What is wrong with negative feedback?


I am not talking about the kind you get as a flaky seller, but as used in amplifier design. It just seems to me that a lot of amp designs advertise "zero negative feedback" as a selling point.

As I understand, NFB is a loop taken from the amplifier output and fed back into the input to keep the amp stable. This sounds like it should be a good thing. So what are the negative trade-offs involved, if any?
solman989
Negative feedback has been used in amps for a long time but the use got out of hand in the 1970s when the "spec wars" got going big-time. Amp designers found they could get very low distortion numbers which looked good in magazine ads.

The catch is these spectacularly low distortion numbers were measured with a static signal. Music is a dynamic, constantly changing signal. After a while, people discovered that the correlation between a very low distortion number and how the amp actually sounded in use was a bit more tenuous than first thought.

Amp design is a balance of competing factors; feedback is only one aspect of that equation. The key is to find the best overall balance for the amp in question. Using zero-feedback. when it is the subject of tunnel vision focus that ignores other parameters, is not a sole guarantee of performance any more than the mindless pursuit of super-low distortion numbers was 30 or 40 years ago.
I think you will find the answer to your question if you read about amplifiers by Soulution. Apparently, their research showed that in conventional amplifiers, the negative feedback that was applied was slightly out-of-time with the signal it was trying to correct, therefore throwing off the coherence of the original signal. I remember years ago hearing a similar criticism of the servo systems in Velodyne subwoofers. Anyway, they supposedly found a way to corrrect that problem, and I think that it is their position that negative feedback is not a bad thing when it is implemented in the way that they do it. The only bad thing is the price of their amplifiers...whew!
There's open loop (global) and closed loop (local). Few designs can be stable into low impedance loads without some feedback and, if you read carefully, some advertise "no global feedback" and sometimes forget a word. In the case of op-amps, it's usually already there.

Easy to find all the negative things about negative feedback. I'm still waiting for someone to advertise positive feedback as being better :)
What about feed Forward ?
Like this?

http://www.wolcottaudio.com/WA_presence.htm

Appreciate Wolcott's integrity.
It makes the music sound less alive. I have a Mesa Baron amp, which has adjustable feedback levels, so it is easy to hear the difference. Increasing the feedback improves the specs, cleans up the bass a little, and robs the mids and highs of life and air. This matters less with heavily processed music (eg., pop or some rock,) which can even benefit (see "cleans up the bass" above) but it is fatal to acoustic or classical music.
I think you may see a response from Atmasphere (Ralph} as he in my opinion is one of the top amplifier designers in the industry;if he replies pay attention to his response.
The main "problem" is that that it's widely misunderstood by both those circuit designers that use it, and those that eschew it. It's also very much out of vogue these days. What negative feedback is, in essence, is the technique of trading circuit gain for circuit bandwidth and linearity.

But the vast majority of audio circuits use some form of negative feedback, regardless of whether or not they're advertised as "zero feedback". It's interesting to notice that many who shun feedback also prefer triodes . . . as most triode circuits have a good dose of negative feedback (based on the tube's internal characteristics). In fact, when a given circuit or active device (tube or transistor) displays the combination of less gain and improved linearity, it's likely there's some kind of negative feedback mechanism that's making it that way.

The common audiophile response is then "well that's LOCAL feedback, which is good!" . . . this usually is explained by lack of "delays" and such. But actually in many cases (i.e. typical solid-state amp), most of the "delay" (really a phase lag, NOT a pure delay) is in one stage (the Miller-compensated voltage amp), and most of the nonlinearity is in another (the output stage), so the stability consequences of global feedback are usually very similar to that of just local feedback around the voltage amp . . . but the global feedback arrangement of course works so much better. Incidentally, this is the main cause for higher-order/frequency distortion products in solid-state amps that use feedback - the distortion rises with frequency because the Miller-compensation technique shifts feedback from global to local as frequency increases, and takes the output stage out of the feedback loop. So the problem is really not with the feedback, but more the lack of it . . . that is, it's not available equally at all the frequencies that need it.

And it's also a misconception that local feedback results in automatically better stability . . . instability in cathode/emitter follower circuits from certain source impedances is a very well-documented condition. In fact, this is the whole reason for the invention of tetrodes and pentodes . . . triodes exhibit poor stability at the limits of their gain and bandwidth, as a result of their internal feedback mechanism. The addition of the screen-grid mostly eliminates the feedback, thus the increase in gain, and decrease in output impedance and linearity.

Oh and as for positive feedback . . . "bootstrapping" networks are extremely common in all kinds of analog circuitry . . . does that count?
Negative feedback extends bandwidth, lowers Harmonic and Intermodulation Distortions and lowers output impedance.

Unfortunately, if not used wisely, is increasing TIM - Transient Intermodulation. In time domain it will show as just small overshoot on fast changing signal like square wave. In frequency domain it shows as exaggerated odd harmonics that our ears are very sensitive to (especially higher order - responsible for perception of loudness). In really bad case it can momentary saturate output transistors that will stop responding for a short time since charge is trapped at the output transistor junctions. Our brain fills small gaps like that but it will make us tired. Whole thing (overshoot) happens because of limited bandwidth that is causing delay thru the amp. Delayed signal when summed (in opposite phase) with input signal that is changing rapidly is coming too late and amp for a moment has much higher gain. Class A amps don't require a lot of global feedback and gain (without feedback) is often as low as 200 but class AB has gains reaching 4000.

How amp should be designed? I would pick the most linear transistors I can find. I would use a lot of local feedbacks. I would measure bandwidth without global feedback and would limit bandwidth of the input stage to that bandwidth (necessary condition). Harmonic distortion would be probably 5-10%. I would use just enough feedback to get distortion below 1%. That would be great sounding amp that nobody would buy because of poor spects (distortion, bandwidth).

No feedback (or low feedback) design might sound more alive because distortion gives this effect (like distorted vs clean guitar) but mostly it would sound pleasant and not tiring instead of sounding brightly Hi-Fiish.

TIM was discovered in 70s. Before that designers went crazy with negative feedback - still claiming that it has to be sounding better than tubes. Logic says that if you see numbers like THD=0.000001% something else has to give. I believe that spects are pretty much useless since amp with greatest spects might sound the worse. People often use amps exact power doubling with 4 ohm load vs. 8 ohm load as a sign of great amplifier. I'm not so sure. It will show that power supply is strong but it will also show that a lot of negative feedback is used (since power supply is most likely unregulated).
Loop feedback in any form is supposed to reduce distortion. It is questionable whether it increases bandwidth, and in some models (see the link I provided) it reduces 'output impedance'. You'll see why I use the quotes if you look at the link.

