Hi Scott, You still in the area? Why don't you contact Dr. R.G. Meyer at CAL Berkeley, and ask him about it? I attributed it to him, but what do I know? I do know that D.O. Pederson (father of SPICE) and Meyer both taught the same courses, alternately. Pederson put the derivation of the 3'rd from 2'nd harmonic through local feedback in his textbook:
'ANALOG INTEGRATED CIRCUITS FOR COMMUNICATION' pp. 110-111 (no footnote found).
Apparently Pederson took the 'non-linear analog' notes (EE140-240) and published them, and R.G. Meyer used the 'linear analog' notes (EE141-241) to make his textbook: 'Analysis and Design of Analog Integrated Circuits'. I do have an updated copy of the original notes for both courses, but who knows its exact source? I know that Meyer told us how he got into trouble trying to use local feedback to create an attenuator for an RF front end with a mosfet, and this was the source of the problem. So either he independently invented it, or he found out, after his problem with excessive 3'rd became apparent. You know, cross-modulation.
I found this noteworthy and I have always remembered learning it. However, it took years before higher order generation and cancellations were published. I asked RG Meyer about it in 1973, and he thought that this was 'over the top' even thinking about such a thing. It is amazing how things change over the years. '-)
'ANALOG INTEGRATED CIRCUITS FOR COMMUNICATION' pp. 110-111 (no footnote found).
Apparently Pederson took the 'non-linear analog' notes (EE140-240) and published them, and R.G. Meyer used the 'linear analog' notes (EE141-241) to make his textbook: 'Analysis and Design of Analog Integrated Circuits'. I do have an updated copy of the original notes for both courses, but who knows its exact source? I know that Meyer told us how he got into trouble trying to use local feedback to create an attenuator for an RF front end with a mosfet, and this was the source of the problem. So either he independently invented it, or he found out, after his problem with excessive 3'rd became apparent. You know, cross-modulation.
I found this noteworthy and I have always remembered learning it. However, it took years before higher order generation and cancellations were published. I asked RG Meyer about it in 1973, and he thought that this was 'over the top' even thinking about such a thing. It is amazing how things change over the years. '-)
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He said that they work differently, and degeneration does not increase higher-order products (unlike feedback). As evidence, he claimed support from Boyk et al and also said that feedback lowers output impedance while degeneration raises it.godfrey said:
Someone showed a section from a Boyk paper which says the opposite of what Thorsten claimed: it described degeneration as feedback, and said that it creates higher order distortion. The change in output impedance behaviour arises because voltage feedback reduces output Z while current feedback (such as regeneration) increases output Z. Basically any form of negative feedback acts to stabilise the sampled variable: stabilised voltage means reduced impedance, stabilised current does the opposite. The maths of distortion reduction and extra high-order products does not depend on the sampled variable.
Now of course it could be that for a particular circuit (whether global voltage feedback, or local current feedback) with a particular input signal level the increase in higher order products takes place so far below the noise-and-masking floor that even an audiophile can't hear it.
It could be that an amplifier with an exponential OL gain characteristic works particularly well with feedback because the extra odd-order products tend to be of opposite sign to the intrinsic odd-order products, but that is a separate issue.
What Thorsten has been claiming is that degeneration is a member of a new category of edible thing. On the surface degeneration looks to the rest of us (yourself and JC excluded perhaps) rather like a vegetable but he claims it does not fit the existing category of vegetable. The onus is firmly on him to provide support for the creation of the new category of edible thing.
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No, not till February we still have not found the right place.
How did he factor out the non-linear C's of the FET's (can't be ignored).
In any case take a follower of ANY technology driving an R, Vout = Vin(R/(1/gm+R)). If the gm has any square law component that depends on its inputs the Taylor series has odd powers. This is about as obvious as one can get, the algebra predates electronics and could describe a mechanical system.
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non-linearity defines physics of harmonic generation
As noted the key issue is any current dependent capacitance or resistance will create a nonlinearity which allows for two wave mixing in an equivalent circuit. In optics for example:
eScholarship: Equivalent Circuit Analysis of Harmonic Distortions in Photodiode
As noted the key issue is any current dependent capacitance or resistance will create a nonlinearity which allows for two wave mixing in an equivalent circuit. In optics for example:
eScholarship: Equivalent Circuit Analysis of Harmonic Distortions in Photodiode
Well, according to my original class notes, a small 3rd harmonic component was added to the square law (prediction) even 40 years ago, because they measured it. However, the 3'rd harmonic got much larger when local feedback was used to make an input attenuator (an obvious choice for the inexperienced). That was the point of the lecture. Please remember, he is slightly younger than me, and I was only 29 years old at the time, then, at that age, we really got enthusiastic about these things. I just have a better memory of such things than most people.
The issue is not that it is feedback, but simply that a signal containing some second-order distortion is allowed to interact again with the original input signal. The result is inevitably some third-order. This is why diode double-balanced mixers need to be properly terminated so that output signals are not reflected back in again - an RF manifestation of the same issue. Pentode screen grid voltage stabilisation is an audio issue - same thing again, second-order gets turned to third-order. Because this crops up in so many different places it is strange that people can still deny it or seem surprised by it.
