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When I was reading the posts concerning Cheever's Thesis I found a intresting post by John Curl and it would be intresting to get some additional info on this subjekt;http://www.audioasylum.com/forums/prophead/messages/2907.html
"It is also interesting that a bipolar transistor's inherent 3rd harmonic distortion can be CANCELLED by using local feedback exactly 1/2 of 1/gm of the device at idle. This turns out to be 13 ohms for a bipolar transistor operating at 1 ma. This scales with current."
Now to my question to John Curl (or anybody else who knows):
Do you have any papers, articels or personal explanition to this. (Why? and What?)I know that this coresponds to the dip in distortion wersus feedback plot. (Fig 2 in Baxandalls article Audio Power Amplifier Design pt6
(WW feb 78)) But why?Enjoy / MAD MAN HARJU
(PS You hawe to exuse me for my bad spelling and grammar, but I'm not used to write in english)
Follow Ups:
I must say I found the uncritically positive commentary on Cheever’s thesis on this forum more disappointing than interesting
this paper quickly mentions 2nd and 3rd harmonic cancellation (and is sure to annoy believers in the evils of feedback by repeating the 50+ yr old theoretical result that the most effective distortion reduction mechanism is global feedback)
I didn’t see this post until now.. But better late than never...“I must say I found the uncritically positive commentary on Cheever’s thesis on this forum more disappointing than interesting”
I’ve read the tread about Cheever’s thesis. Starting with:
“OK, all you hi-RPM propellerheads...........”
http://www.audioasylum.com/forums/prophead/messages/2816.htmlAnd my impression is that most of the “positive” commentary just says that it’s GOOD that somebody brings the subject up and tries to bring some order to it. I don’t fully agree with Cheever and I don’t think there are many people here who think that we should fit the distortion of our systems to the ears aural distortion.
(Almost Maybe…… NONE!!! I would think. But I can’t be sure)
BUT instead there might just be a rather big crowd who have the opinion that higher harmonics have to fall of FASTER than the ears aural distortion and the total distortion have to be as low as possible without conflicting with the listening impressions. Our ear’s has to have the last word, and we have these opinions based on our experience.
“this paper quickly mentions 2nd and 3rd harmonic cancellation”
I’ve read this paper you are referring to and several others written by Lantz and to be blunt I just find them purely mathematical, theoretical AND boring.
“(and is sure to annoy believers in the evils of feedback by repeating the 50+ yr old theoretical result that the most effective distortion reduction mechanism is global feedback)”
I would like to emphasise on the “theoretical result” part because that is what IT is.
Again this is just a theoretical result, with very little to do REAL listening impressions regarding to audio. But that is maybe the reason to why Lantz seem to have chosen to work with such a UNCRITICAL application as telephones and co-wrote this specific paper with a representative from Sweden’s biggest telephone company.
!
It’s a really impressive list of merits, I do agree.
But when I glanced through the award list I could only find one post with a little direct connection to audio:“”James Flanagan (1996) For bringing engineering techniques and speech science together to solve basic problems in speech communication. ””
I never said that telecom employment was an indicator of mediocrity (YOU DID), but telephone communication as such is an uncritical application. And very often the intention from the telecom companies is something like “How cheap can we do this without people losing the ability to understand each other over the phones” or something like that when we are talking about telephone communication.And I’m actually referring to a couple of papers from Bell Labs in my thesis….
Again this is just a theoretical result, with very little to do REAL listening impressions regarding to audio.The application of theoretical results and the use of users' listening experience need not be mutually exclusive though. For example, controlled listening tests have shown that high-order harmonics are annoying to the listener. As a result, one might choose some weighting factor to apply to the distortion as a best estimate of the degree of subjective annoyance to the listener. As an estimate, one might assume that minimizing this weighted distortion might minimize the annoyance a listener might experience. This could then be used to establish one or more design goals.
But once the design goals are established in a concrete way, the manner in which these goals are achieved could be (and should be, I think) purely objective, based on theoretical analysis or simulation or a combination of both.
In other words, there are two babies that could be thrown out with the bathwater. A design based on purely objective criteria risks ignoring scientifically demonstrated data that shows what kind of design defects annoy listeners most. A design based on purely subjective criteria will almost certainly neglect a large body of knowledge that can be used to optimize circuit performance. Certainly some of this knowledge is contained in articles that don't exactly give one a woody from reading them :-). But by ignoring them just because they don't, one might just be limiting the number of useful tools in the toolbox of available ideas.
“Certainly some of this knowledge is contained in articles that don't exactly give one a woody from reading them :-).”This is sooo true, but the articles and papers should at least be interesting in an engineering point of view ;-).
“But by ignoring them just because they don't, one might just be limiting the number of useful tools in the toolbox of available ideas. “I don’t ignore them but many of the “High feedback is good (And sometimes God)” and “If it can’t be measured it can’t be heard” type of guys really ignore the “subjective annoyance to the listener” we encounter.
You raise an interesting point about the differing views of designers regarding audible and measurable differences. Let's look at this another way. Suppose some person is a designer and he believes it's possible for audible differences between power amplifiers to exist without there being any measurable difference between them. You might think this would make him a better designer than someone who thought otherwise.But consider this hypothetical situation, just for the sake of argument. It's a little far-fetched, so bear with me. Suppose we have two amplifiers A and B, and for some reason we don't know, and cannot know the difference between them from a design point of view. We've subjected each amplifier to a barrage of tests, measuring everything we know how to measure. They both measure the same, within the tolerance of the measurement equipment, for every parameter we test. Now suppose a controlled, scientific listening test is performed, and we find that users can indeed determine the difference in sound between the two. But not only that, the listeners can determine that amplifier A is audibly superior to amplifier B.
How can we make use of this information? If we're just buying amplifiers, the answer is easy! Just buy amplifier A. But if we are the designer of amplifier B, we can't make amplifier B sound as good as amplifier A except by random experimentation, which is probably unlikely to succeed. If we can't relate the proven audible superiority of amplifier A to a measurable parameter P, we have no way of, say, studying how to improve on P without sacrificing the performance according to other parameters. So despite our belief that audible differences might not be measurable, and the proven occurrence of this event, we're still no better off than when we started.
So while having the view that it's possible for audible differences to exist without any measurable differences might make a designer appear very open-minded, there really is little practical application of such a view. I suppose that one could accept the design technique of random experimentation to be valid to some extent. But the ultimate expression of that technique is, as one poster on DIYAudio.com stated, equivalent to "an infinite number of monkeys with soldering irons".
[ So while having the view that it's possible for audible differences to exist without any measurable differences might make a designer appear very open-minded, there really is little practical application of such a view. I suppose that one could accept the design technique of random experimentation to be valid to some extent. ]Good designers deal with the 'unmeasurable' in as scientific a manner as possible, using their experience, the experience of others they trust, and logical and controlled experimentation to achieve their goals.
Not exactly the same as the monkeys, nor as worthless.
Why must such an approach (forced upon us due to the total lack of correlation between the traditional measurement suite, and how things listen) be taken as if it has no value? The ancient alchemist who developed gunpowder didn't have to be a chemical engineer and known the periodic table or atomic weights to develop a good mixture, he just had to take good notes and proceed methodically. As far as he was concerned, it WAS magic! However, some magic worked better than others, and if he bothered to notice, then progress was still made, and more satisfying explosions occured.
Here we have trained and educated engineers struggling to push the home playback SOTA, and simple THD just doesn't cut it. So they try the Black Gate caps, the tantalum resistors, even the silver wires. Bottom line is that EVERYONE still has to LISTEN to it to evaluate it. Some folks listen better than others, and have more experience listening. Some even achieve those incremental improvements despite the lack of measurement correlation. Nothing wrong with that.
Good post.I don’t disagree with you really. We are maybe talking about semantics.
“”Suppose some person is a designer and he believes it's possible for audible differences between power amplifiers to exist without there being any measurable difference between them. You might think this would make him a better designer than someone who thought otherwise.””
YEEP! And why?
Because he probably have made a lot of listening tests alongside with the electrical distortion measurements he also made. I have great respect to guys like John Curl and his likes with a lot of years of experience regarding audio amplifier design.
“”measuring everything we know how to measure””
This is actually one of my main points. Do we know how to measure the audible differences we experience? Are we really measuring the right things? Suppose again that we have two amplifiers A and B and both measure the same when measured with a purely resistive load with ordinary THD measurements and two tone IM measurements.
But the designer of amplifier A have also made measurements with LCR networks that simulate the overall impedance of real loads and also with real loudspeakers. And he has also made measurements with multitone test signals (witch actually resembles a real music signal much better than a single sinus tone, because the probability density functions are more like each other). And above that also made a lot of listening during the design process. The designer have adjusted his design according to this.
Meanwhile designer of amplifier B have only made ordinary THD measurements and two tone IM measurements with a purely resistive load.
And suppose that at a scientific listening test the listeners can determine that amplifier A is audibly superior to amplifier B, then I believe that there are differences when we start to do the extensive tests made to amplifier A.
My point is that we maybe are doing the wrong tests and because of that can’t see the differences experienced during listening. How many manufacturers have you seen that provide these extended measurements?
Sometimes (and especially with revivers) there are a expectance effect saying that the more expensive amplifier should be better, BUT as an designer/manufacturer you really want the cheaper solution to be the better to be able to compete on better terms.
“”So while having the view that it's possible for audible differences to exist without any measurable differences might make a designer appear very open-minded, there really is little practical application of such a view. “”
Experience my friend, experience. That is very important because a skilled designer (In my book) have learnt trough the years that audible differences may exist without any measurable differences, and adjusted his design according to this. But someday we might find a solution to this and learn how to measure the differences.