The *big* problem is that loop feedback, in the process of doing all this stuff, exacts a penalty. This comes from the fact that any circuit that can amplify is doing so at speeds that are easily measured on rather pedestrian test equipment. This time is called Propagation Delay- the time it takes for the signal to propagate from input to output.

Now feedback is created by taking the some of the signal from the output, and applying it to an earlier portion of the circuit, which has a propagation delay. So you can see that the feedback signal is arriving ever so slightly too late to do its job right. The fact that it is too late causes the amplifier to become less stable as frequency increases, and there can be inharmonic noise created at the point where the feedback is returned.

This causes feedback to inject a low level harmonic distortion noise floor composed of harmonics up as high as the 81st harmonic into the output of the amp, and it has two audible artifacts.

The ear uses naturally-occurring odd-ordered harmonics to figure out how loud the sounds are. They are the 5th, 7th and 9th harmonics and they get enhanced (distorted) by feedback by a small amount. However, because these are loudness cues to the human ear this small amount **is easily audible** and audiophiles use the terms 'hard' 'harsh', 'bright', 'brittle', 'chalky', 'clinical' and so on to describe this distortion. Keep in mind that this is the case when the distortion of these harmonics may only be 100ths of a percent!! This is why two amps can measure the same frequency response on the bench but one will be bright and the other is not.

The 2nd problem is that the harmonic noise floor, through another hearing principle called 'masking', will block the ear's natural ability to hear into the noise floor of the playback system (the ear can hear 20 db into a natural noise floor like tape hiss or the wind blowing). Any information below the noise floor is not heard by the ear or not detected as easily. Since ambient soundstage information exists at low level, one of the more obvious effects of feedback is to foreshorten the soundstage depth and width.

Amplifiers in particular that use no feedback tend to have a different voltage response in dealing with the loudspeaker and the designer of the speaker has to accommodate this behavior. IMO, a speaker that requires an amplifier with feedback, due to the issues above, will never sound like real music. Speakers that *are* friendly to zero feedback amps at least have a chance.

see
http://www.atma-sphere.com/papers/paradigm_paper2.html for more information
I have read Roger Modjeski address this issue, and his opinion seems to be that negative feedback got a bad name as a result of designers who had no formal training in electronics misusing and not being competent to properly implement negative feedback. In the right hands, it is a good thing. I think it would sort of be like a chisel in the hands of an artist versus a non-artist. The artist makes great things with the chisel, and the non-artist cuts his hands.

I listened in a group setting to a Berning amplifier with adjustable feedback: No feedback, low feedback, and high feedback. We all agreed that the low feedback setting was the best, followed closely by no feedback, and distantly by high feedback. The latter setting was the only setting I would consider unlistenable. The no feedback setting was a little too soft and mellow for my tastes, but I could see someone enjoying that type of sound, and I would not kick it out of bed. For me the low feedback setting provided the best of both worlds - detail, controlled bass, without being irritating.

There are good sounding components using feedback and no feedback, which is simply more proof you need to listen to the component, because the component really is an extension of the skills and philosophy of the designer, and there are good skilled designers employing both methods.
"There are good sounding components using feedback and no feedback, which is simply more proof you need to listen to the component, because the component really is an extension of the skills and philosophy of the designer, and there are good skilled designers employing both methods."

I think this is the bottom line practically for most.

The caveat is you cannot listen to a single component alone, only a system with all the required components (source, amp, speaker/room) together. A single listen can only tell you what each component is capable of, not how good or bad each piece is or sounds. To sort it all out requires doing your homework and listening to as many combos as you can over time.
Mapman - Moderation is the word. Instead of feedback or no feedback we can settle for moderate feedback. Sound coloration comes from dynamic nonlinearity of the system with the feedback. Amplifier itself is far from being first order low-pass filter and feedback creates loss of stability - hence dynamic nonlinearity. Part of the problem is speaker - being complex load. That would suggest to me that things are really complicated and listening instead of reading will bring better results. Speaker choice and synergy with amplifier appears to be very important.
Roger Modjeski has some interesting design philosophies in general. Topics like feedback certainly stir the hornets nest within him. Just don't get him going on cables. At that point it becomes a swarm.

I have to say that the RM-10 manual is one of the best audio reads I've experienced. The amp itself is excellent too, even with 14db of negative feedback.
ULTRAFAST NEGATIVE FEEDBACK
==================================
When an amplifier has difficulty in delivering required voltage and current many forms of distortions will occur. For example, in transistor amplifiers the increased current drawn by speakers will cause a small voltage drop across the source--i.e., the amplifier itself--which will heavily contribute to the unpleasant so-called "transistor sound.” Many transistor amplifiers use global negative feedback to reduce distortions and widen the bandwidth.

The crucial factor in negative feedback is transit time, the amount of time it takes from when an error is detected at the input until it is corrected at the output. For example, a typical transistor power amplifier has three primary sections: a low-noise high-gain differential input stage, feeding a differential-to-single-ended conversion driving a high-current output stage. Each of these three stages is designed for low distortion and noise, but those attributes typically come at the sacrifice of speed.

The typical transit time of linear amplifiers is about 2000-3000 nanoseconds, which is too slow for effective implementation of global feedback and error correction. This lagging results in ringing artifacts and enhances ODD-order harmonics which are particularly annoying to the human hearing so even the smallest amounts of these distortions are highly noticeable. Long delays in feedback also introduces transient and phase discrepancies, susceptibility to transient overload and vulnerability to disturbances at the output such as reactive speaker interactions.

In contrast, many switching amplifiers don't use low-distortion circuits. Instead, they use much faster digital logic circuits. For example, the Spectron Musician III transit time is much less then 200 nanoseconds. Such an ultra-short transit time allows the amplifier to correct for many small errors; and the control loop can follow the input much more accurately. These characteristics result in a more detailed, transparent sound with less noise and louder yet cleaner musical reproduction.
Best thread EVER.
If you can increase the speed of the amp (decrease the propagation delay) theoretically you could speed it up to the point that the odd-ordered enhancement is pushed well outside of the audio band.

Our amps are also pretty fast- 600V/usec is a typical risetime, and we only have one stage of gain. But IME this is still not fast enough, so we resort to other means of getting rid of distortion: class A operation coupled with fully differential balanced operation, which cancels even ordered harmonics not just at the output, but throughout the amplifier. This leaves us with the 3rd harmonic, which is controlled by using only one stage of gain. Odd ordered harmonics are exacerbated by noise problems in the ground and the power supply, so we use star grounding (a lot easier since most of the grounds are balanced) and separate power supplies for the driver and output sections, which also reduces IM distortion.