Well, I was excited in the 5'th grade as well, when we learned Algebra.
Transfer function of 2'nd order error only in the common case looks like:
ax^2 +bx +c
where b defines linear gain, a defines distortions, c defines DC shift.
Now, add feedback and see what you get as the result of multiplication...
In hindsight, ALMOST EVERYTHING looks easy. That is the problem. First, you have to find a 'departure' from what you expect. Then, you have to try to understand WHY there was a 'departure' from what you may have predicted. Then, you come to understand the mechanism that created the 'departure' and you either use it or avoid it. Later, when you tell someone else about the 'departure', they will at first not believe you. Then, when you show them evidence, they will shrug and say that it is obvious, and finally, they will accept it and claim to others that they invented it, 'perhaps in the 5th grade'. '-)
feedback harmonics
? my fifth grade never covered complex algebra or talyor series, or matrix cross products, damn 60's set theory new math for elementary grades.
Anyway correct me if I am worng but I think the highest magnitude third order harmonic terms will be the beating of the second order term against the first order e.g. for the complex current harmonics , one set for the signal first order harmonic against the second order feedback(a1*a2f + a1a2f* ) and the feed back first order against the second order device nonlinearity induced third order (-a1f*a2 + -a1fa2*); if the feed back is not exactly Pi out of phase these terms will not cancel and your syrupy transfer function will become bit strident.
? my fifth grade never covered complex algebra or talyor series, or matrix cross products, damn 60's set theory new math for elementary grades.
Anyway correct me if I am worng but I think the highest magnitude third order harmonic terms will be the beating of the second order term against the first order e.g. for the complex current harmonics , one set for the signal first order harmonic against the second order feedback(a1*a2f + a1a2f* ) and the feed back first order against the second order device nonlinearity induced third order (-a1f*a2 + -a1fa2*); if the feed back is not exactly Pi out of phase these terms will not cancel and your syrupy transfer function will become bit strident.
JC's analysis in post 509 contains a big element of truth.
There is another way of looking at it, though. Someone with a misconception eventually realises it, and then assumes that everyone else has the same misconception so writes a book/article/thread announcing their amazing discovery. They are then disconcerted to discover some people never had that misconception so wonder what all the fuss is about. A variant of this is that the 'discovery' is actually wrong, but it rapidly displaces the actual truth in popularity for about a generation (5-10 years in audio?).
There is another way of looking at it, though. Someone with a misconception eventually realises it, and then assumes that everyone else has the same misconception so writes a book/article/thread announcing their amazing discovery. They are then disconcerted to discover some people never had that misconception so wonder what all the fuss is about. A variant of this is that the 'discovery' is actually wrong, but it rapidly displaces the actual truth in popularity for about a generation (5-10 years in audio?).
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Could I just return to an earlier part of the discussion which suggested that an amplifier that scores well in terms of THD may apparently sound poor because of transient distortion that may, or may not, be due to thermal effects..? The implication seemed to be that we must simply shrug our shoulders because there is no way to measure such an effect except perhaps to look for THD at such low frequencies that the chip has time to warm up and cool down (if thermal effects are the culprit) - and this doesn't seem to convince many people.
Could I ask why it is not possible to measure transient distortion directly in the time domain, rather than always looking for components in the frequency domain? I can see that in the past (pre-digital sampling and computers) THD was probably the only way, but surely nowadays it should be possible to see precisely why an amplifier supposedly sounds different from another by measuring the direct response to any transient signal we like. We can leave minutes between 'pulses' if we choose to, and take a single snapshot, or build up an average over hundreds of tests. There's a signal going in; there's a signal coming out (into a real load not just a resistor, hopefully - why do people only test amps on resistors?), so what's the difference between the two? Even if the result for a single amp is not as apparently directly meaningful as the usual 'proxy' for time domain distortion, THD, the difference between two amps (e.g. tube and solid state) would surely reveal something interesting.
Could I ask why it is not possible to measure transient distortion directly in the time domain, rather than always looking for components in the frequency domain? I can see that in the past (pre-digital sampling and computers) THD was probably the only way, but surely nowadays it should be possible to see precisely why an amplifier supposedly sounds different from another by measuring the direct response to any transient signal we like. We can leave minutes between 'pulses' if we choose to, and take a single snapshot, or build up an average over hundreds of tests. There's a signal going in; there's a signal coming out (into a real load not just a resistor, hopefully - why do people only test amps on resistors?), so what's the difference between the two? Even if the result for a single amp is not as apparently directly meaningful as the usual 'proxy' for time domain distortion, THD, the difference between two amps (e.g. tube and solid state) would surely reveal something interesting.
First, for an amplifier that doesn't have a delay line built into it (99.999% of amps used for hifi service), there is no difference between frequency domain and time domain- they are 1:1 inter-convertible. Even the time delay can be accounted for with the right type of signal transform, but it's a total non-issue for audio amps. Second, you can easily do time domain analysis if you wish- it's more convenient for some phenomena. There's a little-known instrument called an "oscilloscope" often used for these purposes. Third, you can sample and record outputs of amplifiers and see how they differ by subtracting one output from another- Bill Waslo's clever Diffmaker software is just the trick for that.
