Error correction for stages with gain

[Quince]

Hawksford EC is usually done for output stages with gain (near) one. However, in one of the AES papers he mentions that it's generalizable to stages with gain, but there aren't many details. Has anyone actually seen a design where EC is applied to a stage with non-unity gain? I tried to get some comments at diyaudio where there's quite a long thread on EC, but no one seemed interested in that application, as most power output stages are followers. However, I have at least two amplifiers whose output stages have gain and I'm interested in trying it out, but need some help in figuring out the proper way to do it...

 

[bcarso]

Haven't seen an example of that either. I'm surprised a smiling Malcolm hasn't provided us with one :grin:

 

[Quince]

In the "Towards a generalisation..." paper, why does his high-level schematic of EC on a stage with gain (Fig. 3.1) utilize a reference amp on the Vin sample instead of passively divide the Vout sample?

 

[bcarso]

[quote author="Quince"]In the "Towards a generalisation..." paper, why does his high-level schematic of EC on a stage with gain (Fig. 3.1) utilize a reference amp on the Vin sample instead of passively divide the Vout sample?[/quote]

Haven't seen it, but I'd conjecture for faster response. Compare bootstrapping techniques with feedforward ones for example.

Could you give some specific references/links?

 

[JohnRoberts]

[quote author="Quince"]Hawksford EC is usually done for output stages with gain (near) one. However, in one of the AES papers he mentions that it's generalizable to stages with gain, but there aren't many details. Has anyone actually seen a design where EC is applied to a stage with non-unity gain? I tried to get some comments at diyaudio where there's quite a long thread on EC, but no one seemed interested in that application, as most power output stages are followers. However, I have at least two amplifiers whose output stages have gain and I'm interested in trying it out, but need some help in figuring out the proper way to do it...[/quote]

I remember some work published by Cordell also in EC of unity gain power amp output stages. EC is typically applied locally since it is at best an approximation for a modest number of known non-linearities. In stages with gain these errors will typically be multiplied by that gain. It may be more effective to just throw away some excess gain in negative feedback to linearize. I seem to recall some feed forward (?) error correction in audio amps. These appear to have faded away so they may have been championed by the "all NF is bad" crowd rather than a real benefit.

I did some noodling with linearizing an open loop gain stage in a (JFET) phono pre amp front end but lost interest when vinyl went away. Nothing worthy of publication but there are some tricks to linearize JFETs in public knowledge (adding/subtracting a fraction of drain voltage to gate in common source, etc.) FWIW I was going to try using a second part to cancel out error term, but never reduced it to a finished product. The uncorrected circuit measured quite low so this was an exercise in guilding the lilly.

JR

 

[Quince]

The paper I mentioned is at
http://www.essex.ac.uk/ese/research/audio_lab/malcolmspubdocs/C35%20Generalization%20of%20error%20correctiona%20amplifiers.pdf

There's a long discussion at diyaudio about EC and Cordell's implementation of it in his ultra-low distortion MOSFET amp from the 80s (Cordell himself is participating in that thread; his amp is on his website). The thread is here
http://www.diyaudio.com/forums/showthread.php?s=&threadid=89023&perpage=10&pagenumber=1
It's 160 pages long and I doubt many would read that, but one of the interesting conclusions was mathematical (not practical) equivalence of feedback EC to a system with positive feedback within negative feedback, and thus direct relation to other such systems (i.e. Wolcott's designs). Of course, in EC all the available extra gain is used to magnify the error alone rather than the error+signal, and since the EC's effective gain (from the positive-feedback-inside-negative-feedback view) is infinite it can theoretically achieve a perfect error null. Another interesting observation from that thread is that, since it's well known in control theory that all two degree of freedom systems have mathematical equivalence, there are many other topologies that this can be converted to besides these two (Hawksford and Wolcott), but little has been explored to see if any advantages would come from the others.

I'm sort of summarizing that thread here without a great level of understanding, so you'll excuse me if I didn't make sense...

My interest in applying it to output stages with gain is that I have two amplifiers with that configuration, and I would love to try EC in them.

 

[bcarso]

[quote author="JohnRoberts"]
I did some noodling with linearizing an open loop gain stage in a (JFET) phono pre amp front end but lost interest when vinyl went away. Nothing worthy of publication but there are some tricks to linearize JFETs in public knowledge (adding/subtracting a fraction of drain voltage to gate in common source, etc.) FWIW I was going to try using a second part to cancel out error term, but never reduced it to a finished product. The uncorrected circuit measured quite low so this was an exercise in guilding the lilly.