Distortion has the property of masking detail in addition to adding loudness cues, so if you can get rid of distortion you get greater transparency and greater smoothness at the same time, provided your techniques for getting rid of distortion don't enhance the 5th, 7th and 9th harmonics. IOW real reductions in distortion have real, immediate sonic benefits that anyone can hear: extreme detail accompanied by smoothness are the hallmarks to look for.
The typical transit time of linear amplifiers is about 2000-3000 nanoseconds, which is too slow for effective implementation of global feedback and error correction.
I think this description nicely highlights so many of the conceptual and terminological errors that audiophiles and audiophile equipment designers have about negative feedback.

Looking generically at a solid-state feedback amplifier, their frequency response before feedback is defined by a single "Miller-compensation" capacitor at the voltage-amplifier stage. It is generally flat from DC to some frequency (i.e. 1kHz), and then rolls off at at 6db/octave all the way to the point to where the gain falls below unity, which may be something like 2MHz. While the gain and the frequencies may vary, virtually every common audio opamp has a frequency response that can be described like this. Again, we're talking about it WITHOUT feedback.

Since negative feedback only exists if the open-loop (feedback-free) gain is above unity, and since the open-loop response falls off at 6dB/octave . . . the input/output phase response must be 90 degrees or less. So if we're going to talk about "transit time", how would you define that? Since we know that comparing the phase at the input the output will give us 90 degrees, the "transit time" at 100KHz will be 2500 nanoseconds. At 200KHz, it will be 1250 nanoseconds. At 20KHz, it will be 25000 nanoseconds. So it seems that talking about "transit time", or "propegation delay", or "delayed feedback", or whatever . . . is a wholly inadequate way of understanding what's going on. Rather, classical Control Theory uses phase relationships to analyze feedback.

And classical Control Theory is wholly adequate to understand the circuit behavior when feedback is applied. Musical information isn't "time smeared" from "delayed feedback", it's simply that part of the amplifier circuit operates in quadrature for a huge chunk of the frequency range (in the case of our generic SS amplifier). Just like the filter slope of the very simplest first-order speaker crossover. And this phase relationship doesn't change whether or not feedback is applied (because it's defined by the Miller capacitor) . . . the feedback simply corrects the phase response at the output.
This lagging results in ringing artifacts and enhances ODD-order harmonics which are particularly annoying to the human hearing so even the smallest amounts of these distortions are highly noticeable.
Ringing when feedback is applied is indicative of an open-loop response that is something other than a simple 6dB/octave slope, and this may be due to factors both in the circuit itself and the load it's driving. And this is indeed something that commonly can occur in the real world. But this phenomenon is wholly analyzable with classical Control Theory, and a careful analysis of the amplifier's stability. Further, this type of analysis virtually always reveals the specific mechanisms responsible for the subjective complaints associated with negative feedback.
There are good sounding components using feedback and no feedback, which is simply more proof you need to listen to the component, because the component really is an extension of the skills and philosophy of the designer, and there are good skilled designers employing both methods.
Precisely.
Atmasphere - concept is beautiful. Tube class A balanced operation without output transformer. The only problem I can see is that this design requires a lot of tubes and each one has about 2.5A heater current - a lot of wasted power. On the other hand any class A has as low as 12.5% efficiency.

Have you ever investigated ultra high vacuum tubes. Military division of Tesla made them before communism fell and Stereophile posted great review of amp built with them. Such tubes can deliver large currents.
" Odd ordered harmonics are exacerbated by noise problems in the ground and the power supply..."

Fully agree here with Atmasphere. The more regulated (and noiseless) power supply the better sound quality will be. One can assert that the quality of the power amplifier is not in its signal path so much as in its power supplies. And in many (but not all) cases I would agree with it.

Simon
Distortion has the property of masking detail in addition to adding loudness cues, so if you can get rid of distortion you get greater transparency and greater smoothness at the same time, provided your techniques for getting rid of distortion don't enhance the 5th, 7th and 9th harmonics. IOW real reductions in distortion have real, immediate sonic benefits that anyone can hear: extreme detail accompanied by smoothness are the hallmarks to look for.
Absolutely true. And there is absolutely no design technique or topology (tubes, solid-state, Class A operation, balanced push-pull, local or global negative feedback, etc.) that can guarantee meaningful improvements in audible distortion. It of course comes down to the proper implementation of a wide variety of techniques.
Kirkus, my technique for measuring propagation delay is simple: compare the input to output while using a squarewave source. Observe the difference in time between the rising input waveform and the rising output waveform. That's the delay time. I have yet to see an amplifier where I could not see that on the 'scope.

Since negative feedback only exists if the open-loop (feedback-free) gain is above unity, and since the open-loop response falls off at 6dB/octave . . . the input/output phase response must be 90 degrees or less. So if we're going to talk about "transit time", how would you define that?

It really seems to me that something is glossed over here. In this model phase and time become the same, and is inadequate to explain the behavior of an amplifier that has wide (+200KHz) open loop bandwidth. In such amplifiers the model below falls apart:

Since we know that comparing the phase at the input the output will give us 90 degrees, the "transit time" at 100KHz will be 2500 nanoseconds. At 200KHz, it will be 1250 nanoseconds. At 20KHz, it will be 25000 nanoseconds. So it seems that talking about "transit time", or "propegation delay"[sic], or "delayed feedback", or whatever . . . is a wholly inadequate way of understanding what's going on. Rather, classical Control Theory uses phase relationships to analyze feedback.

Propagation Delay does not alter with frequency anywhere near the audio band, and at those frequencies the delay time is easily measurable. In fact, we can see that at low frequencies feedback works pretty well, but as frequency increases, the feedback is progressively inadequate due to the fixed propagation delay of the circuit having a larger effect as the waveform time decreases. This introduces a time-domain distortion- ringing and odd-ordered harmonic enhancement. It is this phenomena that requires networks in many amplifier designs to prevent negative feedback from becoming positive feedback due to the phase at very high frequencies that are out-of-band but can cause the amp to go into oscillation if not addressed. The model you are proposing relies on propagation time being mutable, which it certainly is not. I'm with Spectron on this one. Sounds to me like control theory is being misapplied here.
The model you are proposing relies on propagation time being mutable, which it certainly is not.
Atmasphere, forgive me if I'm being a snot . . . but I think you need to brush up on some basic electrical theory. Pole/zero networks do indeed have different delays based on frequency. If you don't believe me, try constructing a simple R-C lowpass network with, say, a .47uF capacitor and a 750 ohm resistor. Compare the "Propegation Delay" between input to output, using SINEWAVES, at 10KHz and 20KHz. For the former, you will find it to be about 24uS, for the latter about 12uS. For both, the phase shift is about 90 degrees. Or you can do it in SPICE in just a few minutes.