Fourth, of course, is that this "measures good/sounds bad" amplifier is a myth unless one excludes several basic measurements (usually for trolling or marketing purposes, sometimes both), or expects the amp to be an effects box when it's designed to merely amplify, or insists on judging the "sound" by means other than ears. The "low THD" thing is something of a red herring.
Fourth, of course, is that this "measures good/sounds bad" amplifier is a myth unless one excludes several basic measurements (usually for trolling or marketing purposes, sometimes both), or expects the amp to be an effects box when it's designed to merely amplify, or insists on judging the "sound" by means other than ears. The "low THD" thing is something of a red herring.
The difficulty with interpreting time domain measurements is that simple non-distorting filters can make a big change to a waveform. You have to carefully subtract off all these effects by some minimisation technique and then hope that the residual is not too contaminated by minimisation errors. There seems to be a much clearer correlation between sound and frequency components than sound and waveform shape.
@DF96
I was going to include a paragraph about mathematically nulling out designed-in factors like bandwidth-limiting, but thought it was over-complicating the question.
Your final sentence to me sounds like the circular argument I suspected: people are convinced that our ears work in the frequency domain (phase doesn't matter etc.) so even when considering transient effects, they always try to express signals in the frequency domain - even though the frequency domain is pretty meaningless for the transients that we think may be causing our amps problems. So we have a situation where an amplifier measures 'perfectly' for THD but apparently sounds bad, and there is no way forward except for listening to our 'golden' ears.
That is not what I said. There is experimental evidence that waveform shape is relatively unimportant when compared with frequency components. It is from this evidence that one might conclude that our ears work primarily in the frequency domain. Human ear physiology tends to confirm this. So we have experimental data on sound perception, and analysis of how the ear internals appear to work, and they seem to say the same thing. This does not mean that frequency is the whole picture, but it does appear to be much of the picture.CopperTop said:
@DF96
What is it that we suspect the amplifier is doing wrong with these transients? Isn't it something like 'pulling its punch' as the transistor heats up? e.g. changing hfe or some other parameters as it heats up during a single pizzicato violin note? It results in a continuously changing transfer function, where the change is dependent on the previous history of the signal. At any instant, if the transfer function of the transistor could be frozen, the distortion could be revealed very sensitively by feeding in a sine wave, but this is not possible. Edit: Other distorting mechanisms must surely be possible too, e.g. feedback causing instability and spurious clicks, ringing etc. that don't show up with steady sine waves.
Surely there must be some way of showing this distortion if it is real. Are you saying that it cannot be measured at all, or just that the time domain is not a good way to express it, even if it is the only way to acquire the data?
What is it that we suspect the amplifier is doing wrong with these transients? Isn't it something like 'pulling its punch' as the transistor heats up? e.g. changing hfe or some other parameters as it heats up during a single pizzicato violin note? It results in a continuously changing transfer function, where the change is dependent on the previous history of the signal. At any instant, if the transfer function of the transistor could be frozen, the distortion could be revealed very sensitively by feeding in a sine wave, but this is not possible. Edit: Other distorting mechanisms must surely be possible too, e.g. feedback causing instability and spurious clicks, ringing etc. that don't show up with steady sine waves.
Surely there must be some way of showing this distortion if it is real. Are you saying that it cannot be measured at all, or just that the time domain is not a good way to express it, even if it is the only way to acquire the data?
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Yes, frequency and amplitude as each hair bundle seems to respond to a narrow set of frequencies, but wave shape as Nyqest tells us is-nothing but a sum of sine waves. What is even more fascinating is our evolutionary programming to know what is "correct" and what is not. I am not sure what advantage this had in history, but it wound seem to be the case. All this is terrible hard to measure because it is a soft science based on interpretation and statics. What our brain does with a few thousand sets of hairs is totally amazing.
More fun is what we do with phase, time delay, and the amplitude variations that our brain uses for localization and distance. A classic experiment is using very pure tones in a chamber to see how well we can localize. It turns out, in a horizontal plane, we can still localize. But in a vertical plane, we are totally lost.
Something I noticed in college, classic music students almost always had a speed control on their stereo's, but pretty crappy systems. My conclusion was that frequency accuracy was one of the clues for them what was "RIGHT". Where I could not tell if A was 440 or 442, as long as everyone played together.
More fun is what we do with phase, time delay, and the amplitude variations that our brain uses for localization and distance. A classic experiment is using very pure tones in a chamber to see how well we can localize. It turns out, in a horizontal plane, we can still localize. But in a vertical plane, we are totally lost.
Something I noticed in college, classic music students almost always had a speed control on their stereo's, but pretty crappy systems. My conclusion was that frequency accuracy was one of the clues for them what was "RIGHT". Where I could not tell if A was 440 or 442, as long as everyone played together.
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