What is wrong with negative feedback?

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.

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?