First, do a literature review.
It's not "may".
And this is what really gets my goat: for goodness sake go and read the existing literature.
The handful of articles I mentioned a few posts ago (most of which are available outside the JAES paywall eg. Gedlee) cover most of the current understanding (Lee and Geddes have published a few more articles since)
It's not "may".
And this is what really gets my goat: for goodness sake go and read the existing literature.
The handful of articles I mentioned a few posts ago (most of which are available outside the JAES paywall eg. Gedlee) cover most of the current understanding (Lee and Geddes have published a few more articles since)
I'm not certain which "may' you object to. That sentence has two.
The first "may" is, I admit, slightly ambiguous as the word has two meanings in English. 'May be" can mean 'could be, I cannot be certain'; it can also mean 'even if it is, the effect is as though it isn't'. So I am saying that the biggest terms are likely (very likely) to be low order.
The second "may" is conditional. It is likely (very likely)that the higher order terms will dominate audibility, but I cannot be certain - that could depend on other things.
The first "may" is, I admit, slightly ambiguous as the word has two meanings in English. 'May be" can mean 'could be, I cannot be certain'; it can also mean 'even if it is, the effect is as though it isn't'. So I am saying that the biggest terms are likely (very likely) to be low order.
The second "may" is conditional. It is likely (very likely)that the higher order terms will dominate audibility, but I cannot be certain - that could depend on other things.
It's not "may".
And this is what really gets my goat: for goodness sake go and read the existing literature.
I thought we were discussing an algebraic expression for the crossover discontinuity of a class A/B output enclosed in a feedback loop (generally a first order integrator for 70's style op-amps and op-amp on steroids power amps) not a survey of distortion and its effects in audio.
Funny you say that considering the long history of self referential articles from certain authors many from some part of the BE.
I think it varies from person to person. Some realise that low order products must at least be there at something like equal strength perhaps, with the view that the higher orders are more audible. Some think that low order products must be at a much lower level than high orders.
No, that's quite wrong. Please look up fourier analysis. Google <harmonics of trapezoidal wave>. You will get numerous hits that explain it quite well that for the first few terms, the amplitude of the harmonics drops similarly to a triangle wave - a 1, 1/3, 1/5 progresion initially (as for a square wave), then after a few terms, a 1, -1/9, 1/25, -1/49 progression, but for a rounded trapezoid, after the first few terms, it drops off much faster. Depending on just what rounding shape you assume affects the fourier expansion, but in practice the amplitude become negligible after only a few more terms.
I take it you agree that cross-over distortion of a sine wave is indeed an inverse phase rounded trapezoid of the same frequncy added to the sinewave? It is visually obvious on paper.
No, wrong again. Ignoring for the moment that some amplifiers don't just simply clip, thay may hang momentarily or be paralysed for a short time, for equal percentage distortion, clipping is far less audible than cross-over distortion. Most techs and engineers know this quite well, as if you play music while watching the output with a CRO, you can see clipping before you can hear it.
In both cases low order products dominate. In both cases, your ear detects the intermodulation products more readily than simple harmonics.
Cross-over is more audibly apparent and more audibly distressing because the probability density function is, much like white noise, maximum at zero crossings, and minimum at maximum displacement. In ?simple? language, you get more information change if the distortion occurs around zero tha if the distortion occurs at the limits of signal excursion.
It is not the case that the ear is more sensitive to high order stuff. Just a very common misconception. Probably due to THD testing having a long history (THD testing goes back to the late 1920's). Since people noticed that for equal percentage result, cross-over sounds worse than other forms of distortion, there must be a reason. It is only comparitively recently (~20 years) that it has been understood that the probability density function of music is the key.
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Just to clarify: I siad that cross-over distortion does not produce more energy (compared to other forms of distortion) in high order harmonics in amplifiers without neg feedback. Neg feedback changes the situation quite a bit, as I explained in a early post.
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No, that is quite right. I am well aware of Fourier analysis - it is the basis of my comments! As you admit, the more rounded it is the faster the terms tail off. That is precisely what I am saying. The sharper it is the slower the terms tail off.Keit said:
It may not be very rounded, and it may be nearer a square wave, and it may be of either polarity. This assumes, of course, the type of 'clean' crossover distortion you see in textbooks. Real life may not be so simple.
