Bob Cordell Interview: Error Correction

andy_c said:


Hi Jan,

Just edit out the punctuation mark after the ".pdf" in the URL.

On another subject, I think the ongoing controversy isn't much of a controversy at all when all is said and done. Rather, I see it as different people having different ways of looking at the same problem. One person's concept is another person's implementation detail and vice versa. Regardless of whether error correction is a concept in itself or just a particular implementation of a general feedback system, the "con-plementation" is an incredibly useful one.


Andy, you are exactly right. Looking at the error correction in multiple ways gives multiple insights, all of which are useful.

It is fascinating the different ways that this circuit can be looked at, and especially fascinating that it posesses the behavior, as the pot is moved, of reducing error, going through essentially zero, and then coming out on the other side with reversed error sign.

There is a lot in the semantics here, I suspect a lot in the definition of loop gain here, and finally, a lot in the details of the implementation that happen to work out very synergistically in the Hawksford architecture. The Devil is in the details....

If I had successfully convinced myself that the Hawksford scheme was nothing more than NFB in disguise, I probably would never have ventured to build it into my amplifier and achieve such good results. I always like the story about the engineer who did something good because someone forgot to tell him it would not work.

Cheers,
Bob
 
Hi Rodolfo,

Your contribution is undoubtedly appreciated; it is not my intention to give the appearance of flippant ''fire from the waist'' type retorts.

If this was the impression conveyed, i apologise unreservedly; I hope I have not unduly offended you in this respect.

Now, if you consider the rationale for the 1/K block given here, i think you'll see that there really is nothing mysterious about it.
 
Bob Cordell said:

....... fascinating that it possesses the behaviour, as the pot is moved, of reducing error, going through essentially zero, and then coming out on the other side with reversed error sign.

If I had successfully convinced myself that the Hawksford scheme was nothing more than NFB in disguise, I probably would never have ventured to build it into my amplifier and achieve such good results. I always like the story about the engineer who did something good because someone forgot to tell him it would not work.

Cheers,
Bob


I agree. However, i have difficulty classifying error-cancellation-by-feedback as classical NFB in the traditional sense, since the derived quantity to be fed back is differentially extracted.

It is the later attribute, i suggest at this point, which explains why only a finite loop-gain (as opposed to infinite loop-gain in the classical form of NFB) is required for a nominal 100% error cancellation.

Moreover, in contrast to classical NFB, the error correction arrangement appears to possess the attribute that, at balance, loop-gain increases with increasing error extracted, as shown here.

This attribute would go a long way to explaining this system's remarkable output-stage distortion reducing properties.

What do folks think? Bob? :scratch2:
 
Bob Cordell said:
It is fascinating the different ways that this circuit can be looked at, and especially fascinating that it posesses the behavior, as the pot is moved, of reducing error, going through essentially zero, and then coming out on the other side with reversed error sign.

There is a lot in the semantics here, I suspect a lot in the definition of loop gain here, and finally, a lot in the details of the implementation that happen to work out very synergistically in the Hawksford architecture. The Devil is in the details....

If I had successfully convinced myself that the Hawksford scheme was nothing more than NFB in disguise, I probably would never have ventured to build it into my amplifier and achieve such good results. I always like the story about the engineer who did something good because someone forgot to tell him it would not work.

I agree completely. One thing that bugs me is that some (maybe all?) of the equivalency arguments rely purely on linear system theory. I thought the whole purpose of error correction, at least for unity gain power amp output stages, was to keep the nominal gain and bandwidth of the stage intact insofar as is possible, while at the same time linearizing it. After all, if you try to make linear gain corrections, the dynamic range of the error correction circuitry gets partly used up by an essentially useless gain correction. Typical negative feedback is pretty radical by comparison. I like to look at it as an implementation technique whereby significant distortion reduction can be accomplished in return for having to deal with a pretty tame loop stability concern.
 
andy_c said:
After all, if you try to make linear gain corrections, the dynamic range of the error correction circuitry gets partly used up by an essentially useless gain correction.


I think i agree with you here, since, in contrast to classical NFB, the error correction arrangement appears to possess the attribute that, at balance, loop-gain increases with increasing error extracted, as shown here.

This implies, it seems to me, that the system is actually one of active negative feedback.

What think ye? :scratch2:
 
mikeks said:
..... rationale for the 1/K block given here, i think you'll see that there really is nothing mysterious about it.

Oh well, I cannot fail to tease you, again firing from the waist :clown:!!!

Seriously now, this issue harks back from post 888 where I suggested Fig. 1 and 2 were not equivalent and let for you to find out. Of course they are *algebraically* equivalent (algebra is a more compact and spiffy way of putting it anyway), but how on earth do you reroute a signal in bolck diagram from output to input (and insert 1/K1) in the real world.

Again, this may be a personal limitation, by I shudder at the idea of depicting a bock diagram including components that cannot possibly exist, no matter the fact it is basically an abstraction.

