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Amplifier with nested Miller compensation
Amplifier with nested Miller compensation
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Old 21st April 2013, 09:24 PM   #21
jxdking is offline jxdking  China
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Quote:
Originally Posted by matze View Post
Hi jxdking,

What do you mean by performance? Is it just the final result or do you think that we can have a relevant feedback path in the circuit with second-order characteristics, while the overall behaviour is first-order?

Here is what I was talking about. Please see the attachment.

2-Pole performance
1-Pole like frequency response.


C1 is the outer Miller Capacitor.


Actually, you must come up 2 or more pole at inner loop, so that you can have some extra gain (at lower frequency) for outer loop to do the compensation.
Attached Images
File Type: png Nested Miller1.png (91.1 KB, 300 views)
File Type: png Nested Miller2.png (43.4 KB, 283 views)
File Type: png Nested Miller3.png (53.5 KB, 293 views)
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Old 22nd April 2013, 07:13 AM   #22
matze is offline matze  Europe
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Quote:
Originally Posted by jxdking View Post
Here is what I was talking about. Please see the attachment.

2-Pole performance
1-Pole like frequency response.

C1 is the outer Miller Capacitor.
Dear jxdking,

thank you for reasoning and sharing your results. Maybe, I first have to better clarify the main idea proposed in this thread.

With the advent of low-voltage OPA, especially CMOS, IC designers had the problem that the active devices did not provide enough transconductance in order to get good DC gain figures. This was due to the standard OPA architecture with only two effective gain stages: differential transconductance plus transimpedance stage (VAS). Thus, they were forced to throw in more gain stages that had to be compensated somehow. Nested Miller compensation is in my eyes just the simplest scheme, more are discussed e.g. in Johan Huijsing's book. (BTW, also thrilling there: biasing circuits for rail-to-rail A/B output stages [without cut-off], linearisation of rail-to-rail input stages, multipath frequency compensation and discussion of many design examples, including a few important standard OPA)

Lacking DC gain is of course not our problem. But each nested Miller compensation loop does provide, as a side-effect, extra feedback around the output stage. This is what I'm proposing to exploit.

Looking at your schematic, I'm not sure whether the feedback via C1 will work as intended. If I get it right, you first set the VAS gain by the two-pole compensation network with C4 and C7. Then you apply a loop around this stage and OPS via C1. I'm wondering whether this will work as intended, if you do not isolate the two "left-hand sides" of feedback networks. They both are connected to the VAS input and will interfere somehow. Additionally, there is no voltage gain between the "right hand sides" of both networks. In my examples, both "left-hand sides" are isolated by a transconductance stage in between which will provide additional gain. Did you probe the loop gains of both loops?

Cheers,
Matze
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Old 22nd April 2013, 01:58 PM   #23
matze is offline matze  Europe
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Hi David,

thanks for your comments.

Quote:
Originally Posted by Dave Zan View Post
I think one problem with your derivation is that there is an implicit assumption of perfect minimum phase. If phase behaviour is perfectly minimum then every pole but one can be perfectly canceled and the result will be first order behaviour.
This is also the assumption behind Cherry's Nested Dif. Feedback Loops.
Unfortunately, I do not get your point. Do you think that one has to tackle all nested loops at once? My hope was that one can decompose the problem. Then, in each loop on its own, only the pole created by the ULGF of the next inner loop had to be cancelled. Even if that's not exactly possible, the phase margin penalty due to a pole-zero pair just at the ULGF seems to be small, see simulation results.

Quote:
Originally Posted by Dave Zan View Post
If you can do this then do you need nested loops? Just cancel the poles and have a first order loop.
This kind of hidden assumption can be quite tricky.
The hope is still that, using nested loops, the maximum relevant ULGF in the whole circuit can be kept low (and what I see in practice from my breadboard amplifier with its ridiculous number of nested loops, it seems to be the case ...). If one used one loop instead and tried to cancel all disturbing poles therein, then still the relevant ULGF would remain high, if large total amounts of NFB were to be generated with first-order behaviour.