No, right again. The two most common causes of waveform kinks in audio systems are crossover ditortion and clipping. I did not claim that they were equally audible, as I am well aware that crossover is more noticeable, so in stating that they are not you are not disagreeing with me.
Crossover is more audible apparent than clipping because of the PDF, despite having a similar spectrum. It is more audibly apparent than other smoother distortions because it is less smooth, and so has more higher order terms than other distortions.
That is the nub of the argument. I think you will find you are in a minority - primarily because the evidence says otherwise. Some higher order terms are known (just from musical considerations) to be particularly unpleasant. Are you suggesting that known discordant notes are due to an adverse PDF rather than an adverse frequency structure?Keit said:
If it came from semiconductors, we can be fairly sure it will be the sum of a bunch of exponentials. An exponential generates an infinite series of harmonics, but they fall off quite fast. The nth harmonic falls off as n factorial. Adding a load of exponentials together does not change this, because addition is linear.
Of course the point about crossover distortion being more bothersome because it occurs near the zero crossing is valid.Keit said:
But I believe the ear is more sensitive to high order distortion than low, if only because of psychoacoustic masking. This is an effect where a quiet tone is made inaudible by a louder one at a nearby frequency. High order distortion products are further in frequency from their fundamentals, so they are masked less. Subjectively, high order distortion sounds like an annoying hash or buzz that rides on top of the signal.
Yes, masking is a real phenomenon apparently. I've never got around to testing for it in some way. It's been on my "to do list" for years. But there's only so many fun things one can do and still have time to eat, sleep, the day job, and keep the Lady happy.
But a number of boffins have written about masking. In this theory, the further away from the primary sound the the distortion artifacts are, the more easily the ear can detect them. So it isn't about the ear being more sensitive to higher order products, it is how far away (in frequency & other factors) they are. If the primary sound is in the upper frequency range, it is then low frequency distortion artifacts that are more easily detected by the ear.
It is reasonable to expect that frequency should be treated logarithmically. If the primary sound (say a voice) is centred on 800 Hz, frequencies of 80 Hz and 8 kHz are presumably equally disturbing. Don't know if I'm entirely confortable with that.
The question perhaps is: Which is the more significant phenomenon, PDF effects or masking? I'll put my money on PDF.
Incidentally, one area where high order distortion products are the main issue is in multichannel carrier telephone systems. This is a now obsolete technology used by phone companies to multiplex anything from a dozen to hundreds or even thousands of phone calls for transmission between telephone exchanges on one common cable. Each call in each direction is modulated by an SSB technique on to a carrier. The carriers are spaced 4 kHz apart. Each channel hears the intermod products arising from the cross modulation of all the other channels. It sounds like white noise - as you would expect from statistics theory. It suggests why distortion in audio sounds like muffling or a sort of buzz.
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I am not too sure about that: it is pretty certain that level can be treated logarithmically, at least within the limits of our biological accuracy which is not great, but the ear is extremely sensitive to the pitch, even the absolute pitch for some individuals.
I think it is quite different.
On the subject, the fact that Xover distortion is most unpleasant is not disputed by anyone (I think).
The reason for unpleasantness is probably caused partly by the spectral profile, but I think that there might also be another reason: a time domain concentration or crowding effect, where all of the harmonics are phased in a such a way as to produce a maximum effect at precise instant: a rogue wave effect.
Think of a clock ticking at one hertz: the spectrum of such a sound is composed of many harmonics, spaced by one hertz. The closest audible ones are already of a very high order: > than 20, at the very least, much more in practice.
Yet, despite the very low level, this characteristic sound is still very audible and recognizable.
Any of the harmonic taken separately is probably below the threshold of audibility, of very near, yet taken together they form something quite audible.
An interesting experiment would be to rearrange all of the harmonics of a ticking clock in a completely random fashion: I bet that the result would be inaudible, or at the very least unrecognizable.
It IS a fact that for many aspects, the ear does treat frequency logarithmically. It follow a biological rule in that regard - all animals sensory systems are logarithmic or super-logarithmic. It's why dogs can detect smells nothing else can yet enjoy rolling in rotten egs.
For instance, our sense of pitch is logarithmic. The equal tempered scale used in modern Western music is based on the 12th root of 2. Each octave is a doubling of the frequency below it. You can't get any more logarithmic than that.
All of us who are lectronics technicians or engineers have played an oscillator thru and amp and speaker, and swept through the audio range. It is readily apparent that the centre of the range, both in amplitude sensitivity and in pitch range, is around 800 to 1000 Hz.
