Bob Cordell said:
Bob,
My hunch is what you are seeing in both cases is the signature of the compensated error extractor.
For the HEC mode, you have an ideal unity gain positive feedback loop made from controled voltage sources, equivalent to infinite gain front end. I did this a couple of years back and blew my mind (and the computer did not explode either).
For the feedforward mode, you are equally adding correction with an ideal controled source.
Were not for the compensation introduced, then distortion should be null in both cases as expected.
Rodolfo
Rodolfo wrote:
I'm going to refer to another error, Ve2 = Vout - Vin.
In your paper you say that Fig 1 reduces the error, by which I assume you mean Ve2, asymptotically. This is what I have called "hunting for a minimum error equilibrium". You seem to imply that Fig 3 does not do this but instead "cancels" the error. I would like to see this distinction demonstrated algebraically.
This leads me to ask you to define the generic system conditions that lead to "asymptotic reduction" and those that lead to "cancellation".
For, as you've agreed, we have two systems that both exhibit infinite NFB but you are claiming that one is reducing asymptotically and the other is cancelling.
Size isn't everything.
So Ve1 = (Vout/A' - Vdrv) where A' is a constant.
I'm going to refer to another error, Ve2 = Vout - Vin.
This is counter-intuitive to me.
In your paper you say that Fig 1 reduces the error, by which I assume you mean Ve2, asymptotically. This is what I have called "hunting for a minimum error equilibrium". You seem to imply that Fig 3 does not do this but instead "cancels" the error. I would like to see this distinction demonstrated algebraically.
This leads me to ask you to define the generic system conditions that lead to "asymptotic reduction" and those that lead to "cancellation".
For, as you've agreed, we have two systems that both exhibit infinite NFB but you are claiming that one is reducing asymptotically and the other is cancelling.
Rodolfo,
Please can you explain this to me? I have redrawn your Fig 1 and Fig 3 slightly so that they can be more easily compared mathmatically. I trust you will find them equivalent to yours in form and that the top diagram is still conventional NFB.
If we conceptually remove the amplifer A from both systems, so that we are considering only the "correction" parts, we can focus on calculating the value of Vdrv from Vi and Vout. I have shown the two equations. You will notice that they are of exactly the same form...in other words, one could simply choose arbitrary constants and make both systems identical.
My problem is this. If both systems have the same characteristic equation for Vdrv then how can one be said to be "asymptotic" and the other said to be "cancelling"?
Please can you explain this to me? I have redrawn your Fig 1 and Fig 3 slightly so that they can be more easily compared mathmatically. I trust you will find them equivalent to yours in form and that the top diagram is still conventional NFB.
If we conceptually remove the amplifer A from both systems, so that we are considering only the "correction" parts, we can focus on calculating the value of Vdrv from Vi and Vout. I have shown the two equations. You will notice that they are of exactly the same form...in other words, one could simply choose arbitrary constants and make both systems identical.
My problem is this. If both systems have the same characteristic equation for Vdrv then how can one be said to be "asymptotic" and the other said to be "cancelling"?
Attachments
ingrast said:
Yes, you are exactly right. The finite bandwidth in the error extractor is the limiting factor in the amount of correction.
Unfortunately, in the real world, there MUST be some degree of compensation in the HEC circuit. The amount of that compensation necessary depends largely on the speed of the output devices, and that is why Speed is King when it comes to HEC. It also points to the need for the small-signal circuits in the HEC stage to be very fast.
While feedforward EC has no such bandwidth limitation for stability reasons, it unfortunately suffers from the practicalities of being able to add that error back into the high-power output node.
Bob
This is why I consider FB and FF to be chalk and cheese
The diagram shows a FB and FF system, both with non-linear amplifier A which are to be corrected. To illustrate the difference in how they deal with distortion I have shown a "small" error, e, added to the amplifier output. I then show the small change in Vout...which is the same as the change in amplifier output. Because A is non-linear we must make e very small.
Feedback: delta Vout = e/(1 + bA')
where A' is the small-signal gain of A.
Feedforward: delta Vout = e - ec
Note that in the FF case setting c=1 cancels the error exactly. Note that the cancellation is independent of A.
In the FB case the error can only be reduced, never cancelled out, and the reduction depends on A.
With FB it is the characteristics of A that limit the amount of theoretical reduction. FB is doomed because it cannot escape from the charateristics of A. Because A is non-linear and has phase shift there will always be a finite limit on the size of b before instability cripples the system.