It is difficult for me to understand why there is so much debate about THD and whether we can ever measure all that we can hear.
First, THD is a simple test that normally only nominally challenges the component under test. This is especially true with 1KHz THD. However, it can be detected by instrumentation at very low levels (120-140dB below the test tone), because it is so easy to null the fundamental frequency and only look at the residual. Even noise and specific harmonics can be seen by FFT processing the residual of the THD analyzer
The problems with THD are:
1. There is no single number that is meaningful, except for a particular piece of equipment, such as a tube preamp. This is because the higher order odd harmonics are FAR more significant than the lower order harmonics, such as 2nd and 3rd harmonic. Without a very steep weighting applied to the harmonics, the measured result is usually misleading.
Usually, people just give a single number for a given component such as an IC and this is mostly useless.
2. Noise will dominate the test at normal working levels for a component. This is because of the wide bandwidth (80KHz in my analyzer) and the distortion can hide in the noise. Only spectrum analysis or FFT averaging can remove this noise. Then crossover distortion artifacts can be seen in IC's, etc.
3. The test is too easy to really stress the component under test. It doesn't give the wide range of change in input that music will do, including risetime, IM, change in music level, and problems at frequency extremes. It also isn't sensitive to FM distortion that we have already shown can be generated by application of negative feedback.
Knowing the limitations of harmonic distortion, it can still be a very useful tool, IF you compensate for its limitations with subsequent spectrum analysis and spectral weighting.
It is true that the results may appear to be too low in level to be audible, but if higher order distortion is detected, this implies that multitone IM, and real music inputs will produce significantly higher distortion levels than measured by the harmonic method.
To save time and energy. ;-) I define 'IC' in this case as integrated circuit.
"Do we know how to measure the audible differences we experience?"Certainly, if by "audible" you exclude the imaginary.
Now, that doesn't mean that people can't throw out straw men like the ones you posit ("well, if you do an incomplete measurement suite, it's... ummmm... incomplete!"), or that people can't stand logic on its head and claim that they hear differences even when a simple controlled listening test refutes that belief. But then, Sylvia Browne sells a lot of books, too.
We know our measurements are sufficient, because listening tests don't show a difference.We know our listening tests work because there is no measurable difference.
Unfortunately, if it turns out that the listening tests are insufficient or unrepresentative, then the whole house falls down.
As far as I know, there is zero evidence to support the idea that THD and 20Hz-20kHz response measurements ever correctly described "goodness" in an audio component, yet they seem to have become "accepted" as scientifically valid.
30 years ago, Hiraga's asymmetrical tone tests showed wild differences in amplifiers that had similar FR and THD. He also showed that these test tones were much more representative of real music, and much more predictive of the subjective result.
Why did mainstream (not hi-end) audio ENGINEERS not adopt these clearly more stringent tests? The main reason is the dirty little secret of consumer product engineering:
Design goals are NOT driven by considerations of engineering excellence, they are driven by marketing requirements for specifications that can be printed on the box. THD and RMS power numbers became important SOLELY because they supported product differentiation in the marketplace (and because govt. regulation insisted on a uniform presentation of these claims, to avoid "music power" fraud).
Peter
Straw man, coming from (I'd guess, have no way of knowing) too much time reading popular magazines and not enough time reading professional journals and texts.I've known quite a few audio engineers working in all segments of the industry (from mass market to mid-level to high end) and I've never met one who said that THD alone is a suffient measurement. Necessary, yes, but not sufficient. Can you please name one reference in an engineering journal or text which says such a silly thing?
You misunderstood my point.Engineers working on consumer electronics do not, in general, have a free hand to seek optimum subjective performance. They are designing to a spec derived from market segmentation studies and focus groups. If the Marketing dept. calls for an amp with 100W/ch and less than 0.001% THD, that's what they get. Sound quality is secondary. Obviously, a good engineer will try to design for better sound quality within the design guidelines, but it is a secondary consideration. If the sound quality is inconsistent with the design spec, the design spec will win.
The engineering deliverable is then to deliver a product at minimum cost that meets the desired performance target, AND NO MORE. This is the essence of many of Soundmind's posts; once you reach the agreed-upon limit of audibility, any further improvement is wasteful. In many contexts, that is the right and proper answer.Simple example: When I was at Engineering School 25 years ago, part of the reason for studying things like component MTBF was to be able to predict failures rates of complex systems. One of the applications was realte these failures to warranty periods and claims. In other words, we were being taught how to design things that were just good enough, rather than the best possible. In price-sensitive markets, this is unavoidable.
Most of the large consumer electronics companies have demonstrated that they can build great-sounding gear; much of the time they simply choose not to.
Obviously, people designing high-end audio equipment are operating from a different design brief; one in which ultimate SUBJECTIVE performance is the goal. The THD number has been replaced by the subjective experience as the design spec.
Why did I bring this up? There are continual references here to mainstream engineers as if they are somehow closer to God than humble high-end audio designers. The commercial reality is a little different. They are trained in a just-good-enough mindset.
There are certainly plenty of engineers working in environments where maximum absolute performance is the goal, but not all of them.
And yes, I do read things like the AES journal, blah blah blah....
"Engineers working on consumer electronics do not, in general, have a free hand to seek optimum subjective performance."If by "subjective performance" you mean "testing with a lack of controls", then yes, that's often right. But mainstream manufacturers do a lot of controlled listening tests- go visit someone like Harman.
"If the Marketing dept. calls for an amp with 100W/ch and less than 0.001% THD, that's what they get."
Product specs that I've seen have a lot more than that going on. Can you provide an example of an actual marketing spec (as opposed to an anecdote) as narrow as what you're positing?
You are missing the main point...
Enjoy Creating / Mad Man Harju
What's the main point? That THD alone is not a sufficient guarantee of amplifier inaudibility? No one argues that it is.That "mainstream manufacturers" don't do dat voodoo dat yoodoo? No one argues that either.
“”("well, if you do an incomplete measurement suite, it's... ummmm... incomplete!")””“”...I've never met one who said that THD alone is a suffient measurement. Necessary, yes, but not sufficient.””
THD is worthless in telling us how a part of equipment sounds.
I’ll repeat to clarify: WORTHLESS!!!!!!!!!!Let’s look at this in a historical perspective, with a twist:
It was not that many years ago when you so called objectivists did say that THD was the only thing needed to measure and if two amplifiers had the same THD reading they sounded the same…
But when we showed that the amplifiers had different IM readings, the objectivists first argued but did after a while agree that the IM readings made a difference when they where overwhelmed with evidence. But the order of harmonics did still not mater.
But after controlled listening tests that have shown that high-order harmonics are annoying to the listener, the objectivists did say that the order of harmonics made a difference, but only after first arguing against it for a long time. BUT only if the harmonics where high enough in level AND they did absolutely not have any effect at the low levels we were talking about. AND of course they only had effect in the audio band.
Then we showed that high frequency stress in an amplifier caused audible and measurable effects, the objectivists did say that SID made a difference, but again only after first arguing against it for a long time.
With that we are somewhere at present time and despite that we have shown that harmonics are more and more annoying as the order rises and that the number of IM products rises to enormous amounts when exposed to multitone test signals (Witch AGAIN for the record, resembles music much more than a single or dual tone) and the Total InterModulation Distortion (TIMD) rises to much higher levels than with a single tone.
You still argue that the levels are too low to be heard WITHOUT providing any proof, you just say it can’t be heard … … … Show me the evidence to that.
There is loot of more examples of this, with one of the more obvious being the loudspeaker connected to the amplifier, but you can check that out in another post in this tread.
I believe that education and EXPERIENCE combine to make the best estimations as to what is important to audio, and that you have to trust your ears when designing something that in the end is going to be evaluated by the listeners ears and hearing. And if that then includes partly to alter your design without be able to show measurable effects with the measuring tools we have today but only audible effects, may it be so then.
And I fully agree to what Jon Risch said:
“”Good designers deal with the 'unmeasurable' in as scientific a manner as possible, using their experience, the experience of others they trust, and logical and controlled experimentation to achieve their goals.””And I have to say a last thing about listening tests: It’s very difficult to hear differences when you have to make decisions at the moment. I have experience of that myself with one pre-amp prototype I made, at first I could not hear any difference between it and the earlier version (also my own design witch I had listened to for a month). But after two weeks of just listening without the need to make any decisions about the sound I realised that I preferred the earlier version, but I could still not pinpoint down what the differences was. So back to the drawing table again…
Now why shold it come as a surprise to anyone that you could null out thrid harmonic distortion by using just the right amount of negative feedback? And by nesting feedback loops, you can null out other harmonics as well. An exceptionally powerful tool when properly used for improving amplifier performance. (I know I'm probably one of the only ones here who thinks negative feedback is one of the greatest inventions since sliced bread but that's the way I learned it 35 years ago and is still seems to me to be right on target.)
To me it's no surprise that harmonic distortion can be nulled out.
But I have not found any good expanation to why it does so.The texts I'we found to this point only says that "design like this and you can null out certan harmonics..." no explanation to how it works for real and why? Thats what I'm hoping to get now...
Patience, Rolf. Not all will be revealed by what I sent you, but I did send you 8 pages total, with cover.
Of course, this amazed me, more than 30 years ago.
These folks seem to forget that many audio designers know all about the general use of negative feedback. We have taken university courses on it as well. Back in the '60's, I was very sure that negative feedback was the best thing since sliced bread! ;-)
I used to design velocity and position servos for Ampex, for both audio and video tape machines.
