john curl said:
John, the physical explanations for the JFET and MOSFET main deviations from a pure square law are known for decades as well: they are called "carrier mobility saturation" and "channel length modulation".
The Spice JFET and MOSFET model templates do have provisions to model these phenomena; this doesn't mean that a particular model has these features implemented. Simulations can't be better than the models it uses and blindly relying on models provided by device manufacturers is not necessary accurate, therefore one has to calibrate these models against the data sheets and/or, even better, against measurements. Validating models is a difficult and time consuming task; in certain circumstances, I can understand one choosing to build the thing rather than spending time, energy and ultimately money in an pretty abstract exercise that may be beyond the expertise of an audio circuit designer.
Hugh wrote:
That's quite right, Hugh. You can confidently stand your ground here. If Jan does his maths he'll see that the distortion reduction of the NFB loop varies at different points in the loop. The fact that the loop gain is the same at every point does not imply that the distortion reduction is the same every point.
That's quite right, Hugh. You can confidently stand your ground here. If Jan does his maths he'll see that the distortion reduction of the NFB loop varies at different points in the loop. The fact that the loop gain is the same at every point does not imply that the distortion reduction is the same every point.
Distortion reduction doesn't need to be the same at every point. We only need to concern ourselves with distortion at the output. Distortion that exists in between only concerns us to the extent that it results in distortion at the output. Sometimes sacrificing linearity for more open loop gain is very beneficial.
I haven't had time to think this one through as well as I'd like, but let me toss an idea in here before I go home and drink sufficient quantities of eggnog to flatten my brain cells.
I read the Stereophile article that andy_c linked to above and although it didn't say anything that I didn't already know, it said it in slightly different words and it started a train of thought that goes something like this:
1) I've said before that I regard high feedback as creating a problem regarding imaging. I'm not the only one who says such things, but there aren't necessarily that many of us so take this as a reminder of what I've said elsewhere, which leads me to...
2) Imaging, although not exactly mathematically definable, isn't completely an unknown quantity. The human ear is increasingly sensitive to direction as frequency increases. There are two quarries roughly a mile, as the crow flies, from my house and when they blast I can tell the direction of the WHUMP! only as a vague over thataway kind of thing, but if someone whispers, the sibilance is an immediate attention getter, almost as though there's a neon arrow pointing at the person who's whispering. The distance between the listener's ears and phase relationships and a host of other things figure into it, but that's a distraction at the moment. Just take imaging as a primarily mid and high frequency phenomenon.
3) Imaging information is low in level. The difference between the dB level of the direct sound vs. the echoes is large.
4) If we are looking at creation of distortion products at several multiples of the original frequency as a direct consequence of feedback, then low to mid frequency information will reflect upwards throughout the midrange (in the case of low frequencies) or treble (in the case of midrange).
My thinking goes like this:
--Given that the ambient information is low in level, it will be comparatively easy to obscure. Think of it as a special case of S/N ratios (no, I'm not particularly happy calling it that, just take it as an analogy), where the imaging information is partially obscured by the distortion products of frequencies 1/7th (just picking a harmonic at random) of the imaging information. Although the reality is far more complex, if there is a tone at 1kHz, then the harmonic at 7kHz will be competing with any imaging information at that same frequency, making the image harder for the listener to discern.
--Implied within that--assuming that there's anything to what I'm thinking--is the idea that simpler signals, say a solo human voice compared to a full symphony, will image better on a high feedback circuit than a more complex signal because there are few frequencies below it to create troublesome harmonics that compete with the image.
Thus:
Given comparable complex signals, a low to no feedback circuit should image better than a high feedback circuit because it has a better dynamic S/N ratio as regards to imaging. Given a simple signal, the low feedback circuit and the high feedback circuit would image more nearly the same. The difference would become more apparent as the two circuits were given more and more complex source material to work with. Furthermore, the quality of the image on a high feedback amp would vary with the signal. If the cellos, basses, or an organ (St. Saens Third, for example) came on strongly, then the image would deteriorate. The image on a low feedback amp would remain more nearly stable. This could conceivably lend credence to the oft-repeated observation that tube amps (i.e. low feedback) have a "rock solid" image; something not often said in reference to solid state designs.