The audio range is considered to be around 15 to 20 Hz to 15,000 to 22,000 Hz depending on whose book you are reading. It is well known though, that telephones and cheap portable radios are made to reproduce 300 to 3500 Hz.
It is well known to the designers of small portable radios, better quality (but not hi fi quality) radios that one aspect of making a pleasant sound is to have a frequncy range balance. That is the ratio of the lowest frequncy to 800 Hz should be the same as the ratio of 800Hz to teh highest frequency. Failure to do that results in people considreing teh sound too "tinny" or too "boomy".
Yes, we've all got that right. Except I had my doubts about DF96.
Doubtfull. The ear is quite insentive to phase, and not very sensitive to timing. The physically arrangment of the inner ear transducer and the encoding system in the auditory nerve pretty much rules it out.
Actaully, it's more complex than that. The Greinar - type instrument used by clockmakers to diagnose troubles and set the rate shows that each clock tick actually comprises a great mess of resonances at various audio frequencies - resonance of the rocking arm, hairspring resonance, etc etc. Each tick is actually three groups of resonances separated by times too short for the ear to distinguish.
The ear is insensitive to phase. Rearanging the harmonics has no audible effect, as each harmonic is detected separately in a different part of the inner ear's cochlea.
There some fundamental reasons why I've never been comfortable with the idea that higher order / higher harmonic distortion products are more audible or should be weighted upwards in distortion measurements in some way.
Most authors that have proposed weighting of harmonics before calculating a total distortion figure end up with very high weighting numbers for harmonics closer to the top end of the audio range.
Yet, althought it is considered that the audio range is from around 20 Hz to 20,000 Hz, if teh ear were an electronic device, we would calling it a tuned circuit. It's peak sensitive is around 2 kHz, and (depending on level) drops off about 6 dB/octave above that, and a bit less than 6 dB/octave below 2 kHz, then rolling off rapidly below about 70 Hz or so.
How can the ear be extra sensitive to high order harmonics or products, when Fletcher & Munsen found that the ear's "gain" is so low for the frequencies involved?
Most authors that have proposed weighting of harmonics before calculating a total distortion figure end up with very high weighting numbers for harmonics closer to the top end of the audio range.
Yet, althought it is considered that the audio range is from around 20 Hz to 20,000 Hz, if teh ear were an electronic device, we would calling it a tuned circuit. It's peak sensitive is around 2 kHz, and (depending on level) drops off about 6 dB/octave above that, and a bit less than 6 dB/octave below 2 kHz, then rolling off rapidly below about 70 Hz or so.
How can the ear be extra sensitive to high order harmonics or products, when Fletcher & Munsen found that the ear's "gain" is so low for the frequencies involved?
Why don't you present what really happens in a bipolar output stage with the logarithmic relationship between Vbe and Ic? BTW transfer functions are multiplicative not additive.
Well, firstly, this thread is about vacuum tube amplifiers, not bipolar transistor amplifiers.
But more importantly, why use a more complicated math approach, when a simpler approach will do the job? Sophisticated math in this forum will turn a lot of people right off.
An the difference, for a sinewave input, between the output of a cross-over distorting amplifier stage and a perfect amplifier IS a rounded trapezoid waveform. That is visually obvious. If not, plot it on graph paper and see. That is, plot the output waveform you get with a logarithmic relationship with Vbe and Ic if you like, or square law as applicable to FETs and vacuum tubes, then graphically take the result from a sinewave. What's left over is a rounded trapezoid. The rounding is a slightly different shape for each device type, but its still a rounded trapezoid.
And that rounded trapezoid is combined with the driving sinwave additively, not multiplicatively. The concept is "what do we have to add or subtract to a perfect sinewave to get what we get?" We don't care what goes on inside the amp - it's what we get at the output.
No, do you agree that the diffrence is a rounded trapezoid or don't you? Yes, or No? If No, why?
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Ish. Sometimes.
See Figure 5 of Hamm, R. O. (1973). Tubes Versus Transistors-is there an Audible Difference. Journal of the audio engineering society, 21(4), 267-273
No, we were discussing blameless tube amps. A very noisy few have wandered off the garden path and into the mathematical brambles. By the way, Geddes & Lee have already done this work (JAES 2013)
You can be certain. Everyone since Masa 1938 has found this to be the case.