Rodolfo
 
mikeks said:



The 1/K1 term merely shows that you need attenuation of K1, instead of a gain of K1.
.....

Michael, this underscores precisely the dangers I was talking about.

My 1/A' was deliberately notated differently from A, to highlight they are different beasts altoghether. A is a complex nonlinear gain block, 1/A' is an (almost ideally) passive linear attenuator.

By moving from Fig. 1 K1 input to output in Fig. 2, you must per force account for the *inverse transform* of K1, which cannot possibly be simply an attenuator, to be accurate it must also mimick back any nonlinearity and delay but *in reverse*, and this is what I object form the standpoint of a block diagram, admittedly it is nitpicking if yo want, for the final result is algebraically correct.

Rodolfo
 
ingrast said:


Michael, this underscores precisely the dangers I was talking about.

My 1/A' was deliberately notated differently from A, to highlight they are different beasts altoghether. A is a complex nonlinear gain block, 1/A' is an (almost ideally) passive linear attenuator.

By moving from Fig. 1 K1 input to output in Fig. 2, you must per force account for the *inverse transform* of K1, which cannot possibly be simply an attenuator, to be accurate it must also mimick back any nonlinearity and delay but *in reverse*, and this is what I object form the standpoint of a block diagram, admittedly it is nitpicking if yo want, for the final result is algebraically correct.

Rodolfo

Rodolfo,

This clearly represents an active system of nominal attenuation 1/k1; no ''mimicking'' involved.

How you implement the thing in practice has really been covered by Cordell, Yokoyama...etc.

I have demonstrated why this is a requirement for balance in practice.

Remember that the 1/K term comes in only if your output stage is required to have a nominal gain greater than unity:


http://www.diyaudio.com/forums/showthread.php?postid=1066117#post1066117

http://www.diyaudio.com/forums/showthread.php?postid=1066119#post1066119
 
mikeks said:
I suppose you're right. :scratch2:

What bugs me is the Lipshitz/Vanderkooy assertion in that paper that no true cancellation can occur with this arangement unless you have infinite loop gain.

I just cannot see it, and it is constantly gnawing away at moi. :scratch2:


Mike,

I like the way you put it. It gnaws away at me, too. I would think it will tend to gnaw away at anyone who has twiddled that pot. Go figure.

I was never totally happy with the way they put things in that paper, but I guess I just learned to live with it. Both guys are personal friends of mine and I have the highest respect for both of them.

Bob
 
Bob Cordell said:



Mike,

I like the way you put it. It gnaws away at me, too. I would think it will tend to gnaw away at anyone who has twiddled that pot. Go figure.

I was never totally happy with the way they put things in that paper, but I guess I just learned to live with it. Both guys are personal friends of mine and I have the highest respect for both of them.

Bob


Thank you very much, Bob, for this vital insight:

Lipshitz/Vanderkooy, it would appear, took Llewellyn's arrangement, analysed it and then took it as a blanket assessment of a host of other arrangements, including Hawksford/Cordell.

I am thoroughly uncomfortable with this approach, principally because, in the study of Control Systems, you could devise a HOST of different feedback systems (with and without positive feedback loops) that ultimately resolve to IDENTICAL closed-loop transfer functions, while being FUNCTIONALLY completely different!
 
and this is what I object form the standpoint of a block diagram, admittedly it is nitpicking if yo want, for the final result is algebraically correct.
I have to cheer your picking up on the inverse transform requirement, Rodolfo. You are quite right and you should realise you are not nit picking but pointing out an error in the block diagram. The final result is not algebraically correct.
 
Mike wrote:
Note that one of my Majors, many moons ago, was Control Systems Engineering, so tread carefully.
I just cannot see it, and it is constantly gnawing away at moi.
I am sure the thread is grateful to have such a master in its midst. Of course I can only conclude from your admission that your period of education must have preceeded the Greek empire.
 
Bob wrote:
It is fascinating the different ways that this circuit can be looked at, and especially fascinating that it posesses the behavior, as the pot is moved, of reducing error, going through essentially zero, and then coming out on the other side with reversed error sign.
Is it the nulling "miracle" that is the sticking point to accepting the equivalence to NFB?

This is simple to explain. You already know that fig 4 below is Hawksford (only feedback correction: b=0).

The gain G = Vo/Vin = N/(1 - a + N)

The sensitivity of this to N, dG/dN = (1 - a)/(1 - a + Na)^2

The sensitivity to N, ie: the sensitivity of gain to error in N, is minimized when a = 1 and is increased when a > 1 or a < 1. The sign of the sensitivity changes through the null point.

When a = 1 the theoretical loop gain is infinite. It won't be in practice, as Rodolfo has shown, because the PFB contains at least one pole. At the null setting the total distortion will not be zero in a real circuit.
 

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