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? |
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. |
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. |
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. |
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. |
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. |
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.pdfThere 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. |