Unfortunately, I found that negative feedback did not sound as good as it made the measurements. Today, I use negative feedback sparingly in most of my designs, and attempt to eliminate it in my best efforts. The CTC preamp, which is my best effort in preamps, has no loop feedback and it is completely stable, so long as I keep the temperature inside the box at a constant temperature.
The first stage of my Vendetta phono stage also runs without any loop feedback. It has a low frequency gain of over 10,000 and it works fine, unless you blow on the raw circuit. Then it will get very noisy, of course. Feedback is overrated in audio applications.
"I was very sure that negative feedback was the best thing since sliced bread!"Mr. Curl, please get your own writers...and stop stealing my lines ;-)
You are sooo right John..."Back in the '60's, I was very sure that negative feedback was the best thing since sliced bread! ;-)... Unfortunately, I found that negative feedback did not sound as good as it made the measurements."
This is my experience too, but for me the first part was in the late part of the 80's, you know I was born 1968, still young yet...
Many people seem to look at feeback an distortion in the same (but wrong) manner as "Inverse Distortion Cancellation" whith several stages (Or push pull and complementeary stages, whitch work in the same way). I had a hard time to explain to people that only even (2.nd, 4:th ...) harmonics could be cancelled. Julius Postal wrote a good article whith a graphical explanation ("Simplified Push_Pull Theory" Audio Enginering, May 1953) whitch show this in a easy way.
Many of these old papers and articles are intresting to read and most of it still holds true. But yes, there's been progress in many ways and new things has been discoverd. Just look at Walt and SID...
I am patient and I know that all will not be revealed at once...
Some people seem to think that the subjekt of distortion cancellation is easy, but it aint. The 3:rd harmonic cancellation only occur at low levels of feedback whith bjt's and I have not seen it whith other dewices as fet's or tubes.I found the book "Analog Integrated Circuits for Communication" but it will take a couple of weeks untill I get my hands on it.
I'm going to check the info you sent me tomorrow at the electronics department, it's getting real late here now. Got to sleep to.Thanks for the papers and book tip.
Why would the relatively small level of distortion in an audio amplifier or preamplifier with negative feedback be evident when the signal has gone through dozens of stages of amplification with negative feedback in the tape decks and recording and mixdown consoles not to mention the distortion of tape heads, magnetic tape itself, and phonograph cartridges? Surely, the level of distortion of those last three are all orders of magnitude greater than even the worst high fidelity playback amplifier and preamplifier would introduce.
Here's my take on that:
Say we have a series of 10 'stages' and we put a 'pure' musical signal into the first stage and can monitor the output of any stage. Each stage has an equal amount of '?' (whatever a high global feedback stage does). There is (auraly (almost if not equaly))
just as big of degradation between the ninth and tenth stages as there is between the input and the output of the first stage !
I.E. the fact that a signal has gone through 100 op-amps in the studio, doesn't make the affect of the 101s't op-amp in our system any less noticible...........
Do you really want to open that can of worms?
But since you have done it I’m going to answer this as good as I can.To do this I need to explain my “Design philosophy” and some history. I am an electric engineer and have been fiddling around with electronics and loudspeakers since I was 11 years old I built my first own loudspeakers and amplifiers at the age of 16, so I’ve been learning this for over 25 years and are still in the process of learning.
I also used to think that negative feedback was the best thing since sliced bread, but for me the big eye-opener was when I listened to the Monster sometime around 1988. The Monster is a low feedback (around 20 dB) and low power (8 Watt) class-A amplifier design by Jean Hiraga with a very simple design (Only 8 transistors). I know that Hiraga have made some odd statements (It might be translation errors) but he can design well sounding amplifiers.
At this specific time I had the opportunity to compare the Monster with an class-B amplifier of similarly the same size (25 Watt) but with high feedback and a “normal” power supply AND better measurements at full power (I can’t remember the name of it). The other amplifier sounded grainy and metallic in comparison to the Monster witch had a pleasant sound (And don’t come and talk about euphoric distortion or something like that. It was just more true to the original.) The loudspeakers used at that time had sensitivity around 95 dB/W at one metre, and we were putting out less than 1 Watt on average at our listening levels. And actually the Monster had little lower levels of distortion AND of only lower harmonics (2:nd and 3:rd) that where measurable compared to the other amplifier witch had harmonics extending up to the 20:th visible above the noise-floor. (The noise-floor was approximately similar for both amplifiers) This got me to start thinking that high order harmonics are BAD and need to be as low as possible, because they mess up things even at very low levels.
To me the single most important thing in an audio reproduction chain is the source (i.e. the record) followed by the room, loudspeakers, record-player, power-amplifier and the pre-amplifier. In that order! Witch bring us to your question/statement:
“when the signal has gone through dozens of stages of amplification with negative feedback in the tape decks and recording and mixdown consoles not to mention the distortion of tape heads, magnetic tape itself, and phonograph cartridges? “
There are a BIG difference between good and bad recordings, for instance some of Opus-3’s best recordings are made (If I remember correct) with only 3 microphones (A stereo pair and one for the ambience) one mic-amplifier (with no global feedback) per mic and one mix-stage (with no global feedback) before the mastertaperecorder. That’s only two amplifier stages in total and no global feedback before the recording…
But even if you have a big recording console with a lot of stages that can and will introduce distortion, the recording engineer LISTENS to the result at mixdown and tries to eliminate the distortion or compensate for it in the best possible way. The master-recording will have some distortion, sometimes intentional but mostly just something we have to live with but try to eliminate. This recording is what we have to try to be faithful to in the reproduction chain forward on.
I have personally experienced that the same mastertape, but processed at two different pressing-plants (Yes I still prefer vinyl) can give totally different results. And I know that it is the same mixdown. The “bad” pressing is fairly decent but the “good” pressing have much better S/N ratio better dynamics and give me “goosebumps”. BUT I could not hear this until I changed to my present amplifier. (The distortion is aprox the same as the earlier amplifier, but with only local feedback in my present amplifier.)
The distortion in tape heads and magnetic tape rises with signal. That means that with small signals the distortion is also small. And music spends most of it’s time at signals close to zero. I recommend all to read: "Multitone Testing of Sound System Components-Some Results and Conclusions" JAES Vol 49 No 11 2001 November.
Also you could check out “Transient Intermodulation Distortion and Measurment” by Gerald Stanley AES Preprint # 1308, with contains some probability density functions of music and voice. This should not be news to anybody here, and the result is that Class-B amplifiers and Class-AB have their worst distortion performance where the music signal spends most of its time.I’m currently working on my thesis on how our hearing works with emphasis on the ability to hear distortion, and how we should design our amplifiers and pre-amps according to this, so I have given this subject some thought. As a part of the thesis I’m designing pre-amp based on tubes and have done some measurements on the prototype: At 1Volt rms out 2:nd harmonic is at –88 dB and nothing else above the noisefloor at –94dB of my present measurement-rig. (But I have to modify it because my new modified and hopefully better prototype will be hard to measure otherwise.)
At 5 Volts rms out the 2:nd is at –78dB and the 3:rd –82dB.
The noisefloor of the pre-amp itself is at –120dBI have compared the prototype against my current pre-amp of mid-fi design and there is a difference, but not any big one. But the prototype is better and not just in my ears. I did some measurements on my current pre-amp and I could se some peaks of harmonics up to the 6:th above the noisefloor of –94dB. Hmmmmm……..
So the distortion obviously matters.
And to all of you who think that we can measure everything and that the only thing we can do to improve is to get higher resolution (i.e. lowering the noisefloor) I recommend again to read “Multitone Testing…” and think about it. There is a big possibility that we are measuring the wrong thing.
BTW. John I got the papers. Thanks
Mad Man H.,If you like the concept of multitone signals, then you need to look into my Phi Spectral version of a multitone, see:
http://www.geocities.com/jonrisch/PhiSpectral1.htmThis is AES preprint #4803, and some of the graphics are shown at:
http://www.geocities.com/jonrisch/page10.htm
and related pages.Most of the mainstream multitone test signals all make a significant mistake by having the multiple tone frequencies in the signal prone to octave or other similar spacings that allow cover-up of various distortion products by the original tones in the test signal.
If you would like a PDF of the paper, which has all of the graphics in it, e-mail me, however, it is 3.4 Meg in size, so I would not recommend this way via dial-up. I can send hard copy via snail-mail, but for international mailings, I would require some of the international mailing coupons to cover the costs.
If I had a fax number, I could fax a copy, but even with the FAX set on fine, many of the graphics would be mangled. If you send me a fax #, please include all the necessary country numbers, etc.
Hi JonIn the paper I was referring to “Multitone Testing…” they are trying to deal with the issue of overlapping IM-products with logarithmically distributed frequencies and for a 20 tone sequence in the 1 to 10 kHz band the frequencies are:
1000.0 Hz
1128.8 Hz
1274.3 Hz
1438.4 Hz
1623.8 Hz
1833.0 Hz
2069.1 Hz
2335.7 Hz
2636.7 Hz
2976.4 Hz
3359.8 Hz
3792.7 Hz
4281.3 Hz
4832.9 Hz
5455.6 Hz
6158.5 Hz
6951.9 Hz
7847.6 Hz
8858.7 Hz
10 000 HzThis seems to work well but the problem that arises now is the frequency-resolution of the FFT.
I will mail you so you can get the address to my e-mail account at my university so you can send the PDF to me.
Rolf, of course, you are on the right track. When I first tried the Otala amplifier, I found there was a night-day difference through my Stax headphones between it and Marantz, SAE, etc that I had available at the time, 30 years ago. You understand that you must trust your own subjective judgement in these matters or it is difficult, if not impossible, to improve.