Again, some basics here. A real-world amplifier circuit contains mechanisms that produce both frequency-dependent and frequency-independent delays. In a typical well-designed Miller-compensated amplifier, the goal is to choose the compensation capacitor so that the frequency-independent delay is completely swamped by the frequency-dependent delay of a first-order slope, yielding a phase margin of 90 degrees at all frequencies above unity gain.

Here's the conceptual error with your square-wave timing test. If we assume that it's indeed a perfect square-wave on input, and the circuit in question doesn't have infinate bandwidth . . . then the output square-wave will have a longer rise time and more rounded leading edge than the input. So we set up our scope, and use the markers to decide where to measure on the x-axis. For the input side, it's easy to locate the marker because the rise-time is infinately short. But on the output, it's comparatively slopey and rounded . . . so when you look at the output and place the marker, the exact placement across the slope determines for which frequency you're measuring the delay. If you just place the marker where it "looks about right", then you're simply meauring the delay of "kinda one of those frequencies" . . . one of an infinate number contained in the perfect squarewave on the input.

But really the time-honored method is to use X/Y mode on your scope to compare the phase as you vary the frequency of a sinewave. You can then CALCULATE the precise delay for any frequency, based on phase. And no, there won't be just one number.
If a person cares to look in any book covering filter theory, they'll find gain/phase graphs that illustrate propagation or group delay. For lowpass filters, which is what most amplifers are classified as, low frequencies have little or even no delay while higher frequencies have more, such as the nominal 45 degree phase lag at the -3db point. A phase lag corresponds to a delay.
Kirkus you know who Atmasphere is right?
Negative feedback falls into the same category as damping factor both which alot of people dont understand including myself to a point,my counterpoint amp has a damping factor of i think 70 while the great or my bias is NOT GREAT digital amps go on and on about the high amounts of damping factor they trump on their stats.,My Counterpoint has plenty of bass ,it just has to be on the recording in the first place.
Kirkus, I appreciate your input as always, and I am always interested in expanding my knowledge. I don't contest what you are saying, the problem is that it does not address my experience. I went to school too, FWIW.

The issue I see is that if you have a wideband amplifier, and I do, the problem is that the squarewave response looks nothing like you described: it has a lot more in common with the input. It might be kind of strange to think about a tube amp that can do justice to a 10KHz squarewave but that is what I am talking about.

So my test for delay time holds together with very little error from the means that you suggest. If we were dealing with an amplifier with the limited bandwidth product you describe I would be more inclined to agree, except that there is still one problem.

It has been known since the mid-1950s that loop feedback enhances odd ordered harmonics and there were cautions expressed that long ago about excess use of Global negative feedback due to this problem. In the last 55 years that has not really changed- you can add feedback to an otherwise functional amplifier and experience and measure this phenomena. It is as I laid out earlier in this thread.

How do you square that reality against what you have stated?
Coffeey,
What are you talking about, and what does it have to do with this thread?
It has been known since the mid-1950s that loop feedback enhances odd ordered harmonics and there were cautions expressed that long ago about excess use of Global negative feedback due to this problem . . . How do you square that reality against what you have stated?
Atmasphere, this is not reality, it is rather a myth -- there are two soruces that I am aware of. First is Norman Crowhurst's 1957 AES paper on feedback in amplifiers (where he refers to "regenerative distortion"), and the second is from Peter Baxandall's 1978 series of articles in Wireless World (where he discusses the theoritecal possibility of an amplifier with only second-harmonic distortion generating higher orders through intermodulation with feedback). While I greatly respect both authors and recommend especially the Baxandall works for reading, this particular theory simply doesn't hold up in practice.

First of all, the point isn't about even-order distortion products becoming odd-order . . . it's about lower-order products becoming higher-order. In a push-pull topology (which cancels even-order products through another mechanism), that may be a supposition, but it's not part of the theory. Here's how it's supposed to work: If an amplifier has a strong second-harmonic distortion product, the addition of negative feedback causes the distortion and the fundamental to intermodulate and become third-harmonic . . . then the second and third intermodulate and become fifth-harmonic, the first and third become forth, etc. etc.

The counterpart to this is simply that negative feedback on the whole is so much better at eliminating distortion than generating it. I think Douglas Self put it concisely and eloquently in his book on power amplifier design (commenting on Baxandall, of which he is a huge admirer), so I'll quote him:
All active devices, in Class A or B (including FETs, which are often erroneously thought to be purely square-law), generate small amounts of high-order harmonics. Feedback could and would generate these from nothing, but in practice they are already there.

The vital point is that if enough NFB is applied, all the harmonics can be reduced to a lower level than without it. The extra harmonics generated, effectively by the distortion of a distortion, are at an extremely low level providing a reasonable NFB factor is used. This is a powerful argument against low feedback factors like 6dB, which are most likely to increase the weighted THD.
In addition, I've spent some time personally with the math behind this supposition, and done some SPICE simulation to back it up. The beauty of SPICE for this kind of application is that we can examine the feedback itself in its most pure, basic form, where it can exist without bandwidth limitations, stability problems, or any kind of loop "Propegation Delay".

First, I created a voltage stimulus with a controlled voltage source in series, to allow me to easily apply any amount of negative feedback, then another for open-loop gain. I then created another controlled voltage source, that adds a huge amount of pure second-harmonic distiortion (only 34dB below the fundamental!). No other distortion products exist, down to the FFT limits of about -200dB. I then applied various amounts of negative feedback, by changing the amount of open-loop gain. For a loop gain of 4 (12dB feedback), we see the 2nd harmonic drop to -52dB, a 3rd appear at -88dB, a 4th at -122dB, and a 5th at -155dB, and the 6th at -188dB.

So what does this mean? First, virtually any amplifier that's so ill-conceived as to have enough second-harmonic distortion as to be only 34db below the fundamental, will almost surely have some higher-order harmonics as well. But for even such an amplifier, adding just 12dB of feedback puts the third harmonic at -88dB, which will almost always be buried in the noise floor. And the rest (at <-120dB) will certainly always be undetectable and inaudible. But the improvement by knocking down the second harmonic to -52dB will be certainly be audible, and for the better. I think this supports Self's conclusion very nicely.

