite likely another case of not knowing exactly what to measure, driven mostly by our insufficient knowledge of psychoacoustics. I know there are people who believe that we know pretty much all the important things about how human hearing works, but it's possible that some subtle details are still missing. It may turn out that it's the distribution of the distortion across the different harmonics (in other words, the spectrum) that's more important than just the average distortion percentage. As these studies have shown, a band-limited square wave actually came out 'cleaner' after being passed through this distortion spectrum when compared to the original.
And that's about the limit of my understanding of that discussion :)
 

Larry B

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Saurav:
I know there are people who believe that we know pretty much all the important things about how human hearing works,
I have a number of friends who are neurophysiologists (I myself am a neuropharmacologist; close, but no cigar :) ), one of whom studies auditory physiology. I give you my assurance that no one in the field would pretend for even a moment that we have have more than a rudimentary undestanding of the complexities of auditory processing (including both the brainstem and cortical levels).
On a separate note (oops!), you might want to look at some of the work of Vladimir Lamm of Lamm industries (he just changed his name from Vladimir Shushurin) who seems to have a better understanding of the relationship between electronics and hearing than most all others in the field.
Larry
 

chung

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Suarav:
I looked at that thread you posted, and I don't know what the man was talking about:)
Assuming that your understanding of what he wrote is correct. Help me answer a couple of questions:
1. The harmonics of a sinewave increases at different rates, depending on the order of the harmonic, as a function of the amplitude of the sinewave. To illustrate: you double the input level, the second harmonic component goes up 4 times, and the 3rd goes up 8 time, the 4th 16 times, and so on. The ratio of the harmonic terms changes dramatically as the input level changes. How can this "cancellation" or "masking" work over any reasonable range of input signal? Remember music has a large dynamic range; it is not a constant level square wave.
2. You can think of music as composed of a lot of sinuosids with time-varying amplitude and frequencies. When you have multiple sinusoids at the input of the amp, you will have harmonic distortion, as well as intermodulation distortion. The intermodulation products are not harmonically related to the original signal. How can this "cancellation" or "masking" work to suppress the perception of intermodulation products?
There are a lot more questions that one can raise about this theory, but it really does not sound that interesting a theory to me at all. Besides, do you want an amplifier that can create an output that sounds "better" than the original?
 

Saurav

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I think some of your questions were raised in another thread on AA about the same topic.
How can this "cancellation" or "masking" work to suppress the perception of intermodulation products?
I didn't really see anything which said it does :) All I gathered was a theory that a certain harmonic distortion mix could be inaudible to the human ear.
 

Saurav

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BTW, here's the other thread, and I had some of it wrong :)
http://www.audioasylum.com/scripts/t...tubediy&m=9690
To quote:
The "ideal distortion" is described in Feb. and March issues of AudioXpress magazine, an article "Harmony and Distortion", by Jean Hiraga, written in 1981. This "ideal distortion" was found experimentally in 1930 by Wegel and Lane. Later reexamined by Kuriyakawa and Kameoka of Toshiba Labs in the 1960's. In the article, there's Figure 9 and 10 that "shows" that complex signals pass relatively cleanly to the output in the time domain compared to other series of distortions.
The distortions listed are:
2nd: -22 dB
3rd: -25 dB
4th: -30 dB
5th: -37 dB
6th: -46 dB
...
This distortion is about 10% THD and yet it is high fidelity, subjectively. There are lots of even and odd order distortion, something that should seem to wreck a square wave, and it doesn't. The 3rd masks the 2nd, the 4th masks the 3rd, the 5th masks the 4th, and so on.
See, it's 'scientific', not mumbo-jumbo! :)
Jokes apart... this thread does discuss the complexity of real music as compared to a sine/square wave, for instance. Anyway, my point isn't to scientifically prove anything, this is just a pointer to something that I thought was interesting, that's all.
 

chung

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Suarav:

This is taking too much time, but here is what I meant:

The amplifier, whether a SET or a solid state, is described by a transfer function. In other words, output voltage is a function of the input voltage. Most amplifiers are quasi-linear, and the output can be expressed as a polynomial function of the input voltage. This model does not fit amplifiers that have cross-over distortion, or other strongly frequency-dependent distortion, but those are exceptions rather than the norm.

