Bob Cordell Interview: Negative Feedback

[PMA]

Lumanauw, there is no puzzle what happens during that transition.

John, OK, I got your hint. I may try something. Or maybe I even tried. How about this?

[john curl]

Looks good, what is the ratio? Just the mV drop is OK.

[PMA]

In my experience, it is not that difficult into 8 ohm (I speak about non-overall NFB still). 4 ohm, or even 2 ohm, that is a real challenge, and difficult to drive without high order harmonics rise.

[john curl]

But what is the ratio?

[PMA]

Good question. Let me be mysterious as well.

[john curl]

OK.

[Bob Cordell]

Originally posted by john curl
PMA, the whole point is to be in the class AB transistion. Anybody can do OK class A. It is the 7th harmonic generated during the class AB transition that is the MOST important factor to me. It 'may' be that there is an optimum Re to Iq ratio that is not optimum for lowest overall THD, BUT is best for lowest 7th Harmonic distortion for a given Iq. This is where a computer could be very valuable. For example, I usually recommend 15mV-25mV drop across the resistor. However, maybe 35mV gives lowest 7th harmonic distortion at the transistion. I don't know yet. Or, it might be 9mV gives lowest 7th harmonic distortion. Or maybe there is NO 7th harmonic minimum for a given Iq. Who knows?

Hi John,

You make a very good point here. Some of the crossover distortion sims I've done show that different elements of the spectra are smaller at different relative bias points.

What value of closed-loop 7th harmonic would you like to get down to, and for what fundamental frequency?

Alternatively, how far down would you like the 7th order component (i.e., at 16 kHz) of the 19 + 20 kHz CCIF IM test to be?

Cheers,
Bob

[john curl]

Lowest that is practical. Feedback is OK but it should not be infinite.

[Bob Cordell]

Originally posted by morricab
I noticed in the discussion about NFB and distortion that AndyC simulation was beginning with essentially no starting distortion. What has been done to simulate real circuits where the inherent distortion properties of the devices themselves are added into the mix? For example there was a study done by Boyk and Sussman showing distortion for simple single devices and then complementary (or pushpull for a triode) and a differential circuit.

They go far beyond Baxandall in simulating out to I believe the 20th harmonic.

http://www.its.caltech.edu/~musiclab...er-acrobat.pdf

I think it is interesting that for both the BJT and for the Triode they show a full spectrum of distortion products. What is interesting in their simulation is that for a given input voltage the amplitudes of the distortion products for the triode are much lower than for the BJT. It is also interesting to note that they show with NFB that the BJT all harmonics reduce in level.

For the case of the MOSFET they show that in Class A with no feedback one gets only low order and even harmonics for a single ended case but for pushpull if the circuit is not pure Class A there are problems and feedback doesn't improve the situation. For pure Class A with perfectly matched FETS they show no distortion at all and adding feedback doesn't result in the generation of any. Again for a given input voltage the distortion amplitude is higher for a FET than for a tube.

If these results could be combined into one of the more complicated circuit design simulations do you think we would then get a more realistic picture of what is going on audibly?? The problem is, and I agree with John Curl here, that what the meter reads and what we hear don't agree very well with normal distortion measurements.

Someone also mentioned that Self believes that once the distortion is in the noise floor it is no longer audible but is this really true and how low is really low enough? After all distortion is signal correlated and true noise is not. We hear below the noise floor all the time when listening to analog tape (the hiss being true random noise) to correlated music signal. Has this been answered conclusively? If not then perhaps knowing the limit first would be useful for optimizing the designs.

Finally, I remember reading an article on distortion by Crowhearst where he showed mathematically that feedback would multiply the order of the distortion as its fed back with the conclusion that what might appear to be noise floor is in fact a myriad of harmonic and intermodulation distortion peaks making essentially a signal correlated "noise" floor, which in reality was distortion and not noise. I am sure most have read this article but is it discredited or has it still some relevance to the discussion? If it has been discredited then please explain to me where the flaw in his logic lies.