Hi John.I really hope that I am on the right track, because sometimes it’s just tough to explain why I do my designs as I do and have my opinions about audio related things. But at the same time it’s good to be challenged and questioned. (If it’s done in a polite manner, otherwise it just ends in flame throwing.) Because it forces me to really think about my standpoint in a critical way and check the validity in the other parts claims.
And of course if I’m proven wrong I must admit that and give credit to the other part for pointing that out to me. I don’t say that I know everything about audio, there are a lot of people out there with way better knowledge. I have barley scratched the surface but at least I am trying to get an understanding of the interactions between things.
You can’t just look at isolated issues.
Well, the high feed back amplifier and the golden A amp both distort the signal - one in a pleasant way, possibly due to dynamic expansion due to power supply non-linearity and the other ina not so pleasant way, with slew limited distortions. Nothing wrong abouteither amplifier. I remember a demo I did for a customer about 1980 - He wanted to compare two $600 Amps - the Apt-Holman power amp, and the SAE 3000 (this was the third generation SAE product with lots of off seas supplied components and assembly - Generally panned by the audio press.) He brought in his L166 JBL speakers and wedid some listening. Now in our store's (Henry Radio) set-up we could level balance separate amps with the same input applied and we did this in this setup by ear with a pink noise signal. I expected the APT to sound better than the SAE as it seamed to do with most of the speakers we sold (B&W, DCM, Advents, and others...) but in this case the characteristics of the SAE obviously "locked in" with the JBL's - and the SAE was the choice of the customer - dirt bag left and bought it from mail order for a C-note less. A good hour and a half wasted , 'cept as prop head fodder. The Apt no doubt the better amp - whatever nonlinearities the SAE had compliments those of the 166's...
This is misleading. Actually many class A systems, even open loop, have very low distortion at moderate levels. There are many examples of excellent pro electronics that have very low distortion at typical output levels, as well.
Many audiophiles most highly prized recordings based on sound quality alone are analog recordings made with vacuum tube technology and with early transistor technology when the levels of distortion I think you are referring to could not even be measured let alone eliminated. And the medium of choice is the vinyl phonograph record usually recorded on magnetic tape and mixed down to another magnetic tape. Whatever the merits and strengths of vinyl recordings and for that matter analog tape, lack of harmonic distortion and noise isn't one of them.
Soundmind, this is where you are in error. It is not necessary to measure the distortion of a process at ALL operating levels if it is operating class A. What you need to know is the order of the distortion at one level and you can predict the drop in distortion at lower levels. For example magnetic tape.
If O Vu = 0.5% 3rd harmonic Vu=dB in this case
then -10 Vu = 0.05%
and -20 Vu = 0.005%
etc
Second harmonic drops more slowly.
For example 1% second harmonic at 0dB gives .1% at -20dB and .01% at -40dBMany open loop systems operate class A or at least class A at low levels. This includes many tube circuits, analog magnetic tape, vinyl discs, loudspeakers, and many discrete component solid state designs.
The practical actual listening level might have very low to vanishingly small distortion, except for perhaps some residual 2'nd harmonic, since it falls relatively slowly. A little 2'nd harmonic is practically indistinguishable from the original source material when listening anyway, so a little won't have much effect.When we discuss subtle interactions of negative feedback, we are trying to explain why negative feedback can be a potential problem in some cases, because of our direct experience with using it, and finding the subjective results less acceptable than predicted by the static measurements.
At an advanced academic level, we find that negative feedback can actually produce distortion of a higher order. This is interesting stuff to experienced designers often who wonder why their 'perfectly measuring design' was rejected by the users of their product, and something else was preferred.
Of course, this factor is but one of several. Others might include TIM (SID), IIM, PIM, Hiraga distortion, peak current limitations, power supply ringing, etc.
Well, since the gain stage is driven by the difference between the input and a portion of the output, the elimination of a particular harmonic would consist of scaling the inverted output so that the third harmonic component would be just great enough in amplitide to eliminate it from the output altogehter. At least that is the intuitive answer. Of course you could choose a different scaling factor to eliminate any other particular harmonic instead. Completely eliminating it assumes that the percentage of third harmonic distortion is not a particular function of freqeuncy over the desired range. If it is, then eliminating it at one frequency would not necessarily eliminate it at others.
Wow did I struggle with those equations in control theory. Very complex. Then one day about 20 years ago I saw my first PLC and understood immediately what it was about. Modern industrial controls in machine design or building automation systems are unthinkable without PLCs and there is little more useful in a PLC than the ability to use negative feedback to exercise control over just about anything. I've taken a few hands on seminars in PLCs and tried a couple of simple programs but most PLC projects I've been involved in was as a project manager. However, in some of them, the overall concepts were my own. These involved HVAC controls to maintain positive pressure in laboratories with variable use of fume hoods. I also was involved in automation of a chiller plant. Negative feedback between a set point and a sensor output difference is invariably the driving force in every system I've seen. Amplifier circuits without negative feedback are actually completely out of control. No compensation at all for countless variables from temperature to bias drift. I would not think of buying one or owning one that didn't use negative feedback skillfully. OTOH, those who can't use this technique effectively are wise to stay away from it. In the wrong hands, it can be an unmitigated disaster.
[ Amplifier circuits without negative feedback are actually completely out of control. ]I don't know where you learned to design amplifier circuits, but this statement is false. In fact, there have been several successful amplifier designs in the audio field with no negative feedback that worked just fine, and were not "completely out of control".
This kind of statement, coupled with your complete misinterpretation of the scope shots at the Cardas site ( see http://www.audioasylum.com/forums/prophead/messages/9848.html
and the Cardas info is shown at:
http://www.cardas.com/content.php?area=insights&content_id=10&pagestring=Measuring+Cable+Resonance
)
is showing that you have a very poor grasp of some basic concepts in audio engineering, and concerning measurement technology.Add in the nearly complete miss by you on the Phi Spectral multitone concept, as well as that of multitones in general, and we have someone who seems far from qualified to make any sort of pronouncements about audio quality issues.
Jon Risch
Hi JR. I think that I will pull out your multitone CD and start measuring again.
Years ago, when you first sent me the CD, it was fine, BUT I had trouble finding a CD player that was linear enough to test my own circuitry without a lot of mental subtraction. Then, I was using the HP3580 or the MAC FFT program and they were both single channel.
However, now that I have a dual channel FFT system with the HP3563, it might be practical to cancel out the source by digital subtraction, and just look at the residual !
For the record, the reason that I have used a single sine wave in my usual analysis, is because it is so easy to null. However, you know as well as I do, that a sine wave is not the most sensitive waveform that you can use to find distortion. Keep up the good work!
Perhaps Soundmind might have been referring to open loop operational amplifiers or perhaps feedback systems where time integration occurs between two logic states (as say with a digital PLL phase comparator).
JR: ""and we have someone who seems far from qualified to make any sort of pronouncements about audio quality issues.""
The thread was going quite well until you injected this bs.Stick to the topic at hand...you are not one in a position to tout your own understandings.
As for amplifiers without feedback, you must mean "global" feedback.
I believe Soundmind is referring to gain stages that do not have any rearward coupling, such as the current the load draws from the output stage. Many systems can work by monitoring the load draw, such as a resistive element with a temperature dependent resistance, but this feedback method is usually not fast enough to control the environment, lending towards instability...not an issue when the load draw is the controlled variable.
Please leave the arrogance elsewhere, stop attacking individuals..and contribute nicely.
I just have to make a small comment about this when you are comparing control theory with audio amplifiers.“Negative feedback between a set point and a sensor output difference is invariably the driving force in every system I've seen.”
Yes this is true when you are dealing with position servos (or what ever you are controlling but lets take them as an example). The servos just have to be in a certain position within the error margin and get there in a specified time.
BUT position servos don’t have ears and a brain that is constantly processing what the ears hear. I’ve studied control theory and power electronics at the university to widen knowledge in electrical engineering. And in my opinion control theory is closely related to basic signal theory. (And obviously my university share this opinion because they have joined these two separate 5 credit courses to one 10 credit now)
Don’t be angry but you just can’t compare control theory with audio amplifier design.
It doesn't mean that they are identical, but share a common set of characteristics.I am sure you didn't mean to imply that audio amplifer feedback networks have "ears and brains", but that is what it looks like :-)
The theory and equations are identical. One has to interface with the physical world using transducers, servo motors, and sensors. The other is purely electronic. But that's where the difference ends. Admittedly, given the bandwidth and range of signals to be contolled in electronic circuits makes satisfactory solutions to the very difficult and complex equations much much harder. The limitation is in the success of the engineering application of the theory, not in the theory itself.
I’m fully aware of that control theory and audio amplifier design share characteristics and I didn't mean to imply that audio amplifier feedback networks have "ears and brains", I was just referring to the end-user. (And a P-regulator is truly nothing else than a feedback amplifier.) The difference lies in that in control theory it doesn’t matter if the error consists of 2:nd, 3:rd… 7:th or 20:th order harmonics, as long as the total error is small enough. Like when you measure THD without specifying the harmonics… ;-)“One has to interface with the physical world using transducers, servo motors, and sensors. The other is purely electronic. But that's where the difference ends”
“The other is purely electronic.”????????
Don’t you listen to music with your ears? If audio where purely electronic our brains would be connected directly to the amplifiers via cable, without the need of loudspeakers and our ears. Actually this is an intriguing and interesting idea. But until this comes true we need our EAR-BRAIN system to hear things.
