Uli Brüggemann's article, "The Second Harmonic Distortion Myth" just published today in AudioXpress (March 2024 issue) is a worthwhile read, in particular by those who still believe high amounts of H2 is the holy grail. He shows mathematically that a circuit that produces second-order harmonic distortion also produces intermodulation distortion. It's pretty well established that IMD is not pleasant to listen to. He also offers some sound samples, including of the distortion residual. Listen and be your own judge.
Tom
Tom
Picking up on the original point of this thread, namely capacitor distortion, here is a quick sim showing the effect of DA
here is the model I used
You can see that if the capacitor is undersized, you will create an AC voltage across the main capacitor which will then result in a higher phase-shifted voltage across the DA capacitor (0.22uF). However, that phase-shifted DA component Vda is coupled back through the 1Meg resistor, so any backfeed component remains very small. If you oversize the cap as recommended by Bateman, Self, et al, the problem - if it exists at all - is negligible. Note I used 100 Hz as the stimulus here, at higher frequencies, the DA voltage at Vda is even smaller.
here is the model I used
You can see that if the capacitor is undersized, you will create an AC voltage across the main capacitor which will then result in a higher phase-shifted voltage across the DA capacitor (0.22uF). However, that phase-shifted DA component Vda is coupled back through the 1Meg resistor, so any backfeed component remains very small. If you oversize the cap as recommended by Bateman, Self, et al, the problem - if it exists at all - is negligible. Note I used 100 Hz as the stimulus here, at higher frequencies, the DA voltage at Vda is even smaller.
Another source with Uli Brüggemann's article:
http://www.acourate.com/freedownload/k2/TheHarmonicDistortionMyth.pdf
Of course any nonlinearity will produce IMD when multiple frequencies are present (and in some cases distortion of the first-order distortion products may become significant). To say otherwise would be a myth, but there should be no such myth. The difficulty humans have hearing 2nd harmonic distortion is a fact of psychoacoustics. It has to do with masking theory and with testing actual humans to find out at what distortion levels an average human starts to notice whatever they may consider to be distorted sounding reproduction. For 2nd harmonic, depending how how its measured, it turns out in addition to masking the brain tends to ignore what it doesn't expect to hear. Moreover, most people don't find very low level distortion to sound like what they consider to be the sound of a distortion (someone may have to be trained to notice the tell-tale clues when very low level distortion is present).
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Except in physical DA the RC ladder network model is not so simple as two-stage lumped approximation. Also someone can contrive a hypothetical approximation to support a desired result.
In amplification devices 2nd and 3rd harmonics are correlated with a DC component and a non-linear fundamental at the point where these occur as they are the result of non-linear transfer functions. The existence of 2nd harmonic predicts some magnitude of AM detection if the fundamental amplitude is modulated in the audio band or well beyond it. Intermodulation is an extension of amplitude modulation detection being called distortion.
Its intuitive,,, peanuts anyone...
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Low 2nd harmonic can be a predictor of low DA artifacts, whereupon psycho acoustic attributes can be falsely attributed to 2nd harmonic. This has to do with using a pure steady state sine wave as the source of testing. In AM receivers there is no sound without AM modulation. In this case the carrier frequency is so high that the modulation frequency can be viewed that audio signals are created from DC shifting. In normal amplification networks using DC correction back to zero volts by way of capacitors, the correction is thereupon subject to DA artifacts as correlated to the magnitude of the 2nd harmonic. From this it can be realized that for networks like moving coil head-amps the DC shifting and the second harmonic can be largely separated whereupon DA artifacts are magnified in relation to the 2nd by subsequent RIAA filtering.
This suggests that there can be a mistake being made between the cause of the psycho-acoustic effects being attributed as suggested solely to the 2nd harmonic, particularly that 2nd harmonic cannot exist on its own without a DC spectral component, seemingly most often ignored. The question becomes as to how the DC component is being handled in the variance of 2nd harmonic psycho-acoustic testing?
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Here is a plot derived from my earlier sim showing the distortion with the DA part switched in and out along with a 3-volt DC offset upon which the 1V signal is superimposed. In short, there is no 2nd, 3rd or any other harmonics. The grass and the stuff at 10 kHz are simulation artifacts. DA is not a distortion-producing mechanism in audio amplifiers. DA cannot smear audio signals because the DA component is orders of magnitude down on the main capacitor and importantly, the associated time constant places any effects it may produce at frequencies well below the audio band.
Imagine a capacitor with an infinite number of floating shells between the plates, all of which in series reaches 470uF. The shells can have infinitely higher capacitance between shells than the total capacitance. This notwithstanding I would be interested to see at what point the distortion is a maximum. In your example is the distortion a maximum when R1 equals R2 and C1 equals C2? This is the more interesting question for me Bonsai.
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That statement makes no sense. Second order harmonic distortion, regardless of how it's measured, results in intermodulation products.
I think you may be conflating harmonic extension and harmonic distortion. They're not the same thing.
[citation needed]
People, on average, prefer lower harmonic distortion. That's clear in the data by Geddes (and others) quoted above. I don't understand why you keep implying otherwise.