Hi Morricab,

You raise a lot of good questions here, and I’ll try to answer them, at least as far as I see it.

Thanks for bringing the paper by Boyk and Sussman to our attention. It made for some interesting reading. As I’ll discuss below, their findings are not at variance with what Baxandall found or with what has been presented here in some earlier posts. Indeed, I’m quite surprised that they did not reference Baxandall’s work in their paper.

As a curious aside, here we have two professors, one from MIT and one from Cal Tech, writing a paper on distortion simulation in the year 2003 and not breathing a word about SPICE. They used numerical analysis procedures written by Sussman and suffered with crude device models instead. What is wrong with this picture? Are they unaware of the capabilities of SPICE in this application? On the other hand, if they were aware of SPICE’s capabilities and thought them unsuitable, one would have expected them to mention that somewhere. Very curious.

While Boyk and Sussman went out to the 20th harmonic, I would not say they went usefully beyond Baxandall. Indeed, Baxandall did a much better job of showing how the distortion is affected by varying the amount of negative feedback. Boyk and Sussman do a poor job in this regard.

Much of the bottom line remains the same, however. And that is the fact that the application of small amounts of negative feedback around a nonlinearity can definitely introduce new distortion spectra that were not there in the first place. This is particularly so for the JFET.

What is important, however, is how big the new distortions are and what happens to them as the amount of NFB is increased beyond 10 – 20 dB. For example, it was shown in an earlier post that a BJT stage with about 17 dB of emitter degeneration would have all of its distortion spectra decreased monotonically by the addition of any amount of global feedback around it.

One might also ask, if the 7th harmonic of a JFET stage is at -140 dB without NFB, and the application of NFB raises that to -120 dB, how much do we care?

This touches on your point (and Boyk & Sussman’s speculation) about the audibility of distortion spectra below the noise floor. Since the distortion is correlated, it is very likely that it is audible to some extent below the noise floor. Then, of course, comes the question, how low is good enough? Is -100 dB low enough? Is -120 dB low enough?

Or does “low enough” depend on the order of the distortion products? For example, Maybe -70 dB is low enough for second, -80 for third, -90 for fourth, -100 for fifth, -110 for sixth, -120 for seventh and higher?

I would point out that Boyk and Sussman’s results for the triode versus the BJT have to be interpreted very carefully in regard to drawing conclusions based on input voltage. I say this because tubes by their nature may tend to operate at higher signal levels than undegenerated BJTs.

Although Boyk and Sussman rightly point out the re-entrant distortion mechanism of NFB, they go on to say “Thus, in the case of the BJT, feedback improves the nonlinear distortion of the amplifier. Although the no-feedback BJT amplifier started out much worse than the no-feedback JFET amplifier, it is vastly improved by feedback.”

Here is a summary of what was presented in some earlier posts. Baxandall’s results were first duplicated by simulation for both the JFET and BJT cases. This provided confidence that SPICE simulation could be used to evaluate these kinds of questions. The plot below shows the results for a BJT with no emitter degeneration. As Baxandall demonstrated, these results show an increase in certain distortion spectra as NFB is applied, but a consistent decrease in all distortion products by the further application of NFB after about 20 dB of NFB. Note that this BJT stage is being driven quite hard, producing second harmonic distortion without NFB of about 14%.

Cheers,
Bob

[jan.didden]

Bob,

Thanks for that post (above), it is always good to recap and summarize stuff lest the significant findings get lost in the ongoing barrage.

On your graph I noticed that, whatever the NFB (beyond 20dB or so), the 7th harmonic seems to flatten out at -110dB. That makes me feel uncomfortable. Many authors concede that the relative importance of harmonics shoulg be weighted heavily towards their order. For instance, I think it was Crowhurst who proposed a square order, meaning that the 7th level should be weighted 49 times. And 49 times -110dB compares with about -80 2nd harmonic. Suspiciously into audible territory, I would think.

With 0dB feedback, the number would be -140dB comparing with -110dB 2nd....

I would be interested in your views on this.

Jan Didden