Don't need to believe. Plenty of trees have died for this (eg. Bareham @the SAE 1986 reports that -70 dB of 9th and up is audible)
BTW: Probably the best summary of what we do and don't here is in David J M Robinson 2002 "Perceptual model for assessment of coded audio" PhD thesis, University of Essex.
Keith Howard put together a nice summary article back in HiFi news 2005, which was responded to by Geddes & Lee
This is very similar to the line of reasoning used by Crowhurst (1957) in "Some defects" and supported by Steve Temme "Audio Distortion Measurements" 1992 - that is, point non linearities need to be analysed as stand alone signals.
When it's not, it's because the amplifier has a design or component fault. An faults should be corrected before going any further.
Assume a fundamental of 1 kHz played thru a loudspeaker at reasonable volume. the 9th harmonic (9 kHz) is then 70 dB down in sound pressure level. At 9 kHz, the sensitivity of the ear relative to 1 kHz is about 6 to 10 dB down for a healthy young listener. So the 9th harmonic is perceived per 76 to 80 dB down. That's a level you would be battling to hear in a quite room, if that was all that the loudspeaker was emitting, without the fundamental and the amplifier noise.
There's a simple experiment you can do. I've done it and it is very enlightening. Use an oscillator to play a sinewave thru an amplifier at a level corresponding to that needed for a reasonable volume. Load the amplifier not with a speaker but with a L-R network to simulate the loudspeaker impedance to taste. Also run the amplifier output to a THD test set. Run the audio output into a second amplifier and connect the 2nd amplifier to a loudspeaker. The loudspeaker thus just gets the distortion products and not the original sinewave. Adjust the gain so that the THD set and teh 2nd amplifier overal have unity gain. You are now listening to the distortion at the same level you would normally be, but without the 1 kHz fundamental to hide it.
You will find with just about any commercial amplifier made in the last 40 years, tube or transistor, that you can barely hear anything apart from some hiss. A lot of people won't hear anything.
This demonstates the nonsense that a) distortion below 0.03% matters, and b) the ear is sensitive to high order harmonics. You just don't have enough "gain" in human hearing.
Regarding Geddes & Lee:-
I haven't found any evidence that their work has much acceptance among other professionals.
Having said that, the probability density function explantion for cross-over distortion being more audible than other forms of distortion is all very well, but it is programme dependent, and doesn't in itself tell you how to numerically quantify an amplifier's performance. Geddes & Lee's criteria provides such a measure purely dependent on the amplifier transfer curve and independent of the music the amp is used for. It is in that way not incompatible with the PDF theory. It is not the only way that has been proposed. Slotted noise testing has been routinely used in telecommunications for decades.
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If all of the "mess" repeats itself precisely at 1s intervals, the waveform is periodic and purely composed of a fundamental and its harmonics
still on the ticking clock.
If we have a noise duration that lasts 10ms with noiseless period of 990ms and this repeats every second then there can't be a 1Hz fundamental in there.
There is no signal for 990ms and that equals no 1Hz signal.
All the fundamentals and all the harmonics MUST be inside the noisy period of 10ms..
The same applies to crossover distortion.
All the unwanted crossover distortion occurs in a short period around the crossover voltage.
Outside that period crossover distortion is effectively zero.
Other distortions related to the fundamental will be in there, but the low Hz distortions are not the crossover distortions that we are measuring.
If we have a noise duration that lasts 10ms with noiseless period of 990ms and this repeats every second then there can't be a 1Hz fundamental in there.
There is no signal for 990ms and that equals no 1Hz signal.
All the fundamentals and all the harmonics MUST be inside the noisy period of 10ms..
The same applies to crossover distortion.
All the unwanted crossover distortion occurs in a short period around the crossover voltage.
Outside that period crossover distortion is effectively zero.
Other distortions related to the fundamental will be in there, but the low Hz distortions are not the crossover distortions that we are measuring.
Andrew I don't think that is correct. Anything that repeats at 1 sec intervals has a 1Hz fundamental.
If the signal is zero in most of the period time, that only tells you that there are some harmonics in a specific phase and frequency combination that they sum to zero amplitude in that zero level part of the period.
Jan
If the signal is zero in most of the period time, that only tells you that there are some harmonics in a specific phase and frequency combination that they sum to zero amplitude in that zero level part of the period.
Jan
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