The diagram shows a FB and FF system, both with non-linear amplifier A which are to be corrected. To illustrate the difference in how they deal with distortion I have shown a "small" error, e, added to the amplifier output. I then show the small change in Vout...which is the same as the change in amplifier output. Because A is non-linear we must make e very small.
Feedback: delta Vout = e/(1 + bA')
where A' is the small-signal gain of A.
Feedforward: delta Vout = e - ec
Note that in the FF case setting c=1 cancels the error exactly. Note that the cancellation is independent of A.
In the FB case the error can only be reduced, never cancelled out, and the reduction depends on A.
With FB it is the characteristics of A that limit the amount of theoretical reduction. FB is doomed because it cannot escape from the charateristics of A. Because A is non-linear and has phase shift there will always be a finite limit on the size of b before instability cripples the system.
Attachments
traderbam said:
This is an interesting angle Brian. Your numbers ar right, now look again at the equations.
The first form - conventional NFB, features in the second term the loop gain ab (A has been factored out bt you in both cases) while the second form has in place the equivalent loop gain as shown in my pdf, eqn. [3].
In the limiting case for NFB, you can make this loop gain infinite making the front end gain a infinite, this is what I call asymptotic correction.
In the second case, you can make the loop gain infinite making 1-bs=0 instead, and I call this cancellation.
It is beyond dispute both that infinite gain a, or exact cancellation 1-bs=0 are unreachable. In fact for the error correction scheme, I clearly stated in the pdf that there is not even danger of 1-bs=0 for any frequency except DC, inasmuch as b being usually a passive network (b < 1) implies s > 1 i.e. active therefore with at least one pole, in turn implying a non null imaginary part for any nonzero frequency. True cancellation is consequently not possible but asymptotically for DC.
Another form of looking at cancellation is substituting in eqn. [2] in the pdf, BS=1. System gain then colapses to A'S - independent of A - which was the main objective, to slave an imperfect power stage to a passive or low level high quality stage.
Rodolfo
Rodolfo,
I think I'm getting closer to understanding of what you mean by cancellation.
You agree that the two Vdrv equations are of the same form, so from the point of view of the amplifier A the two systems are the same? Therefore, it must be that any characteristic of A is being treated identically in the two cases. So either they are both cancelling or they are both asymptoting.
How can it be otherwise?
It would appear to me that your identification of cancellation is independent of the input signal to A. In other words, you are taking into account only the behaviour of the correction network.
If (1-bs) is finite is there still "cancellation" going on?
I think I'm getting closer to understanding of what you mean by cancellation.
You agree that the two Vdrv equations are of the same form, so from the point of view of the amplifier A the two systems are the same? Therefore, it must be that any characteristic of A is being treated identically in the two cases. So either they are both cancelling or they are both asymptoting.
How can it be otherwise?
It would appear to me that your identification of cancellation is independent of the input signal to A. In other words, you are taking into account only the behaviour of the correction network.
If (1-bs) is finite is there still "cancellation" going on?
Re: This is why I consider FB and FF to be chalk and cheese
Duh!
This proves nothing we did not know already.
Yes, Brian, if you have an ideal summer at the output, feedforward error correction is better than HEC, and theoretically perfect.
Why don't you do some work on that output summer.
Cheers,
Bob
traderbam said:
Duh!
This proves nothing we did not know already.
Yes, Brian, if you have an ideal summer at the output, feedforward error correction is better than HEC, and theoretically perfect.
Why don't you do some work on that output summer.
Cheers,
Bob
janneman said:
If you are willing to refer to it as bootstrapping, it removes my
primary issue with your description.
😎
traderbam said:
Brian, this is precisely the issue with you from the begining. It was never in discussion both topologies are equivalent inasmuch it is possible to arrive to a functionally identical system description.
The differences in viewpoint are that with NFB one substracts an output sample from the input and finds out system improves with larger loop gain. With EC on the other hand, one definitely extracts only the error, but reckons this cannot be done (*) perfectly for any frequency except DC.
Rodolfo
(*) Edit, to be more precise ... the error cannot be reinjected perfectly ....
Nelson Pass said:
Nelson,
Agreed. If you go around in the 'inner loop' from the input of N, through the error summer, through the input summer back to the input of N you can view that as bootstrapping. The error summer (whether passive or active) bootstraps it's own non-inverting input. Which others see as 'infinite pfb gain'. Same difference.😉
Jan Didden
Rodolfo wrote:
Then why in your paper do you say that the difference between NFB and EC is that one asymptotes and one cancels?