Best regards,
Matze
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Old 22nd April 2013, 02:25 PM   #24
Dave Zan is offline Dave Zan  Australia
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Quote:
Originally Posted by matze View Post
The hope is still that, using nested loops, the maximum relevant ULGF in the whole circuit can be kept low (and what I see in practice from my breadboard amplifier with its ridiculous number of nested loops, it seems to be the case ...).
I probably should have asked this at the start to clarify what to discuss.
Have read Cherry's articles on Nested Diff. Feedback Loops?
There are several in ETI and at least one in JAES.
Have you read JCX's posts on TMC?
These disprove claims similar to your proposition. I think the extra return ratio may not be evident in the outer loop but it will exist in some loop and will have consequences on the phase of that loop and the overall behaviour of the amp.
The ULGF can be kept low but the phase below that frequency must reflect the increased rate that the return ratio declines.
Thanks for the mental work-out

Best wishes
David.
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Old 22nd April 2013, 03:15 PM   #25
jxdking is offline jxdking  China
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Quote:
Originally Posted by matze View Post
Dear jxdking,


Looking at your schematic, I'm not sure whether the feedback via C1 will work as intended. If I get it right, you first set the VAS gain by the two-pole compensation network with C4 and C7. Then you apply a loop around this stage and OPS via C1. I'm wondering whether this will work as intended, if you do not isolate the two "left-hand sides" of feedback networks. They both are connected to the VAS input and will interfere somehow. Additionally, there is no voltage gain between the "right hand sides" of both networks. In my examples, both "left-hand sides" are isolated by a transconductance stage in between which will provide additional gain. Did you probe the loop gains of both loops?

Actually, C1 could be any value, as the maximum ULGF is restricted by 2 pole compensation. It will be stable anyway. At very high frequency, the equivalent Miller Cap value will be (C1+(C4//C7)).

C1 is intended to do Miller Compensation including output stage. That's our goal, isn't it?

1. The tricky part is what the 2 pole compensation is doing here. Why has to be 2 pole configuration. In order to keep output stage stable, the ULGF should be restricted even if C1 is not added. Thus, you have 2 choice.
(1) one choice is traditional miller compensation for inner loop. In this case, it makes outer Miller Cap useless but lower the ULGF.
(2) another choice is 2 pole compensation for inner loop. 2 pole will be 40dB/Oct rolling down, you will get a big hump at low frequency response. At low frequency, you will have lots of extra gain comparing to 1 pole. Thus, you can use outer loop to Compensate the extra gain. C1 will dominate at low frequency. The overall frequency response will look just like 1 pole.


2. You mentioned using extra stage. Yes, you can do that, but it will be more complicated. Here is my rule. The whole amplifier should be stable even if removing all the outer Miller Caps, because the most inner loop should be dominant at high frequency to make sure everything is stable. It will be pretty tricky to achieve that rule with extra stage.

3. After playing around simulation for a while, I find the THD performance is pretty equivalent to TMC compensation. Actually, it should be. The beautiful part is that they can work together. Should I call it Nested Transitional Two Pole Compensation?

Last edited by jxdking; 22nd April 2013 at 03:21 PM.
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Old 22nd April 2013, 07:43 PM   #26
matze is offline matze  Europe
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Hi David,

thanks again for your comments. I will try to do my homework; the Cherry paper left the printer.

Quote:
Originally Posted by Dave Zan View Post
Thanks for the mental work-out
You are right. It's time to pause a bit. But I fear I will come back and make noise with my spoons.

Best regards,
Matze
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Old 22nd April 2013, 08:14 PM   #27
matze is offline matze  Europe
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Quote:
Originally Posted by jxdking View Post
2. You mentioned using extra stage. Yes, you can do that, but it will be more complicated. Here is my rule. The whole amplifier should be stable even if removing all the outer Miller Caps, because the most inner loop should be dominant at high frequency to make sure everything is stable. It will be pretty tricky to achieve that rule with extra stage.

3. After playing around simulation for a while, I find the THD performance is pretty equivalent to TMC compensation. Actually, it should be. The beautiful part is that they can work together. Should I call it Nested Transitional Two Pole Compensation?
Hi jxdking,

the whole idea is really about adding new gain stages. This allows to obtain excellent performance without ULGFs in the MHz region. TMC does promise a THD20 improvment of, say , factor 5. Extra transconductance stages with nested Miller compensation can provide improvments of orders of magnitude, see the examples with Bob's amplifiers in earlier posts. In this respect, the undertaking is more comparable to OPS error correction approaches with the difference that no trimming would be necessary.