But there's another aspect of looking at this in SPICE -- these results exist in a world without any phase shift ("Propegation Delay") . . . meaning that they are equally valid for both local and global feedback! And the phase shift evident in real-world circuits can indeed introduce instability and transient-response problems (ringing), but it doesn't change the distortion-reducing effectiveness of feedback. So if you're truly worried about "regenerative distortion" . . . you'd better avoid all forms of local feedback as well. (Good luck with that!)

So again, if properly implemented, in the real world . . . negative feedback reduces ALL manners of distortion.
The issue I see is that if you have a wideband amplifier, and I do, the problem is that the squarewave response looks nothing like you described: it has a lot more in common with the input. It might be kind of strange to think about a tube amp that can do justice to a 10KHz squarewave but that is what I am talking about.
Thought I'd address this as well . . . I do applaud that you build amplifiers with wide bandwidth, and especially applaud that you're up front about some of the side-effects of your design approach, namely certain speaker incompatability from high output impedance, and poor power efficiency. These are quite reasonable choices for a niche product in an enthusiast market.

But in order to understand the theoretical basis for the proper application of negative feedback, you must understand the phase response of the amplifier in the frequency range(s) where the response rolls off - the stability of a feedback amplifier is inexoribly linked to its transition-band behavor. This is true no matter how extended the open-loop bandwidth may be . . . if it rolls off in an idiosyncratic manner, there will be instabilities if global feedback is applied.

Also, we can definately agree that there are many amplifiers out there using global negative feedback, that do indeed exhibit high-order distortion products and poor transient response (ringing). The point of my previous post is that these high-order products are virtually always present before the feedback is applied, and it's extremely common in many amplifiers for the feedback only to be effective at reducing the lower harmonics. Since a conventional three-stage solid-state Class B bipolar amplifier remains the poster child for global negative feedback (and higher-order distortion products) I think it makes the best example of why this is NOT caused by the feedback itself.

For this type of amp, all of the voltage gain is provided by the second stage, a transresistance amplifier . . . which can provide extraordanary amounts of gain with extremely good linearity. Its drawbacks are that it's very sensitive to loading, and the exact amount of gain you get is determined by the transistor's beta (the most variable characteristic of a bipolar transistor). But both this voltage amplifier stage and the differential input stage that preceeds it (if properly designed) will deliver extremely low distortion even without any global negative feedback.

Rather, virtually all the distortion comes from the output stage . . . in the real world, this is further exacerbated by the fact that thermal bias control is frequently inaccurate, the large half-wave currents drawn by the output stage can crosstalk into other parts of the circuit . . . it's also tough to keep nonlinear drive currents away from the preceeding voltage amp. So suffice it to say that there are lots of all kinds of distortion products being produced, of both low and high order harmonics, before feedback is ever applied. On top of it, the output stage is by far the slowest and most bandwidth-limited, with a rather unpredictable multi-order rolloff slope.

Now for the feedback. In order to have good stability, we need to have the open-loop gain and rolloff, and consequently the phase-shift, be predictable as frequency increases . . . this is done by applying freqency-dependent local feedback around the voltage amplifier in the form of the Miller compensation capacitor, reducing the gain at the rate of a tidy single-order slope as frequency increases . . . thus keeping the phase margin with feedback at 90 degrees.

So the open-loop response of a conventional solid-state amplifier, with compensation, is NOT wideband . . . its rolloff starts very much in the audioband, maybe at 200Hz or so? It's tough to measure and calculate, because the actual value is beta-dependent, and the low-frequency gain is super-high an difficult to measure. But as frequency rises and local Miller-capacitor feedback takes over, the open-loop gain becomes both lower and more predictable. And since the amplifier will have a flat closed-loop gain to well outside the audioband, what's happening is that as the frequency increases, the amount of global negative feedback actually decreases.

And when we look such an amplifier on the test bench, we might notice that for mid-band distortion, there are virtually no lower-order distortion products, but there are some higher-order harmonics. We also notice that the THD percentage rises with increasing frequency. But this is NOT a result of the feedback creating high-order products from lower-order harmonics . . . the distortion is all coming from the output stage and exists with or without feedback. What's actually going on is that for the higher harmonics and frequencies there's TOO LITTLE feedback to get rid of the distorion, because the compensation capacitor is causing the open-loop gain to fall at 6dB/octave. Also, the feedback has the benefit of lowering the noise floor, which can cause previously undetected/inaudible higher-order distortions to be uncovered.

The problem with solid-state feedback amplifiers in the 1970s was twofold: first, the power semiconductors of the day were SO slow that any form of compensation had to be pretty heavy-handed just to keep it from oscillating. And second, there were so many high-order distortion products from other aspects of the circuit that what little higher-frequency feedback was left had no chance of getting rid of it. The feedback was simply the big flashlight shining into the dark basement . . . and likewise it isn't the flashlight's fault when rats are discovered.
Kirkus: Nice post. Accurate and true to practice. One point of interest - distortion is a consideration for all type of signal processing. I spent decades designing signal acuisition and processing circuits for medical research applications. Negative feedback is employed in every discrete application that I saw or worked with - clinical as well as research. Although an amateur radio operator for decades and an electrical engineer by education and occupation for decades, I never encountered the "bad bad negative feedback" argument until I started looking around audiophile websites. Kind of wonder where the better theory is, huh? Thanks for the information as to the origin of this myth in audiophile circles. Also nice cite to Self's book
Thanks Kirkus for your response. I tend to go with Norman Crowhurst rather than Baxandall. However I've been researching this issue myself for some years and while I regard ignorance of the past as foolhardy, I also try to keep an open mind.

I would like to direct you to an article written by Nelson Pass that is on his website, the one about distortion. I think you will see right away what the issue is, he, like myself, tends to work with empirical measurement rather than simulation. Spice is great for a lot of things but I regard it as inaccurate when subjected to the real world- it is quite good for economizing the design side though.

In a nutshell Nelson encountered some odd orders in his study, that in order to eliminate them, he figured levels of feedback that are in excess of 50 db, requiring increased gain, which means more distortion, so more feedback...

OTOH these distortion levels are absent in zero feedback amplifiers of proper design. You can count on one hand the number of transistor amps that meet that description (Nelson's is one of them and no surprise that his amps get high accolades).

I've been looking at what Chaos Theory has to say about negative feedback. What I have been seeing is that Chaos Theory describes an audio amplifier with feedback as a chaotic system with stable areas of performance. The problem here is that we are dealing with non-repetitive signals, but for our tests we use sine and square waves. The behavior of an amp with feedback with repetitive input signals is your stable area of operation; when non-repetitive signals are used the amplifier can become chaotic, particularly at higher powers but can do it at any power level.