Actually, Olive (2003) showed that trained and untrained listeners have the same preferences. The trained listeners are just harder to please.
Ref.: Olive, S.E. (2003). Differences in Performance and Preference of Trained versus Untrained Listeners In Loudspeaker Tests: A Case Study. AES, 114.
Tom
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It would take you a few seconds to set up the simulation.... Then you can play with it to your heart's content.
Tom
That’s not a model of DA though is it? The reason DA is not a problem is the fact that the DA capacitance is a small fraction of the main capacitance and is fed through an effective high resistance. And the voltage appearing across the main capacitor terminals is low (mV).
Suppose you play middle C on a piano, and by some undefined process you also lightly play C above middle C at the same time (the 2nd harmonic). Does it sound like distortion?
Of course if you then run the sum of the frequencies through a nonlinear transfer function then you get IMD as a result. And it may sound like distortion, depending its level.
OTOH, if you only run only middle C through the nonlinear transfer function then you may only get middle C and its 2nd harmonic as the result. Does it sound like distortion?
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No. But that's also not second order harmonic distortion. Hence my comment about harmonic extension.
Tom
In case it wasn't clear the piano note example can be indistinguishable from 2nd harmonic distortion, depending on how you measure. If you do a single tone test of HD then its not necessarily any different from the first piano example. You end up with a fundamental and a 2nd harmonic. That should have been obvious. It doesn't necessarily sound like distortion. That should be obvious too.
Also if listening to real music, if it is simple lounge music or even an operatic aria, so long as it is mainly a single note melody, it is much like the piano analogy (or like a Wes Montgomery guitar melody). You can't tell if the natural note contained some 2nd harmonic, or if it was added by a nonlinearity. Only when there are multiple input frequencies can you potentially hear if there is audible IMD. Also the amount of nonlinearity at the output is dependent on the transfer function and also dependent on the relative levels of the intermodulating input frequencies. IIRC, when the intermodulating input frequency amplitudes are equal then the distortion products are greatest relative to the output level. Anyway, it is a issue of psychoacoustics to say at one extreme 10% 2nd harmonic can be inaudible, yet .01% of some other distortion can be plainly audible. Those are their numbers, where "they" are the psychoacousticians.
Moreover I am not here to defend the claims of psychoacoustics, which I feel are likely clouded by multiple such problems. I also don't trust the reproduction systems they use for some testing of hearing (their systems certainly weren't at today's SOA levels). I don't think they know how to make a really clean system if they are primarily relying on measurements like THD or THD+N. Yet they come up with the numbers they do. And the numbers they come up with are the ones I quote when I want to make a point about the utility or lack thereof of THD or THD+N.
Also if listening to real music, if it is simple lounge music or even an operatic aria, so long as it is mainly a single note melody, it is much like the piano analogy (or like a Wes Montgomery guitar melody). You can't tell if the natural note contained some 2nd harmonic, or if it was added by a nonlinearity. Only when there are multiple input frequencies can you potentially hear if there is audible IMD. Also the amount of nonlinearity at the output is dependent on the transfer function and also dependent on the relative levels of the intermodulating input frequencies. IIRC, when the intermodulating input frequency amplitudes are equal then the distortion products are greatest relative to the output level. Anyway, it is a issue of psychoacoustics to say at one extreme 10% 2nd harmonic can be inaudible, yet .01% of some other distortion can be plainly audible. Those are their numbers, where "they" are the psychoacousticians.
Moreover I am not here to defend the claims of psychoacoustics, which I feel are likely clouded by multiple such problems. I also don't trust the reproduction systems they use for some testing of hearing (their systems certainly weren't at today's SOA levels). I don't think they know how to make a really clean system if they are primarily relying on measurements like THD or THD+N. Yet they come up with the numbers they do. And the numbers they come up with are the ones I quote when I want to make a point about the utility or lack thereof of THD or THD+N.
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Maybe we have vastly different tastes in music, but any music I'm aware of has more than a pure tone playing at any given point in time. Even a single note played on a piano will result in multiple tones. Have a look at the harmonic spectra of various musical instruments and you'll see. Your argument falls apart pretty quickly.
I still maintain that the playback chain should be as close to ideal/transparent as possible. That means output = input, amplified. One measure of that is low harmonic distortion. But that's not the only measure.
Tom
I still maintain that the playback chain should be as close to ideal/transparent as possible. That means output = input, amplified. One measure of that is low harmonic distortion. But that's not the only measure.
Tom
This should be common knowledge on a forum like this but acoustic instruments are not synthesizers so "single" tones have a number of overtones or harmonics.
Here are the typical harmonics of C3 on piano (from https://portlandpianolab.com/the-harmonic-series/).
So a playback chain with only 2nd HD will produce a multitude of IM tones even for this "single" C3 tone.
Here are the typical harmonics of C3 on piano (from https://portlandpianolab.com/the-harmonic-series/).
So a playback chain with only 2nd HD will produce a multitude of IM tones even for this "single" C3 tone.