My goal is to use rather slow, but stable and rugged output stages as well as low ULGF in all feedback loops of the topology. Considering the available devices and e.g. the surprisingly simple, yet really high-performance approach of Dadod's TT-TMC, this may seem a bit strange. But the point is more in exploring the applicability of principles that are routinely used in other areas of analog design, but not yet appreciated in audio amplifier construction.

Cheers,
Matze
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Old 22nd April 2013, 08:49 PM   #28
jcx is offline jcx  United States
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slow, rugged seems like a handicap - why not fast rugged?

or improving less rugged, fast devices with paralleling

fast is really helpful in allowing stable use of more gain in the working band - more "distance" in frequency to "unwind" the excess phase

Bode only gave preliminary hints for properly measuring multiloop systems

I think the simple view is if you can cut the amp signal path in a spot that cuts all of the loops, and everything relies only on individually stable negative feedback - then you have a chance to see the stability in a single loop gain plot


I try not to miss any chances to recommend BJ Lurie's work - although his books are hard to understand and "buggy" - needing 2nd editions but he really shows how to use Classical Control techniques - you can still view his old site with archive.org
Dr. Boris J. Lurie's Homepage: Classical Feedback Control
looks like there is now a 2nd edition

one thing Lurie does really well is show that the “conservation” relation for the total amount of feedback - the “Bode Integral” is exactly such a practical "good theory" - and has been the underpinning fundamental argument behind my posts in this thread

http://trs-new.jpl.nasa.gov/dspace/b.../1/98-0905.pdf



of course the real bottom line is that audibly "transparent" amps are trivial - especially if spending a few 10s of W heavy Class AB bias is possible

I like control theory, electronic design - electronic power amplifcation just isn't where the limitations in audio reproduction are - its in speakers and room

Last edited by jcx; 22nd April 2013 at 08:57 PM.
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Old 22nd April 2013, 09:03 PM   #29
jxdking is offline jxdking  China
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Quote:
Originally Posted by jcx View Post
slow, rugged seems like a handicap - why not fast rugged?

or improving less rugged, fast devices with paralleling

fast is really helpful in allowing stable use of more gain in the working band - more "distance" in frequency to "unwind" the excess phase

Bode only gave preliminary hints for properly measuring multiloop systems

I think the simple view is if you can cut the amp signal path in a spot that cuts all of the loops, and everything relies only on individually stable negative feedback - then you have a chance to see the stability in a single loop gain plot


I try not to miss any chances to recommend BJ Lurie's work - although his books are hard to understand and "buggy" - needing 2nd editions but he really shows how to use Classical Control techniques - you can still view his old site with archive.org
Dr. Boris J. Lurie's Homepage: Classical Feedback Control
looks like there is now a 2nd edition

one thing Lurie does really well is show that the “conservation” relation for the total amount of feedback - the “Bode Integral” is exactly such a practical "good theory" - and has been the underpinning fundamental argument behind my posts in this thread

http://trs-new.jpl.nasa.gov/dspace/b.../1/98-0905.pdf
How fast is fast? 1MHz ULGF?

Most books tell me 500KHz ~ 800KHz is the safety region. Actually, I have never thought about it before. I just reference others experience. You give me a good question.
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Old 22nd April 2013, 09:14 PM   #30
jcx is offline jcx  United States
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I think Bob's MOSFET amp, measured inside the error corection loop manages ~4-5 MHz
Bob Cordell Interview: Error Correction

probably RET bipolars can do nearly the same, somewhere not much higher standard packaging, mounting limits with parasitic lead inductance likely becomes an issue for local RF oscillation, and added loop phase shift

faster than old school 100s of kHz seems a no brainer with faster output Q - but faster than low-middling single digit MHz runs into the other probelms

but even a gain intercept frequency increase of only 4x is very worthwhile if you have 2nd order loop gain - adds 24 dB feedback in the working frequency range

Last edited by jcx; 22nd April 2013 at 09:33 PM.
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