Our ear-brain system is constantly listening for changes in the sound information and tries to interpret that. Take noise as an example, if the noise is constant in its character we don’t hear it as easily opposed to when its constantly changing. A friend of mine gave me a good example of this; When you are driving a car you don’t recognise the background-noise from the tyres against the tarmac after a while. BUT if the asphalt surface changes you immediately recognise the CHANGE and start hearing the noise again.
This is probably one of the reasons to why vinyl works despite the S/N-ratio of around 70 - 75 dB at it’s best, the noise character is constant. And as Fielder pointed out in one of his papers; we have the ability to hear information 10 to 15 dB BELOW the background-noise. That would make a "true" S/N-ratio of up to 90 dB because I believe that the low-level information is there in the noise and that we can hear it.
Our ear-brain system is sensitive to high order distortion as pointed out by Shorter and Crowhurst already in the 50’s but the root cause might not be that high order distortion products are dissonant, but instead the enormous number of IM-products with several simultaneous tones.
In music the number of simultaneous tones can be very high when considering all the natural harmonics of musical instruments, just look at a guitarist playing one chord; 6 tones and I don’t know how many harmonics but just say it ads up to 20 something (Probably more).
If we look at a system with only 2:nd order distortion and 20 simultaneous input tones we get 380 IM-products and with a total distortion level that is almost 9 times higher compared to what it would be with a single tone.
If we look at a system with only 3:rd order distortion and 20 simultaneous input tones we get 5320 IM-products and with a total distortion level that is 95 times higher compared to what it would be with a single tone.
If we look at a system with only 4:th order distortion and 20 simultaneous input tones we get 53 960 IM-products and with a total distortion level that is 123 times higher compared to what it would be with a single tone.
If we look at a system with only 5:th order distortion and 20 simultaneous input tones we get 437 560 IM-products and with a total distortion level that is 93 times higher compared to what it would be with a single tone.
And this just gets worse with higher harmonics and our systems don’t just have one order of distortion but 2:nd, 3:rd, 4:th and so on. This means that higher order harmonics create a constantly changing “noise-floor” witch is modulated with the input signal. This may explain the metallic and grainy sound we encountered with systems with high order distortion.
This implies that harmonic distortion with constantly changing character is detected by our ear-brain system, while listening to music, even if it’s at very low levels. And because our brain is trying to interpret this “information” witch isn’t relevant information listening-fatigue will occur.
And that brings me back to why I don’t think that you compare control theory with audio amplifier design. In control theory the order of harmonics don’t matter, only that the error is small enough matter. And in control systems you often only have to cope with only one input signal. That’s one tone. ;-)
But to our ear-brain system the order of harmonics and the number of IM-products matter and we obviously have the ability to hear information down below the noise-floor of our system and since changes are interpreted as information………… Hmmmm! Well I think I made my point clear now and won’t go on. I only want to wish a happy new year to all of you.
"If audio where purely electronic our brains would be connected directly to the amplifiers via cable, without the need of loudspeakers and our ears."Well an audio recording/reproduction system (you have to look at the entirety of the process from beginning to end, this is where I disagree with some of the other posters here) will require transducers to interface the real world, amplifiers are purely electronic and the feedback loop is confined go them. In the controls systems example, the loops include the mechanical response too. When TOTAL harmonic distortion is measured in tenths and hundreths of one percent, it doesn't matter how it is spread out. I believe that they are all inaudible. BTW, if you don't think errors in control systems are important, think again. If an amplifier feedback system fails, the worst that can happen is it goes into spontaneous oscillation and blows up destroying a device which at most is worth a few thousand dollars and frankly its parts are worth only a few hundred. If an industrial controls system fails or the design is faulty, the damage to equipment and machinery can easily run into the millions and that doesn't even count the consequential damages such as loss of production or use of a facility which might contain laboratories, data centers, offices which countless other people depend on to earn a living.
BTW, I think 70 to 75 db S/N ratio for vinyl is a little optimistic. I think realistically, at least for most of what was produced in the real world, 55/60 is more like it. Not that it matters for most music such as pop or rock which has a dynamic range of about 10 to 15 db. It's only when you get to classical music that you push the dynamic range envelope to its technological limits and that only represents a small fragment of the market.
Please, Soundmind, leave it to the experts! IF higher order distortion did NOT matter much, virtually all amps would be OK. This just is not the case.
Rolf, you are on the right track. For decades there have been weighting factors for higher order harmonic distortion. The most extreme that I have seen is: Multiplier = (n-1)! / 2
The one that I think is closer is: Multiplier = n (squared)/4
Either way, higher order distortion, even in small amounts is very important.
Also you should look into 'triple beat distortion' for max distortion values.
Finally, 2'nd and 3'rd IM is actually related to the music itself. With higher orders, it deviates greatly from falling on a note that is in tune with what is being played. That Is why it is sometimes referred as 'metallic' sounding.
So at what threshold percentage as a function of f and N does each of these harmonic distortion components become audible?
It has nothing specific to do with individual harmonics. IM does the most damage.
At what level?
Soundmind you are really an old dog that can’t learn to sit, and clearly under your sun there are nothing new…I gave you perfectly good examples of what could be causing the things we hear, but you didn’t really address any of them in your responses. Why? Is it because you know that you can’t argue against them? And put attention to that I said “could be causing” I have never proposed that what I am saying is the only truth like some others, but as long as I hear differences I have to seek answers.
“When TOTAL harmonic distortion is measured in tenths and hundreths of one percent, it doesn't matter how it is spread out. I believe that they are all inaudible.”
If you can’t hear it, then it’s good for you. BUT just because you can’t hear it you can’t sit there and say that it doesn’t matter. I have to trust my ears. I talked with my brother about this yesterday, and we compared this issue with the ability to hear the difference between different acoustical-guitar brands. I can hear the difference between a guitar with steel strings and one with nylon strings, and I can hear the difference between guitars of different size and shape. BUT I can’t hear the difference between different brands if they are of similar shape and size, but there are people who can do this and just because I can’t hear it I can’t say that it doesn’t matter…
“BTW, if you don't think errors in control systems are important, think again If an amplifier feedback system fails, the worst that can happen is it goes into spontaneous oscillation and blows up destroying a device which at most is worth a few thousand dollars and frankly its parts are worth only a few hundred. If an industrial controls system fails or the design is faulty, the damage to equipment and machinery can easily run into the millions …”
You know that I was referring to the error between the wanted output and the actual output in a control system, the error signal. But you respond by talking about money and system failure??? Money is NOT the issue here!!! If an audio amplifier goes into spontaneous oscillation it’s just a bad design and a competent electrical engineer would have corrected it for this, and if you have encountered control system failure because of faulty design from your part and lost a lot of money, bad for you.
(And I’m fully aware of that control systems can be unpredictable and cause problems, but that was not the issue here)“I think 70 to 75 db S/N ratio for vinyl is a little optimistic. I think realistically, at least for most of what was produced in the real world, 55/60 is more like it.”
What I said was that “vinyl works despite the S/N-ratio of around 70 - 75 dB at it’s best”. “at it’s best” means that this figure is not reached all the time. And there has been development in this area too in resent years resulting in much lower surface noise and hence better S/N-ratio. I have a couple of records with I think surpass 75 dB S/N-ratio, maybe I should make some measurements… Hmmm
BTW Vinyl is still produced and most of it surpasses those records produced in the 80’s regarding to technical specifications.“So at what threshold percentage as a function of f and N does each of these harmonic distortion components become audible?”
Soundmind you are again showing your incompetence and inability to grasp the whole picture by asking for a blunt number of distortion %. The answer is that it depends! I recommend you to read
“Just detectable distortion levels” by James Moir Wireless World Feb 1981
“Some Defects in Amplifier Performance Not Covered by Standard Specifications” by Norman Crowhurst. JAES Oct 1957
“Do your ears deceive you?” by Tom Farrimond. Practical Hi-Fi Jan 1980
“Inaudible High-Frequency Sounds Affect Brain Activity; Hypersonic Effect” by Oohashi et al. The American Physiological Society.
And the AES preprint # 3207 September 1991“Capturing Music: The Impossible Task” by James Boyk. Seminar at the University of California, San Diego April 2004
When you have read these papers you should be aware of that it depends on frequency, level, what you are listening to (i.e. how long, in time, are the high level peaks in the program material) and the order of harmonics among other things. So you just CAN’T just give a blunt number, but maybe it works in your simplified world.
The article by James Moir says most of it, so if only care to read one, read that one.
This far we haven’t talked about the interactions between the amplifier and the loudspeakers because of EMF, and then there are other even bigger cans of worms we haven’t touched yet. It’s interesting to se that with every step of “development” we end up with less linear devises, with DHT-tubes being the most linear device ever made. I know that tubes have their problems and limitations and that bjt’s with local feedback can have better measurements, but the listening impressions can tell another story…
“could be causing”Engineers and scientists don't work on "could", they work on IS. It's the same silly arguement as the cables. Proponents of certain equipment just like certain cables are long on theories and generalities and very short of facts and data. They would have you believe that the process of improvement is infinite, and that there is no point beyond which further electrical improvement doesn't offer any usable audible benefit. They claim they can hear what can't be measured. This is extremely self serving to those in the business of making and selling products because it opens the door to an infinite number of new and improved models which can never be tested to see if they actually are of usable value over the previous art. This is rediculous and it is not the way of science. Scientists establish the absolute criteria beyond which further improvement cannot be usable because of the limits of human perception and then they find a way to measure their designs against those criteria. Once they have bettered them, there is no need to go any further except to make their designs cheaper, smaller, more efficient or more reliable.