If there's anything to this, even if it lacks a mathematical solution it would at least go part way towards providing a theoretical answer for the question "How could feedback possibly harm the image when it should in theory improve it?"
Grey
I read the Stereophile article that andy_c linked to above and although it didn't say anything that I didn't already know, it said it in slightly different words and it started a train of thought that goes something like this:
1) I've said before that I regard high feedback as creating a problem regarding imaging. I'm not the only one who says such things, but there aren't necessarily that many of us so take this as a reminder of what I've said elsewhere, which leads me to...
2) Imaging, although not exactly mathematically definable, isn't completely an unknown quantity. The human ear is increasingly sensitive to direction as frequency increases. There are two quarries roughly a mile, as the crow flies, from my house and when they blast I can tell the direction of the WHUMP! only as a vague over thataway kind of thing, but if someone whispers, the sibilance is an immediate attention getter, almost as though there's a neon arrow pointing at the person who's whispering. The distance between the listener's ears and phase relationships and a host of other things figure into it, but that's a distraction at the moment. Just take imaging as a primarily mid and high frequency phenomenon.
3) Imaging information is low in level. The difference between the dB level of the direct sound vs. the echoes is large.
4) If we are looking at creation of distortion products at several multiples of the original frequency as a direct consequence of feedback, then low to mid frequency information will reflect upwards throughout the midrange (in the case of low frequencies) or treble (in the case of midrange).
My thinking goes like this:
--Given that the ambient information is low in level, it will be comparatively easy to obscure. Think of it as a special case of S/N ratios (no, I'm not particularly happy calling it that, just take it as an analogy), where the imaging information is partially obscured by the distortion products of frequencies 1/7th (just picking a harmonic at random) of the imaging information. Although the reality is far more complex, if there is a tone at 1kHz, then the harmonic at 7kHz will be competing with any imaging information at that same frequency, making the image harder for the listener to discern.
--Implied within that--assuming that there's anything to what I'm thinking--is the idea that simpler signals, say a solo human voice compared to a full symphony, will image better on a high feedback circuit than a more complex signal because there are few frequencies below it to create troublesome harmonics that compete with the image.
Thus:
Given comparable complex signals, a low to no feedback circuit should image better than a high feedback circuit because it has a better dynamic S/N ratio as regards to imaging. Given a simple signal, the low feedback circuit and the high feedback circuit would image more nearly the same. The difference would become more apparent as the two circuits were given more and more complex source material to work with. Furthermore, the quality of the image on a high feedback amp would vary with the signal. If the cellos, basses, or an organ (St. Saens Third, for example) came on strongly, then the image would deteriorate. The image on a low feedback amp would remain more nearly stable. This could conceivably lend credence to the oft-repeated observation that tube amps (i.e. low feedback) have a "rock solid" image; something not often said in reference to solid state designs.
If there's anything to this, even if it lacks a mathematical solution it would at least go part way towards providing a theoretical answer for the question "How could feedback possibly harm the image when it should in theory improve it?"
Grey
Just before the sleeping giant is awoken, let me clarify because my earlier reply was poorly written. The simple point I was trying to make is that the rejection of distortion at the output varies with the location of the source of that distortion within the loop. Output distortion is much more sensitive to distortion in the input subtractor than distortion in the output stage. This is easy to prove mathmatically.
Your point, that distortion reduction does not need to be the same at every node, is right but you could really tighten the screws on this statement without losing any of its truth.
Oh, I am a big fan of North American egg nog...the stuff in the cartons in the supermarkets. I can't get enough of it when I'm over there at this time of year. Sadly, I have never found it anywhere in the UK. But I suppose my coronary arteries are probably grateful.
Brian
BTW, the egg nog is working well for you.
I do remember the article by Peter Baxandall where he showed that, as long as you have reasonbly low distortion (I think his limit was -60dB), the output distortion with undistorted input is equal to the input distortion required to have an undistorted output. Or vice versa.
Brian, are you saying that if I have two amps, one with a linear output stage but a distorting input subtractor, and another with a linear input subtractor but a distorting output stage, that these would have different closed loop distortions? All else being equal, of course?