Distortion is known as bifurcation in Chaos Theory; what we see in an amplifier with feedback is the bifurcation elements do indeed behave as Crowhurst predicts, and interestingly enough and apparently not coincidence, the formula he shows for feedback in an amplifier are startlingly similar to the formulas used in classic Chaotic systems. He goes so far in his books to actually show an example of the strange attractor that models amplifier-with-feedback behaviour, years before Chaos Theory was established.

Nelson Pass, while not mentioning Choas, does point to a tell-tell aspect of chaotic behavior, that of having to add more and more feedback to get rid of the higher odd orders (with attendant greater amounts of gain required to do so).

This is very similar to the way noise behaves in digital circuits, due to Cantor Dust and is the reason we use parity bits in all digital communications. When IBM was first studying the problem of noise in digital circuits, they were trying to make the signals bigger to overcome the noise, which Chaos showed was not going to work. The parity bit was the solution- IOW don't try to fight the Cantor Dust.

In a similar way, its telling us the same thing about feedback. IOW, negative feedback is a **destabilizing** aspect of amplifier design. Amps without feedback are inherently stable. I have seen this borne out in practice: some amps with feedback oscillate just by the use of certain speaker cables, but there is no zero feedback amp that will do that. More importantly, Chaos supports Crowhurst with regards to bifurcation and predicts harmonic and inharmonic generation in the way that Crowhurst specified. In fact it appears that we are not altering the energy of the bifurcation- we are taking the energy and spreading it out over frequency. Some of these frequencies are well past the band-pass of many amps, so in a way we are getting rid of the energy to a certain degree, OTOH the ultrasonic behavior of an amplifier often says a lot about how it sounds. I am sure you have encountered that!

It is a fascinating study. If you are not familier with Chaos Theory you can start at http://en.wikipedia.org/wiki/Chaos_theory
Ralph is there a relationship that exists between negative feedback and damping in relation to how the amp(s) react to the what a speaker reflects back to the amp? So when you see a amp with high damping specs it means a large amount of feedback is being used;would that be right or wrong?
Rleff, that is mostly right; damping factor is the ratio of load impedance vs that of the amplifier driving it, and can be increased by adding negative feedback. Some amps achieve a high damping factor with zero feedback, the Ayre is an example of that.

The question is whether high damping is desirable. There are no known speakers requiring a damping factor of over 20, and there are some that are better off if the damping factor is between 0.1:1 and 2:1.

This is very much a part of the equipment matching conversation!
"There are no known speakers requiring a damping factor of over 20"

I am not aware of any speakers that publish damping requirement specs. What are some?

I am aware that different designs benefit differently from varios damping factors, but not that vendors specify damping requirements for their speakers in that determining which combos sound good is often a largely subjective determination?
Thanks Ralph good information.

I'm not sure if DF>100 makes much sense since inductor in series with the woofer has resistance in order of 0.08ohm.

8/0.08=100
Ralph, this is the wrong place to ask, but would you care to answer the math as proposed by:

http://www.transcendentsound.com/amplifier_output_impedance.htm

Just trying to get a grasp on the "how". The other controversial article is not related to this thread.

Fascinating relating electronics to chaos theory. Maybe we can use it to predict long term digital format forecasts.
The math is fine right up the 2nd to last paragraph where an assumption is made that is incorrect. It matters a lot what the output section topology is. An excellent example is the difference between a triode gain stage and a cathode follower using the same triode. The CF will be found to have a lower output impedance, according to Rp/1+mu where Rp is the plate resistance and mu is the 'voltage gain' of the tube.

So if we take the example given we get 17.5/3 = 5.767 (the mu of a 6AS7G is 2), which is for a simple CF circuit. For a Circlotron, which is a CF variant, the formula is similar, the 1 is replaced by a 2 as above so we get 17.5/4 = 4.375

In these cases it is assumed there is no feedback.
It is like a boob job. Too much and you are all over the place.
I don't believe it is fair to talk about damping factor without mention of speaker 'Q'.
A hi DF and a 'Q' of over say....1.3 will still produce sloppy bass as will a very low DF and a critically damped 'Q' of .707
Also, no mention has been made of Voltage source vs Current source amplification, and the speakers which are best suited for each.
'Current source' is what I call the Power Paradigm, as amps in that category try to make constant power, rather than constant voltage. Its the intention of the designer of the speaker that puts the speaker into the Power camp as opposed to the Voltage camp.

The pivotal issue herein is feedback: Voltage source amps tend to use feedback to create the voltage source aspects. A price is paid for this: odd ordered harmonics, which is responsible for brightness or hardness.

Nelson Pass' 1st Watt amps are an example of a 'current source' (Power Paradigm), just like many low powered SETs.

The Power Paradigm vs Voltage Paradigm is really what we are talking about here, the same is true of tubes vs transistors and the importance of amp/speaker matching:
http://www.atma-sphere.com/papers/paradigm_paper2.html
I would like to direct you to an article written by Nelson Pass that is on his website, the one about distortion. I think you will see right away what the issue is, he, like myself, tends to work with empirical measurement rather than simulation. Spice is great for a lot of things but I regard it as inaccurate when subjected to the real world . . .
I take it this is the article to which you're referring? http://www.passlabs.com/pdfs/articles/distortion_and_feedback.pdf
There are numerous problems with this paper -- namely, Pass (in his Fig. 9 test circuit) doesn't analyze the likely difference in the bandwidth between the forward path and the feedback path, as a result of the high output impedance of the circuit coupled with the mosfet's input capacitance. Second, he didn't necessarily keep the drain load constant with or without the feedback in place, which may affect circuit linearity. And then there's the source degeneration resistor R4 . . . this is feedback exactly like R2, no? Why is it somehow more okay? And then there's the drop in noise floor that could reveal higher-order harmonics that were there before feedback. No offense to Nelson Pass, I like him and his work, but this paper definately shouldn't be considered cannon.
I've been looking at what Chaos Theory has to say about negative feedback. What I have been seeing is that Chaos Theory describes an audio amplifier with feedback as a chaotic system with stable areas of performance. The problem here is that we are dealing with non-repetitive signals, but for our tests we use sine and square waves. The behavior of an amp with feedback with repetitive input signals is your stable area of operation; when non-repetitive signals are used the amplifier can become chaotic, particularly at higher powers but can do it at any power level.
I have two huge problems with this argument . . . first is that an audio amplifier does NOT qualify as a chaotic system, and second, a thorough classical analysis of an amplifier provides excellent correlation with both measured and subjective listening data. In audio, there's only one good reason to jump straight to "quantum" or "chaos" explanations . . . and that is to obfuscate the presence of misunderstandings of traditional electrical theory.