"BUT just because you can’t hear it you can’t sit there and say that it doesn’t matter."
Take my word for it, if you can hear it, it CAN be measured. OK, don't take my word for it. Next time you take a hearing test, ask your audiologist. And if you can't hear it, it really doesn't matter. In fact, many times reproducing what is inaudible creates new problems without offering any benefits. There would be no reason for a television set to be designed to reproduce infrared and ultraviolet colors. They also add nothing of benefit.
"Soundmind you are really an old dog that can’t learn to sit, and clearly under your sun there are nothing new…"
Under my sun, there are facts and there is hype. Hype is used when there are no facts to sell to uninformed or untrained people what more knowledgeable people will pass off with a laugh. At least in that regard, you're right, there is nothing new. And you are also right about the fact I don't just sit passively for a lot of it.
“Under my sun, there are facts and there is hype. Hype is used when there are no facts to sell to uninformed or untrained people “This is why I design and build my own amplifiers, pre-amplifiers and loudspeakers, because the hype causes the investment needed to by some of these up-hosed amplifiers climb to a ridiculous level. And I’m currently working on a idea of an record-player in the back of my head based on some ideas from J C Verdier, if I pull that of I can have a complete reproduction chain of my own design…
BTW I didn’t mean to attack you personally in any way Soundmind, but this time you just have to accept that you have to take the heat for all of your peers…
For Soundmind, 'is' appears to be delimited by what is accepted orthodoxy among certain of his peers.
Happy new year..hope yours is a good one..Tom: ""For Soundmind, 'is' appears to be delimited by what is accepted orthodoxy among certain of his peers. ""
I know that when I work on systems that are mission critical, or are needed for human safety, I will always use "known orthodoxy". To do otherwise is to invite disaster..my employer expects it, as I am sure yours as well as Sound's...So, his approach of "show me the proof, and I will learn", is certainly a valid one.. he just doesn't seem to want to blindly accept gratuitous handwaving..can't blame him, really..
I'm happy, though..that this thread, with one exception, has been a delightful one to read..I thank all..
This is, IMHO, how it should be..
Cheers, John
Happy New Year back atchoo!I agree - this is one of the more interesting threads overall. I feel that 'engineering' can encompass a wide range of approaches, depending on what the objectives and available resources are.
Statements like this:"When TOTAL harmonic distortion is measured in tenths and hundreths of one percent, it doesn't matter how it is spread out."
certainly suggest that Soundmind is pretty fixed in his worldview. He made a statement that is completely unsupportable. I'm sure the response to any objection will be to demand proof that higher-order harmonics are audible...sigh...
How about if HE did a little research into the work others have done over the last 20 years BEFORE making ten commandments-type pronouncements? Engineering has moved on....
Here's an intersting question: did anyone ever PROVE that THD meant anything? It seems to have developed a near-mythical importance as a measurement, but I don't recall seeing any evidence that all harmonics ARE equal..
BTW, thanks for the New Year email -- right back at ya! I was off in Death Valley for the week, so I missed most of this wonderful thread...
You ask questions I cannot answer..There are two things that are really bugging me at the moment...
1. What mad man harju said about 10 uSec lateralization delays being audible....somewhere, I've heard that before...of course, I've been saying 5 uSec.
2. The fact that Bill Haley and his comets are not a current band, with today's recording technology available..I made some CD's with fifties stuff for a n.y. eve party, and I can't stop singing shake, rattle, and roll.
From what I am seeing here, we are all saying pretty much the same thing, in different ways...I had this same argument with MTRY a while back, when I started skin effect measurements and wire inductance modelling solely based on the anecdotal accounts of others, with the desire to back into possible audibility...whereas he condsidered that a backwards approach..correct, he was, with respect to scientific methodology, but I consider the cows to be already out of the barn...so approach the problem from the opposite direction..looking for what is causing the anecdotal accounts..yes, one has to always consider the possibility that one is seeing what one desires, so my method requires closer self inspection and peer review...but it's fun.
Oh, JC....while I will acknowledge successes of designers such as yourself, I do not consider a list of publications one reads as an indicator of one's ability to understand those publications..I can drop the names of some, shall we say, "high end" physics guys I've worked with, but that doesn't necessarily mean I understand one iota of their work..
As for the power amps of today, when one views 5 uSec temporal accuracy at these impedances, all the amps that have been built today are inadequate...not a one has been designed correctly to that speed when pushing a reactive load in the 2 to 8 ohm region. And, not a one can test to those requirements, say 1 uSec for margin.....power load technology is entirely inadequate..and design layout is shabby.
Cheers, John
(see ya later, alligator...)
PS...tis a wonderful thread, isn't it!!!!
"As for the power amps of today, when one views 5 uSec temporal accuracy at these impedances, all the amps that have been built today are inadequate.."Hahahahahahahahahahahahahahahahahahahaha
My reference sound system in some modes has 4,500,000 microsecond delays and more.
"1. What mad man harju said about 10 uSec lateralization delays being audible....somewhere, I've heard that before...of course, I've been saying 5 uSec."I didn't know that ;-)
1. What mad man harju said about 10 uSec lateralization delays being audible....somewhere, I've heard that before...of course, I've been saying 5 uSec."MMH: ""I didn't know that ;-)""
Perhaps you should get out more??? :-)
Nordmark provided 5 uSec lateralization capability without jitter, in the 500 to about 1.2 Khz regime...and down to 1.5 uSec in the 2Khz to 12Khz regime when one includes jitter in the 6 uSec arena.
I note that a 6 uSec jitter is well within the capability of most dynamic drivers simply as a result of excursion at low SPL's. So, there is a reasonable mechanism already there, to provide for the enhancement of lateralization up to 12Khz..
When's the last time anyone measured an amp for power/timing accuracy at a Meg (1 over 1 uSec), with a reactive load??
Cheers, John
Engineering is NOT a haphazard process. It starts with a specified set of design criteria. These criteria are established for a reason. In the case of a state of the art high fidelity audio amplifier, the criteria may include power output, bandwidth, harmonic distortion, intermodulation distortion, noise, frequency and phase response. The levels and types of distortion must be established by knowing what levels are audible and what aren't. If they vary by frequency or by the percentage of particular harmonics present in the output which are not present in the input, that must be known too. If the levels of distortion needed to be inaudible are unknown, the engineer approaches a scientist who makes a study to determine what they are. If the methods of measurements accepted by industry are deemed unsatisfactory or inadequate, the engineer approaches scientists as well who study where they fall short and devise improved methods to yield a more accurate or truer useful picture. All of these scientific studies need to be published in professional journals documenting every step and conclusion so that they can be judged independently by professional peers, not in consumer magazines where they are bandied about by amateur hobbyists. Certainly not in publications like Stereophile magazine. And not on internet web sites owned by the proponent. Until that is done, all of the talk is just a bunch of unproven theories. Then when the design criteria and the methods used to test the results are established, the engineer goes to work designing, building, and testing the circuit to determine whether or not it meets the initially specified criteria. That is not orthodoxy, that is engineering. Not just electrical engineering but ALL engineering. Anything less, even by well thought of, well reputed, and financially successful people is just tinkering and they are not engineers, they are dilletentes. It is easy for these people to make claims that neither they nor anyone else can substantiate. However, while they might be taken seriously by neophyte consumers and hobbyists, they will not garner acknowledgement by other engineers until they have successfully passed the rigorous criteria I have outlined.
then what?
was engineered in the same way.NOT !
The final voicing of any instrument or device designed to faithfully produce or reproduce music requires a test instrument having two ears.
rw
I recall seeing a television program about Steinway. As I recall, the method he used to make the world's greatest piano and the brand most widely used by performing and recording artists even today was to hire people from all of his competitors and steal their best ideas. Now I think that's pretty clever. This was in the days before anyone ever heard the term "industrial espionage."
I have been a professional design engineer for 37 years, and have been a member of the IEEE for 40 years.
Soundmind, are you a member of the IEEE? If so, what journals do you read monthly? I subscribe to:
'Proceedings of the IEEE'
'Circuits and Systems'
'Solid State Circuits'
'Instrumentation and Measurement'
'Consumer Circuits'
'IEEE Spectrum'
I have been a member of the AES for an equal length of time, and read the Journal every month. I also read 'EDN','Electronics Design','NASA Tech Briefs', 'The Industrial Physicist', 'EE', 'Sensors', and a number of other smaller technical magazines.Who are you to say how an engineer should design?
It just so happens than audio design needs another feedback mechanism rather than one in a circuit or implied by a mathematical calculation. It needs: THE HUMAN EAR.
Without this feedback mechanism, it is you who is tinkering about blindly, wasting time, effort and money. Both Rolf and I have the education and experience to know this. This is the difference between a successful audio designer and a time waster.
I have nothing against your process, I which things could work this way…“If the levels of distortion needed to be inaudible are unknown, the engineer approaches a scientist who makes a study to determine what they are. “
Why couldn’t the engineer do that, or don’t you trust your own ability to do that. And who would pay for this since most of those who have the means to do this kind of study in the audio industry are in it to earn money.
“All of these scientific studies need to be published in professional journals documenting every step and conclusion so that they can be judged independently by professional peers, not in consumer magazines where they are bandied about by amateur hobbyists…. Until that is done, all of the talk is just a bunch of unproven theories…. Anything less, even by well thought of, well reputed, and financially successful people is just tinkering and they are not engineers, they are dilletentes”
Exactly how many papers have you published in this way?
Regarding audio amplifier design?