Is it not the case that they BOTH asymptote until the special condition is reached, a=infinity and 1-bs = 0 (both equivalent to infinite forward gain) when output error is zero?
Whether, in the unachievable special case when the output error is zero, you call this "canellation" or you call it "reduction" is immaterial.
Am I Right?
They are equivalent?
Then why in your paper do you say that the difference between NFB and EC is that one asymptotes and one cancels?
Is it not the case that they BOTH asymptote until the special condition is reached, a=infinity and 1-bs = 0 (both equivalent to infinite forward gain) when output error is zero?
Whether, in the unachievable special case when the output error is zero, you call this "canellation" or you call it "reduction" is immaterial.
Am I Right?
Bob wrote:
Then why complain? There's no need to chomp at the bit. I will respond to your various posts shortly.
traderbam said:
Because in EC one first computes the error (scaled output - input) and in NFB not. The topologies are inherently different no matter whether the end result is the same.
You can make an active 2nd. order filter Sallen Key, or state variable, different topologies same result. Why is it there exist different versions? Because at implementation time, one may be advantageous over the other in a particular context.
Brian, I am afraid little more can be said at this time and it is my belief other members may start to find this discussion boring, I am dropping it if you allow me.
Rodolfo
That's fine, Rodolfo.
You are saying that the topology of the feedback network is different and this impacts he circuit design.
You are also saying that the system behaviour is identical. There is no difference between conventional NFB and EC feedback.
I agree.
This is not how I initially interpreted the wording of your paper.
I suggest that it is the system behaviour that the readers of this thread are firstly concerned with, as the purpose is to correct erors in the system behaviour. And it is at the system level that the erroneous assertion that the two systems are different has been argued by others.
That's all.
You are saying that the topology of the feedback network is different and this impacts he circuit design.
You are also saying that the system behaviour is identical. There is no difference between conventional NFB and EC feedback.
I agree.
This is not how I initially interpreted the wording of your paper.
I suggest that it is the system behaviour that the readers of this thread are firstly concerned with, as the purpose is to correct erors in the system behaviour. And it is at the system level that the erroneous assertion that the two systems are different has been argued by others.
That's all.
janneman said:
Well, I'm kinda dim when it comes to these things, so I go back
to Bob's original figure 12 with the Q22 and Q23 doing the
error correction. When I look for positive feedback there, what
I see is the follower function provided by Q24-27 which raises
the impedance seen by the Collectors of Q22-23 by virtue of
bootstrapping, otherwise the networks of R40, R41, etc will
load the Collectors of Q22-23 (which loading occured in my
orignal dynamic bias circuit).
Toward that end, I like the phrase "bootstrap" because it provides
a distinction from other forms of positive feedback, much in the
same way that the word degeneration provides clarity when
describing a form of negative feedback.
😎
Nelson Pass said:
Nelson,
As most of these things, there is a multitude of ways to look at this. The reason why I would not see Q24 as 'bootstrapping' the correction signal from Q22 is the following.
In Bob's fig 12, the error pick-off ref is taken by R44 (not R40) from the gate of Q28. Actually that is conceptionally a non-optimal point. It would be better to take that signal from the base of Q26, or even base of Q24, because then not only the output device but the whole triple output darlington is enclosed by the error loop!
When you do the latter, the bootstrap as I see it is even more clear: The correction signal from Q22 collector is hardwired to where it picks off the error ref at the base of Q24: Q22, the error amp, is bootsrapping it's own input (top of R44)!
Jan Didden
I'm not sure what the accepted definition is in electronics. The term is normally used to change other aspects of a circuit other than its gain, often to boost its input impedance. Like pulling on your own bootstrap won't cause you to increase your altitute.
The PFB used in HEC schemes and many other applications is different in so far as it is used to boost the gain; hence the huge loop gain that jcx shows in his simulations (eg: post #2230).
courtesy of Merriam-Webster
Nelson Pass said:
Just to highlight how different the same thing may look depending on how you look at it (and insightful), think of this:
The inner unity gain positive feedback loop - what we now may as well see as a bootsrap engine - receives at its input port both the original input signal and a sample of the output signal substracted.
Now, the bootstrap engine will not tolerate any deviation violating the loop gain, so the circuit somehow must find a way to cancel this difference between input an output sample. This implies in turn perfect correction.
Rodolfo