On Chaos Theory . . . please re-read in the link you provided the three required properties for a system to be considered chaotic:
In common usage, "chaos" means "a state of disorder",[19] but the adjective "chaotic" is defined more precisely in chaos theory. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[20]

1.it must be sensitive to initial conditions,
2.it must be topologically mixing, and
3.its periodic orbits must be dense.
An amplifier certainly is NOT sensitive to initial conditions, this refers to the STIMULUS condition, NOT circuit operating parameters. It may be topologically mixing to a small degree if one considers the possibility of intermodulation with uncorrelated noise. But its periodic orbits are anything but dense, and feedback reduces the density of those orbits, which is why it reduces noise and distortion. Even considering an unstable oscillation-prone feedback amplifier . . . the oscillation state itself corresponds to the least amount of density in its periodic orbit. (Density of periodic orbit has NOTHING to do with the complexity of the input signal).
OTOH the ultrasonic behavior of an amplifier often says a lot about how it sounds. I am sure you have encountered that!
Oh, absolutely, especially if feedback is involved . . . but Chaos Theory isn't necessary or appropriate to analyze why this is so. Classical filter theory shows that for the most accurate in-band transient response, the transition-band behavior should correlate to a minimum-phase (first-order) slope, or a Bessel function. So as I said before . . . an idiosyncratic rolloff slope, coupled with rising THD vs. rising frequency (due to limited open-loop bandwidth, as I explained in my previous posts) . . . is more than enough to explain pretty much all of the negative subjective opinions of negative feedback.

That is to say . . . harsh and strident sound? Poor imaging? Fatiguing to listen? Artificial, mechanical, and non-musical? Yes, these impressions fit perfectly with measured data of many amplifiers that use lots of feedback, and also with many that don't. And in my experience, that measured data points clearly to innumerable other mechanisms that can be clearly linked to the problem.
Roxy Ah lets make this simple,feedback is touted as bad correct? Got that?
High damping factor is touted as good. correct?
What i said was these figures are often misunderstood.Meaning that they can be irrelevant to the actual sound of a component,IE low feedback or no feedback doesn't have to equal good sound,High damping doesn't have to equal better sound either,its the final sound that counts.
Kirkus, I do have a problem with this:

And then there's the source degeneration resistor R4 . . . this is feedback exactly like R2, no? Why is it somehow more okay?

Degeneration occurs in real time against the signal and so is not part of this argument. It is different from loop feedback in that regard and that is why it is 'somehow more okay'.

Further, Nelson has succeeded in building wide-bandwidth amplifiers wherein the passband is unaffected by the addition of feedback, much like our amplifiers are. So the -6 db slope issue does not play into this. Now I have mentioned this before but I see in your responses that you always go back to the rolloff issue. I concede your point that that regard, but don't see it as relevant- it applies to opamps and similar circuits of the type you have described. However I should point out that it is those circuits that do enhance odd orders, so if not my explanation than what is it?

I have avoided the proof in the pudding aspect of all this, but at some point it will come to bear on this in a big way if Nelson's and my explanations are not to be accepted by you, I am hoping you will explain what the phenomena really is, since your explanations so far have not addressed that.

As to Chaos, an initial comment: we are really, seriously, **NOT** talking about *anything* with the word 'quantum' in it! As far as audio goes, use of the word 'quantum' is the nutbag identifier, IMO/IME :) Seriously. Chaos theory OTOH is a science of complex systems, wherein a simple set of rules governs what seems a complex behavior, often with unexpected results.

FWIW, in any field of endeavor, when Choas theory is applied, there is usually a howl of protest from the establishment. That is, until said establishment realizes the actual implications. The result has been improved weather forecasting, improved aircraft efficiency, improved hydraulic pumps, improved genetics, improved disease control, improved exhaust and combustion and now I am suggesting that it can improve audio reproduction as well.

So, to Chaos:

In common usage, "chaos" means "a state of disorder",[19] but the adjective "chaotic" is defined more precisely in chaos theory. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[20]

1.it must be sensitive to initial conditions,
2.it must be topologically mixing, and
3.its periodic orbits must be dense.

condition 1 is satisfied, as the signal and gain conditions are always different. Even a digital source can't be assumed to be 100% *exactly* repeatable, humidity in the room can affect the way the loudspeakers behave, which will affect the way the amp responds. Keep in mind that we are talking about a wide range of amplifiers here.

There is a great example of how water dripping from a tap is an example of a Chaotic system. People walking in other parts of the building, variations in water pressure, temperature and actually a huge variety of other issues all come into play. The same is true of an audio signal, there are all sorts of variations that affect it as audiophiles are only too keenly aware: line voltage, noise on the line, noise in the environment, warmup of the amp, break-in considerations, interaction of cables, corrosion of components (such as inside semiconductors and inside switches) and connections; this is a list that knows no end!

condition 2 is satisfied by the fact that the bifurcation that arise are not consistent. The problem is the only means we have of analyzing distortion is through steady-state waveforms, which tell us nothing about the dynamic state of the amp.

condition 3 is satisfied by the strange attractor, which is quite dense. I refer you to Norman Crowhurst on that one. His writings may be old, but it would be foolhardy indeed to cast them aside by using the logical fallacy known as 'guilt by association'.