If none then you too are a dilettante…
Or someone who just repeats what he has read or heard without thinking for him self.
> Why couldn’t the engineer do that
"“If the levels of distortion needed to be inaudible are unknown, the engineer approaches a scientist who makes a study to determine what they are. “Why couldn’t the engineer do that"
He can. But when he does, he has taken off his engineering hat and put on his scientist hat. It's a different function, basic research compared to applied science (engineering.) Engineers are not precluded from performing scientific work as well. Some are even good at it.
"Exactly how many papers have you published in this way?
Regarding audio amplifier design?
If none then you too are a dilettante…"Absolutely....none. Am I a dilettante? No, I'm not even that. In audio I'm just a hobbyist (although I do have a US patent but that's a different story and I'm not getting into it here and now.) However, while I may not be an expert or even an experienced amateur in amplifier circuit design (it's been 35 years since I studied it in college) I am highly experienced with the methods and processes engineers and scientists use and that cuts across all disciplines. BTW, the current terminology for proving that the performance of complex engineering systems meet their stipulated design criteria is called "validation." When you see an ad for a validation engineer or meet someone who is a validation engineer, it's his job to put engineering equipment and systems through its paces to prove that it meets its specified design objectives. And this too cuts across many disciplines and industries such as pharmaceutical, nuclear power, manufacturing, and power generation and is required by government regulatory agencies. Just proving that a specific piece of equipment meets its specifications (design goal) is called acceptance testing and documentation is called certification. This is nothing new, at least not under this sun.
"Or someone who just repeats what he has read or heard without thinking for him self."
You read it over and over again in the required processes from those specified by NRC to ISO and ANSI among many more. To put it succinctly in the words of an ISO 9000 compliance officer of one company I worked in, "say what you mean, mean what you say, and have the (tests and) documentation to prove it. And when I think about it, it makes perfect sense to me.
“To put it succinctly in the words of an ISO 9000 compliance officer of one company I worked in, "say what you mean, mean what you say, and have the (tests and) documentation to prove it.“Yes I know to well about it, when I worked at one of the Swedish Army’s repair shops earlier in my life I was working with certifying the whole business against ISO 9000…
This thread has got little of topic now and clearly lost some steam. So we might just have to start up a new one on some other interesting topic… This is how it should be, you have interesting and intriguing discussions and might in the process lean something. Thanks for me!
I have been a professional design engineer for 37 years, and have been a member of the IEEE for 40 years.
Soundmind, are you a member of the IEEE? If so, what journals do you read monthly? I subscribe to:
'Proceedings of the IEEE'
'Circuits and Systems'
'Solid State Circuits'
'Instrumentation and Measurement'
'Consumer Circuits'
'IEEE Spectrum'
I have been a member of the AES for an equal length of time, and read the Journal every month. I also read 'EDN','Electronics Design','NASA Tech Briefs', 'The Industrial Physicist', 'EE', 'Sensors', and a number of other smaller technical magazines.Who are you to say how an engineer should design?
It just so happens than audio design needs another feedback mechanism rather than one in a circuit or implied by a mathematical calculation. It needs: THE HUMAN EAR.
Without this feedback mechanism, it is you who is tinkering about blindly, wasting time, effort and money. Both Rolf and I have the education and experience to know this. This is the difference between a successful audio designer and a time waster.
“Both Rolf and I have the education and experience to know this.”This is dangerous territory John, I don’t consider myself that experienced that I can compare myself, my knowledge and my designs with the likes of you… YET
There might come a day to that, but I have a lot of learning to do until that.
Rolf, you are on the right track. IF you can get a technical education and THEN realize that there is more to audio design than just numbers on a computer or from a piece of test equipment, then you can make real progress. The problem with many with audio, is that some become technically educated, but remove themselves from discerning audio differences, and think that it is all hype. Or else, they never get a technical education and just constantly tinker with circuits and loudspeakers, never really refining any general principles, but they still may achieve some success with what they put together. It just can't be duplicated by anyone else, in general.
The trick is to be open minded to what works in audio, but having the technical background to ultimately make sense of what you hear, and perhaps derive a test procedure, or a design approach that is more successful than the typical mid fi design approach.
Hi JohnI have a technical education and have been upgrading it the latest four years and am supposed to write my thesis so I can get my degree in electrical engineering AGAIN but at a higher level. And I realize that there is more to audio design than just numbers on a computer or from a piece of test equipment. So I might have big chance to get the grasp of audio related things in amplifier design.
“The trick is to be open minded to what works in audio, but having the technical background to ultimately make sense of what you hear, and perhaps derive a test procedure, or a design approach that is more successful than the typical mid fi design approach.”
I think you are right on the spot here.
In the past I have been a member of IEEE, AES, ASA, and AIP. I've read their journals but no longer have any time for them or my memberships which have lapsed. This does not address the points I raised.
I need to keep up with what is happening in engineering. Are you telling me that you don't need technical journals to keep up-to-date?
I just don't have the time anymore. I certainly wish I had. Unfortunately my work, my current interests, and my other responsibilities do not allow me the luxury of the time to pursue them anymore.
That's OK, Soundmind, I understand.
For me, subscribing to journals is necessary to keep current and to subject me to heavy math and concepts so that I don't forget what I learned in university, 40 years ago. ;-)
With the normal analog engineering that I do, heavy math is not important on an everyday basis, and what you don't use, you lose. You are obviously working on stuff that keeps you sharp. Nothing wrong with that.
My point is that I am not just some sort of tinkerer with circuits. I take engineering seriously, just like you do.
Unfortunately, I have had designs fail to sound good, without initially having any reason for it. I have learned to trust in 'what works' and at the same time I try to design circuits that measure well.
It is very easy to fool yourself and come to the wrong conclusion about why something seems to work well or poorly. This is why we have this rigorous science. It's not to put down anyone who wants to be innovative or to invent something that is better, even much better. But when you want other people at your level to respect what you have to offer, they need to be convinced that you know why or if you are guessing, even if it's an educated guess, you are not precluding the possibility that there isn't something we're missing.Engineers and scientists make mistakes just like everyone else. That's why we need other people to check what we do to be certain we haven't overlooked something. The more critical the project, the more important the second opinion. In the nuclear power industry, it's called "independent design review" and the engineers who check out a project in this function have no connection with the project itself. If you're in my boat, you never know if you haven't made some horrible mistake until they throw the switch. When the smoke clears, suddenly everyone's an expert. (thank god that hasn't happened to me...yet.) If I don't take home audio equipment too terribly seriously, maybe it's because the consequences of being wrong don't seem that catastrophic to me.
In my world, it is called independent listening feedback.
“Engineers and scientists don't work on "could", they work on IS.”
“…what more knowledgeable people will pass off with a laugh.”Did you also laugh when Otala and later Walt Jung presented their theories of TIM and SID, because before that it was never heard of, among your kind of people, that amplifier stress at high frequencies could cause audible effects. Today this is accepted and a part of every good engineers “checklist”.
“Scientists establish the absolute criteria beyond which further improvement cannot be usable because of the limits of human perception…”
Is the limit of human perception really reached yet? Take as an example our ability to distinguish changes in the direction to a sound-source of less than ONE degree in the frequency-range around 2 kHz. This corresponds to a time difference between the ears of 10 us or a frequency of 100 kHz. This would imply that the phase and frequency response of a system is important beyond 100 kHz.
“Take my word for it, if you can hear it, it CAN be measured.”
Nobody knew how to measure the effects of SID before Walt Jung showed how to do.
And what I am pointing at is just the fact that I can (and many others with me) hear differences but our current measurement methods don’t reveal this. That is why we are looking at different measurement methods to se if they correlate with what we hear, and since this is yet to be proven we must say “could be causing”.BTW People “who work on IS” ONLY will never be the ones who bring the progress into new territory.
And about the really big can of worms with cables that you brought up, my take is like this; I think that much of it is exaggerated but that there are very small differences, which may depend of a number of reasons. A cable is also a capacitor connected in parallel with the load, and the capacitance isn’t that linear regarding to frequency and amplitude. Well not even good capacitors are that so why would a cable be that. (And maybe, just maybe, skin-effect can be a small part of what might cause the capacitance to change and hence causing phase modulation and that is perceived as “time smear”). And we all know that a frequency response that is modulated by signal-amplitude cause signal dependent phase modulation. And then we have the issue of the inductance of the cable witch also can be non-linear regarding to frequency and amplitude.
And a part of the “problem” may in some cases be just an interaction issue, the pre-amp or amplifier with or without a feedback loop might not work well with that particular load.
And when we are talking of loads, why do people of your kind Soundmind persist on making measurements of power-amplifiers with a purely resistive load? The answer I usually get is that every loudspeaker is different and there is no point to try to make measurements with a load that resemble an average load. This is to be blunt JUST PLAIN WRONG.
Loudspeakers (and I mean all loudspeakers) store quite significant amounts of resonant energy, and for relatively long periods of time (tens to hundreds of milliseconds) and this back-EMF interacts with the non-linear amplifier and creates new distortion terms. Just ask any skilled loudspeaker designer. And amplifiers connected to these real loads will not behave as nicely as measured with a purely resistive load If we use LCR networks that simulate the overall impedance of the speaker in our measurements we get a bit closer to the real thing, but to get all the way we need to measure with real loudspeakers and preferably with several different loudspeakers.
And again Soundmind you haven’t addressed my examples of what could be causing the things we hear. You are just so hell-bent on insisting that “if you can hear it, it CAN be measured”. It doesn’t matter how much we tell you that we hear differences that don’t relate to the measurements. And as long as we hear differences we have to seek answers.