JR[/quote]

Vinyl went away? :razz:

Of course the half-drain feedback for use of FETs as VCRs is well-known and extremely effective. Plunkett, when a newcomer to UREI, played around with some additional local feedback and got another 5-6 dB out of their existing FET-based limiter IIRC; he remarked to me that he thought it didn't amount to much, but evidently Bill Putnam was very pleased and along with consideration of Brad's other work promoted him to VP.

As a consequence of doing work for various clients, any one of whom would be properly upset if what they paid me for got re-used "verbatim," I have developed a lot of circuit variants. Recently I tried to get a very poor-performing FET-based limiter, as supplied by a Far East vendor, to work a lot better, and discovered that at least within the spice model constraints, the parasitic drain and source resistances had a surprisingly strong effect on nonlinearity. See also in this connection the thread in here a while back about the paper on IM distortion products and their order in the presence of feedback by Boyk and Sussman.

 

[bcarso]

[quote author="Quince"]The paper I mentioned is at
http://www.essex.ac.uk/ese/research/audio_lab/malcolmspubdocs/C35%20Generalization%20of%20error%20correctiona%20amplifiers.pdf

There's a long discussion at diyaudio about EC and Cordell's implementation of it in his ultra-low distortion MOSFET amp from the 80s (Cordell himself is participating in that thread; his amp is on his website). The thread is here
http://www.diyaudio.com/forums/showthread.php?s=&threadid=89023&perpage=10&pagenumber=1
It's 160 pages long and I doubt many would read that, but one of the interesting conclusions was mathematical (not practical) equivalence of feedback EC to a system with positive feedback within negative feedback, and thus direct relation to other such systems (i.e. Wolcott's designs). Of course, in EC all the available extra gain is used to magnify the error alone rather than the error+signal, and since the EC's effective gain (from the positive-feedback-inside-negative-feedback view) is infinite it can theoretically achieve a perfect error null. Another interesting observation from that thread is that, since it's well known in control theory that all two degree of freedom systems have mathematical equivalence, there are many other topologies that this can be converted to besides these two (Hawksford and Wolcott), but little has been explored to see if any advantages would come from the others.

I'm sort of summarizing that thread here without a great level of understanding, so you'll excuse me if I didn't make sense...

My interest in applying it to output stages with gain is that I have two amplifiers with that configuration, and I would love to try EC in them.[/quote]

Thanks for that information.

If you have a simulator I'd just jump in and try things. If you can support your results on the bench all the better. Your success with the sims may well hinge on the amount of experience with the real world stuff you've had and how much you have learned from it, and I know from reading other threads that you've been in a mostly academic atmosphere for some time now.

 

[Quince]

My maths may be wrong, but what I figured was this:
Again looking at figure 3-1, consider his equation 3-1:
A_h = N - b(N - R) / (1 + a(N - R))
Now, if we only have error feedback and not feedforward, b = 0 and the equation becomes
A_h = N / (1 + a(N - R))
With E_h = A_h / A_t - 1, solving for E_h = 0 you get the condition a = 1 / A_t and R = A_t, where R is the reference amplifier's gain.
Now, if trying attenuation of the output sample instead, then R = 1 and the second N term is replaced with N / A_t:
A_h = N / (1 + a (N / A_t - 1))
If then a = 1, A_h = A_t, and E_h = 0 achieves error null.
Thus, this approach also works.
So, which is easier to make more precise, a quality passive attenuator 1 / A_t, or a reference amplifier of gain R = A_t and an attenuator a = 1 / A_t?

 

[bcarso]

Passive attenuators are traditionally thought of as being easy to make precise.

 

[Quince]

Which leaves it as a mystery to me why Hawksford chose to add another amplifier instead. Perhaps thermal drift is more of an issue with the smaller signals by taking the attenuation route, but then again, high precision resistors are easy to come by nowadays.

 

[Guest]

[quote author="Quince"]Which leaves it as a mystery to me why Hawksford chose to add another amplifier instead. Perhaps thermal drift is more of an issue with the smaller signals by taking the attenuation route, but then again, high precision resistors are easy to come by nowadays.[/quote]

May be, he needed something "new" in order to get the patent?

 

[Quince]

I don't think there's a patent. It's just an academic paper. On the other hand, Wolcott patented his stuff.