So we can express

Vout=a1*Vin + a2*Vin**2 + a3*Vin**3 + higher order terms.

By the way, a2, a4 and so on contribute to the even harmonics, and a3, a5, etc. the odd harmonics. If you put Vin= Asinwt, and do the expansion, you will find terms of sin2wt, sin3wt, and so on in Vout. These are the harmonic distortion terms. You will find that if the input level (Asinwt) doubles, the 2nd harmonic term will increase by a factor of 4 (due to a2Vin**2) and so on. So the harmonic distortion terms are strong functions of the input level. You can also set Vin=Asinw1t+Bsinw2t to find the intermodulation terms, and convince yourself that those are not harmonically related to the input.

If only a "golden" set of harmonic distortion terms sound "good", I don't see any way a SET amplifier or any amplifier being able to maintain the ratios of those harmonic terms, over the usual dynamic range of the input.
 

Saurav

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If only a "golden" set of harmonic distortion terms sound "good", I don't see any way a SET amplifier or any amplifier being able to maintain the ratios of those harmonic terms, over the usual dynamic range of the input.
OK, that makes more sense now.
As always, thanks for your inputs.
 

chung

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Suarav:

I apologize if I sounded rude. I'm in a hurry to a presentation. The power series expansion is a pretty fundamental concept in understanding distortion, and I would be happy to clarify things later.
 

Saurav

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No problems. Let me think about what you said, I don't remember my Taylor's (or whatever) expansions any more :) I do think that the constant multipliers would be such that the higher power terms would be smaller in magnitude than the fundamental. However, you're talking about maintaining linearity across a range of input values (I think), which is a different thing from driving the amp too hard and into a non-linear region. Also, I don't know why an amp's transfer function would expand in terms of powers of the input, instead of frequency multiples. For instance, trivially, the power series expansion doesn't hold at DC.
In any case, I'm sure this wouldn't hold across a wide dynamic range. And that's normal for any amplifier, THD goes up as signal level goes up. Nevertheless, even if the device could stay within a reasonable tolerance level of this distortion over a reasonable dynamic input range, that's still interesting, to me. To use your term, if a specific "golden" distortion sounds 'perfect', then something close to that would sound 'almost perfect', with the sound getting subjectively worse as one deviates further from that 'golden' (set of) number(s). So, it's not an all-or-nothing situation.
 

chung

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To use your term, if a specific "golden" distortion sounds 'perfect', then something close to that would sound 'almost perfect', with the sound getting subjectively worse as one deviates further from that 'golden' (set of) number(s). So, it's not an all-or-nothing situation.
The point is that those ratios change very fast as the input level changes. The 5th harmonic, for instance, rises as the 5th power of the input level. I just cannot see any way those ratios can be held anywhere close to the "golden" values for music that is dynamic. And what about intermodulation?
 

chung

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sin^2(x)=1/2*(1-cos2x)

sin^3(x)=1/4*(3sinx-sin3x)

So the 2nd order term gives rise to sinusiods at twice the input frequency, hence 2nd harmonic distortion. The 3rd order term leads to sinusiods at 3 times the input frequency, or 3rd harmonic distortion.

In general, if the input is A sinx + B siny, there will be terms at frequencies mx+ny, where m and n are positive and negative integers.

It's hard to design an amplifier that generates -22dB 2nd harmonic distortion over a range of input levels. Again, intermodulation will hurt you in a very bad way, since the products are not harmonically related to the inputs.
 

Saurav

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Again, intermodulation will hurt you in a very bad way, since the products are not harmonically related to the inputs.
Understood. It seems the paper has test data showing that a complex (musical/multi-frequency/whatever) waveform passes through the distortion function relatively unscathed, compared to other combinations of distortion components. Since I haven't seen the paper, that's just hearsay at this point.
 

Saurav

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OK, I exchanged a few emails with Kurt, and he pretty much agreed with what you said. End of story.
 

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