Frankly, given the research I have done, I suspect that Crowhurst is spot on. Occam's Razor suggests that when his writings and Chaos agree on so many points (only a few of which have been touched on here), the simple explanation is that he is probably right. The very complex explanation is that he is wrong, but it just turns out that in spite of that, things behave the way he and Chaos say they do but for entirely different reasons. I think the point of this is that there is a frontier here; I find the idea that we know everything already is arrogance and nothing more.
Ah, Atmasphere, thanks for your response . . . I think we're getting somewhere here. Let's start with:
Degeneration occurs in real time against the signal and so is not part of this argument. It is different from loop feedback in that regard and that is why it is 'somehow more okay'.
The source degeneration and drain load resistor are indeed identical mechanisms, and both occur in "real time", it must because the same current flows through both resistors! (see Kirchoff's laws) Yes, they do behave differently, but this is simply because the output impedance is higher from the drain than from the source. In both cases, the bandwidth available for the negative feedback is defined by the gate capacitance of the mosfet, but when it's driven by the higher impedance of the drain, the rolloff of course starts sooner (higher impedance driving the same capacitance). So if you build two circuits with identical low-frequency gain, one with a capacitor-bypassed source resistor and a feedback ladder from the drain, and the other with only source degeneration, the amount of feedback available as the frequency rises is less from the former. THIS is why it is less linear, and has poorer phase margin, and is more likely to have a peak in its ultrasonic response before rolloff (less feedback makes its gain increase).
Further, Nelson has succeeded in building wide-bandwidth amplifiers wherein the passband is unaffected by the addition of feedback, much like our amplifiers are. So the -6 db slope issue does not play into this. Now I have mentioned this before but I see in your responses that you always go back to the rolloff issue. I concede your point that that regard, but don't see it as relevant- it applies to opamps and similar circuits of the type you have described.
I always go back to the rolloff issue, because analyzing relationships between open-loop and closed-loop bandwidth, a.k.a. rolloff, is the fundamental cornerstone of understanding how feedback works. And as far as I'm concerned, if one condemns the use of negative feedback, and hasn't gone through the process of figuring out where the poles and zeros in the response fall, and analyzing the phase margin . . . they simply haven't a leg to stand on.
However I should point out that it is those circuits that do enhance odd orders, so if not my explanation than what is it? . . . I am hoping you will explain what the phenomena really is, since your explanations so far have not addressed that.
I think I have, several times. They are the result of circuits that have the following:
-Nonlinear open-loop transfer functions that cause both low- and high-order distortion
-Topologies (i.e. differential, push-pull) that are more effective at cancelling even-order distortion products than odd-order
-Feedback (and hence closed-loop linearity) that decreases as frequency increases.
Put the three together, and you have a system that enhances higher-order, and odd-order distortion products. But the root cause is NOT the feedback.
FWIW, in any field of endeavor, when Choas theory is applied, there is usually a howl of protest from the establishment. That is, until said establishment realizes the actual implications. The result has been improved weather forecasting, improved aircraft efficiency, improved hydraulic pumps, improved genetics, improved disease control, improved exhaust and combustion and now I am suggesting that it can improve audio reproduction as well.
Well, I'm definately with you on the idea that the entire reproduction/perception chain can be thought of as a Chaotic system. But in order to be applicable, there needs to be a large volume of data that's both accurate, and seemingly uncorrelated . . . of which we must make sense. And the required function of an amplifier is pretty damn simple - this is what's meant by a lack of density in periodic orbits. Now if you have a large mixing console with a few hundred or so cold solder joints and dirty potentiometers, then we have a chaotic system . . . the various possibilties of output voltages from various sections of the console cover a dense cloud of results.
Frankly, given the research I have done, I suspect that Crowhurst is spot on. Occam's Razor suggests that when his writings and Chaos agree on so many points (only a few of which have been touched on here), the simple explanation is that he is probably right.
Einstein's razor is frequently quoted to counter Occam's:
It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.
To paraphrase - the best explanation is as simple as possible, but no simpler. And in discussing negative feedback in audio, I find it very unfortunate that the data resulting from a proper stability and bandwidth analysis are surrendered without representation . . . an alarming percentage of the time.
The source degeneration and drain load resistor are indeed identical mechanisms, and both occur in "real time", it must because the same current flows through both resistors! (see Kirchoff's laws) Yes, they do behave differently, but this is simply because the output impedance is higher from the drain than from the source. In both cases, the bandwidth available for the negative feedback is defined by the gate capacitance of the mosfet, but when it's driven by the higher impedance of the drain, the rolloff of course starts sooner (higher impedance driving the same capacitance).

There are a couple of problems I see with this. First, we have a capacitance involved, so there is a time issue associated with the related phase issues of that capacitance. If we have a series of these circuits together, we will be able to measure a delay time to it. So- where does it come from? It probably the circuit itself, ergo it has a delay time too.

And as far as I'm concerned, if one condemns the use of negative feedback, and hasn't gone through the process of figuring out where the poles and zeros in the response fall, and analyzing the phase margin . . . they simply haven't a leg to stand on.

And if one *did* go through that exercise, and still finds the feedback to be detrimental, what then?

I think I have, several times. They are the result of circuits that have the following:
-Nonlinear open-loop transfer functions that cause both low- and high-order distortion
-Topologies (i.e. differential, push-pull) that are more effective at cancelling even-order distortion products than odd-order
-Feedback (and hence closed-loop linearity) that decreases as frequency increases.
Put the three together, and you have a system that enhances higher-order, and odd-order distortion products. But the root cause is NOT the feedback.

This **sounds** like an argument for adding feedback to an SET, although I suspect that its not. But an SET can lack the issues above, yet still be degraded by the use of feedback. I myself use fully differential circuits and have to jump through a lot of hoops to prevent odd-ordered generation (we wind up with the 3rd but none of the higher orders) but otherwise our amps don't have the issues you present above either. Yet when feedback is added, increased odd ordered harmonic distortion can be measured (although its tricky as the increase is very slight; OTOH it does not take much as the human ear uses odd orders to gauge volume so tiny amounts are instantly audible).

Frankly, this last quote seems to indicate that feedback should not be used as the circuits that have these issues would seem like something to be avoided.

Of course a complete audio system has a Chaotic behavior. But amplifiers do too. If you look at the formula for feedback, its nearly identical to the feedback formula for classic chaotic models. IOW, we have a strange attractor that models the amplifier's behavior under feedback, we have the other conditions of classic chaotic systems: if it walks like a duck, quacks like a duck... BTW, 'dense orbit' refers to the strange attractor. If you look at a simple pendulum, it is a classic example of a chaotic system and we have been using them for mechanical timing mechanisms for several hundred years. It is often the utter simplicity of chaotic systems that is what throws people off- why they initially don't want to look at things as being Chaotic. BTW its important to understand that the term 'Chaotic' is not the same as the typical dictionary meaning.
You guys are in way over my head! I can sort of follow the tech talk but have no way to translate that into results regarding actual sound quality to expect via the various design approaches.

I'm curious to see the bottom line in the end ie what key points relating to feedback and sound quality you two agree and disagree on. Perhaps also if there are any amps most might be familiar with that are good representatives of how the different technical approaches sound.
That might actually be simpler- the proof in the pudding. Kirkus and I have had plenty of exchanges in the past and I have always respected his demeanor, but at the same time I do not think there is anything that I could say that would change his mind- he clearly knows his book larnen'.

OTOH, I'm pretty sure that I'm likely to stay put too. If I had not spent so much time doing this, I might be easier to convince.

So maybe, we choose the amps from the two camps that we think are the best examples of feedback and no feedback.
The tech talk is over my head too, but I'll say that the best amp I've heard of late that uses feedback is the Music Reference RM-10 MkII.