Jan Didden
Brian, are you saying that if I have two amps, one with a linear output stage but a distorting input subtractor, and another with a linear input subtractor but a distorting output stage, that these would have different closed loop distortions? All else being equal, of course?
Jan Didden
Others have used this argument as well. In the Barrie Gilbert article "Are Op-Amps Really Linear?" that's been discussed at length here, Gilbert assumes an undistorted sinusoidal output signal and works his way back to the input, calculating what the distorted input would have to be to get that output.
Also, Cherry uses the same argument in his AES article "Estimates of Nonlinear Distortion in Feedback Amplifiers", coining the "anti-distortion" phrase.
One argument that shows this assumption can't possibly be true in general is to assume the output of the amplifier is an undistorted sine wave whose maximum rate of change exceeds the amplifier's slew rate. That's an unrealizable condition, so there is no input signal that can be found that results in the assumed output signal.
Also, Cherry uses the same argument in his AES article "Estimates of Nonlinear Distortion in Feedback Amplifiers", coining the "anti-distortion" phrase.
One argument that shows this assumption can't possibly be true in general is to assume the output of the amplifier is an undistorted sine wave whose maximum rate of change exceeds the amplifier's slew rate. That's an unrealizable condition, so there is no input signal that can be found that results in the assumed output signal.
Ok Andy. I was going to look at something like a gain block with, say, an x^n function and then, for perfect correction, you can see the "inverse distortion" required at its input is x^(1/n). Then if the % THD for the two functions is not the same then Baxandall's conjecture is false in general. I'd be surprised if all or even many functions have the same THD% as their inverses. This is without taking more pernicious distortions into account, like delays and clipping, as you've pointed out.
<edit>
Fizzard, have you got a proof?
<edit>
Fizzard, have you got a proof?
traderbam said:
There's formulas for the Taylor series coefficients of the inverse of a function in terms of the Taylor series coefficients of the function itself. I suspect that using a "weak nonlinearity" assumption and these formulas, one could make a good case. It seems like it would be really hard to prove in the case where the nonlinearity is not memoryless though.
Edit: Cherry's paper only covers the second and third harmonics. It's been a while since I've read it, so maybe it would be worthwhile to look at it again.
Yes of course, if you are clipping (or, rather, your amp ;-) ) or assuming a physically impossible output wave (like a pure sine with a slew rate too large for the amp to handle), of course the conjecture doesn't hold. That is self-evident, and doesn't diminish the idea as such. I find Baxandall's reasoning very elegant and coinvincing.
What Brian mentioned for the 'inverse' distortion assumes that Baxandall means that the inverse distortion would be the same level, shape, spectrum and phase as the output distortion view. I don't think he said that; I read that he means that the TDH (RMS?) is the same. And, if that is true (within reasonable limits), it lets him use a different way to calculate THD from the amp characteristic - by viewing it as distorted input necessary for undistorted output. So, rather than a dogma that it is always perfectly true, he presents it as a usefull tool that gets the job done. And that is how it should be judged.
Jan Didden
What Brian mentioned for the 'inverse' distortion assumes that Baxandall means that the inverse distortion would be the same level, shape, spectrum and phase as the output distortion view. I don't think he said that; I read that he means that the TDH (RMS?) is the same. And, if that is true (within reasonable limits), it lets him use a different way to calculate THD from the amp characteristic - by viewing it as distorted input necessary for undistorted output. So, rather than a dogma that it is always perfectly true, he presents it as a usefull tool that gets the job done. And that is how it should be judged.
Jan Didden
janneman said:
Yes, I agree. But then it raises the question of "what are the set of conditions under which the assumption does hold?". This question is an important one I think, because having a clear answer to it prevents the potential problem of leaning on the result in a situation in which it does not apply.
andy_c said:
The central condition for it to be true is that, at the input, the signal fed back to the input is very nearly equal to the undistorted input signal Vin; the two cancel to a high degree, leaving the distortion signal as the effective input signal. This already shows that things like slew rate limiting and clipping, where the fed back signal is rather smaller than the undistorted Vin, are outside of this conjecture.
Jan Didden
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