And yes I’m also very suspicious when somebody comes with a “new” explanation to some of the things I’m hearing. But I almost get MAD when somebody is trying to tell me that I can’t be hearing what I’m hearing because we can’t measure it.
BTW Last time I checked my hearing, my threshold of hearing was almost 10 dB lover than the normal hearing limit in the range of 1000 to 3000 Hz. But I don’t hear as good as I used to in the high frequency range with my hearing starting to fall of above 15 kHz, due to age and exposure to loud sounds. But my hearing did fall of above 18 kHz already at an age of 15 so I haven’t lost so much or the years…
"And when we are talking of loads, why do people of your kind Soundmind persist on making measurements of power-amplifiers with a purely resistive load?"I agree. On this one you are preaching to the choir. The methods for measuring and specifying amplifier performance do NOT correspond to the way they are used in the real world. If you have read my postings on the subject, you will see that I have said that much more work needs to be done to bring those measurements into conformity with their normal application. And I agree that not only are loudspeaker loads not ordinarily purely resistive, they are not even passive loads. That explains at least in part why different amplifiers measuring the same by our antiquated methods sound different. This however does not excuse the maker or marketer of amplifiers to make claims he cannot substantiate. What it does is to prod him to hire or become the scientist who develops new objective criteria and present them to his peers so that they will accept his claims. It is not good enough for Otala to theorize about TIM, he had to define it, devise a way to measure it, and show that his designs were a valid improvement in reducing it. I am not opposed to progress. But mere claims are not progress. That is why we have a scientific method and peer groups who challenge and duplicate test results. When they are proven, they become part of the science and are legitimate fodder for the ad men, not before.
“Take my word for it, if you can hear it, it CAN be measured.”
I'll stick with that. We have sound transducers much more sensitive than the human ear drum and we have the electronics and mathematics to analyze anything fed into or coming out of them. Once again, if it isn't being done yet, that does not give anyone license to make claims based on the unproven and expect to be taken seriously by other engineers. You do the science, publish it for all to see, and when the majority of us are convinced, we accept it as the new expanded version of the science.
"And yes I’m also very suspicious when somebody comes with a “new” explanation to some of the things I’m hearing. But I almost get MAD when somebody is trying to tell me that I can’t be hearing what I’m hearing because we can’t measure it."
I am not necessarily suspicious about someone coming up with a new insight into sensory perception or how our brain interprets it. But because our senses are so easily tricked, especially our hearing and because our memory of sensory perception is so fallable, here more than ever, carefully devised and performed experiments must be conducted to determine what people actually can and can't hear. And again, the criteria of proof is the ability of other skilled scientists and engineers to look at claims, data, methods, results, and try to repeat them or shoot holes in the logic which connects them. Then when a difference you think you hear is proven to exist, it becomes incumbent upon people studying it to correlate the difference with objective differences in electrical and mechanical performance to explain how and why those differences come about, not to advance unsupported theories as proof. That is what science is all about and that is what is usually lacking in the consumer audio industry insofar as "high end" products as well.
“But mere claims are not progress”The papers and articles I recommended you to read are not mere claims.
Check them out."Multitone Testing of Sound System Components-Some Results and Conclusions"
JAES Vol 49 No 11 2001 November.“Just detectable distortion levels” by James Moir Wireless World Feb 1981
“Some Defects in Amplifier Performance Not Covered by Standard Specifications” by Norman Crowhurst. JAES Oct 1957
“Do your ears deceive you?” by Tom Farrimond. Practical Hi-Fi Jan 1980
“Inaudible High-Frequency Sounds Affect Brain Activity; Hypersonic Effect” by Oohashi et al.
The American Physiological Society.
And the AES preprint # 3207 September 1991“Capturing Music: The Impossible Task” by James Boyk. Seminar at the University of California, San Diego April 2004
There are more but this have to do for now.
""“Inaudible High-Frequency Sounds Affect Brain Activity; Hypersonic Effect” by Oohashi et al.
The American Physiological Society.
And the AES preprint # 3207 September 1991""As best as I recall, there were some significant methodology errors in that paper, but cannot for the life of me remember what they were..do you recall the problems?
John
“Inaudible High-Frequency Sounds Affect Brain Activity; Hypersonic Effect” by Oohashi et al.There are three different versions of this paper first the preprint to The American Physiological Society Convention and then the AES preprint and lastly the version from the Journal of The American Physiological Society. The first two are little sloppy but the third (witch I found on The American Physiological Society’s homepage if I remember correct) are pretty Ok. But it was a while since I’ve read it and I can’t recall any problems now at the moment, I have to read it again…
This is not the paper where they used a tweeter witch couldn’t handle the high-frequency information and distorted because of that. And I only included it to show that there may be measurable differences in our brain activity du to high-frequency effects.
MMH: ""And I only included it to show that there may be measurable differences in our brain activity du to high-frequency effects. ""
I personally can prove with 100% accuracy that this is so, and that is based entirely on experience on the production floor.I'm also confident that the ultrasonic welder guys, like "sonics and materials", located in Conn., can relate the same thing. I am starting work on some 40Khz tansducers, 700 watt thingy's, so I will be able to relate experience with that freq soon enough.
What I was not happy about, was the OSHA criteria for workplace limits of exposure at these frequencies. They spec'd limits based on one of the weightings (I forgot which one), and the meter was incapable of measuring the U/S energy that affected my hearing. So, we used ear protection in the app...clearly, OSHA had not really covered long term U/S exposure vs hearing damage, we didn't want to take a chance.
http://www.audioasylum.com/forums/prophead/messages/9965.html
Why not?
I spent years designing control systems and they do nothing without NF!
I don't have Baxandall's article, but I would assume that it is related. The math is derived in full in advanced non-linear design college courses, at least at UCB.
Hi John.The fig in Baxandall's article that I'm refering to is similar to Fig 2-16 (Calculated Distortion versus feedback level)on page62 in Cheever's Thesis whith the dip in the 3:d harmonic, but whith actual measurments up to the 6:th harmonic included.
BTW Cheever has ript of a large part of his math from this article.
I remember that you credited Cheever for his for his idea and history, I belive that it's a good idea BUT as several others have mentioned I don't belive that we should "aim" to fit the distortion in our systems to the ears natural aural harmonic distortion.Instead aim should be that the distortion in the system is "low enough" (I can't and don't wan't to give a specific number... It's a difficult task, I hawe studied this for several years and been learning how our hearing works in regard to distortion. But if someone forces me to put out a number it would be less than 0.1% for amplifiers and less than 0.01% for preamps at full power/signal-level when all aspekts SID and EMF etc is included.)
And the most inportant aspect is that the distortion falls of faster or at least as fast as the ears natural aural harmonic distortion whith rising harmonics. Where the 7:th and higher absolutley should be down at vanishing small levels.
I ran across a wery intresting paper from AES whith very god distortion-measurment histoty and conclusions:
"Multitone Testing of Sound System Components-
Some Results and Conclusions" JAES Vol 49 No 11 2001 Nowember.
Wery good readingI have been "fideling around" whith electronics and loudspeakers for some 20 years now and I am an electric engineer working whith both tubes and transistors (low (20 to 30 dB) or no global feedback), but ower the yerars by learning more I'we discoverd that there is more and more to learn and that I know less beause there are more and more questions to answer. I'we read the articles written by You, Walt, Otala, Baxandall and others. Done a lot of tesing and measurments of my own but ewery time you learn something new there are also new questions.
To come back to the issue here, I known that the dips in the harmonic distortion stucture is there whith bjt's (There are sewerall present in the higher harmonics) But I haven't got the real grasp on why they are there and why fet's don't have them. What function is in work here? Ofcourse fet's have a near parabolic transter function and bjt's have close to a exponential transter function and this is a part of the answer (Or the key point actually?)
MMH, I could FAX you the info, if you have a fax #. It is too difficult to post here, and my E-mail send isn't working properly. You can, however, e-mail me your fax #, if you have one.
Thanks John!I will mail the fax # to you
Rolf, I received your E-mail. I will attempt to send you the info I have. The analysis was developed for an advanced course by Dr. R.G. Meyer and Dr. Don Pederson, (and perhaps others as well) as working notes for a course in nonlinear circuit analysis in the early 1970's. Subsequently, Dr. Meyer wrote the book: 'Analysis and Design of Analog Integrated Circuits' , a very good textbook, BUT it is for an other course and it covers only the usual aspects of negative feedback, known to almost everyone interested in this subject.
The cancellation of 3'rd harmonic distortion by local feedback is, however, on page 94 of 'Analog Integrated Circuits for Communication' by Don Pederson and K. Mayaram. You might find this textbook in your university library.
In 1973, I did ask Dr. Meyer, privately, whether higher orders were easily cancelled as well, but he said that he did not know of any approach at the time. I am not surprised at this time after rereading the class notes on the subject, because:
"The term involving a(3) in (1.42) is due to third order distortion in the forward amplifier. The term involving a(2) is due to second order distortion in the forward amplifier being fed back and combining with the fundamental signals to produce third order distortion. Thus the error signal S(e) contains second order distortion as well as linear terms. These two combine in the second order nonlinearity to produce third order distortion. This process is called second order interaction. It is interesting to note that if a(3) is zero, but a(2) is non-zero, then b(3) will be finite. That is, even if the original amplifier had no third order distortion, the application of feedback can create third order distortion via second order interaction. ..."
The basic equation relating to the above commentary is:b(3) = {a(3)[ 1+a(1)f ] - 2a(2)squared times f } / [ 1+a(1) times f ] to the fifth power
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