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
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