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Old 26th May 2011, 09:39 PM   #12471
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Dave is this for me or for Ed?

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Old 26th May 2011, 09:52 PM   #12472
DF96 is offline DF96  England
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Sorry, for simon7000. I'm not sure what problem he is trying to solve. It seems obvious to me that order of cascaded amplifiers matters, so I am surprised that anyone might think otherwise.

However, if two amplifiers have unity gain then the order does not matter as the transfer function will be simply the product of the two individual functions. There is a small caveat: low levels of odd-order distortion otherwise there will be expansion or compression so the effective gain will vary.
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Old 26th May 2011, 10:14 PM   #12473
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We are not in general disagreement. If you go through almost any of the threads here you will find adherents of no feedback, lots of global feedback, local feedback etc. I really don't want to cite any of the oversimplified papers because life is too short to explain to the authors where they went wrong because if they didn't get the math when they wrote it they probably still don't understand it. My quick google found many simplified explanations. There are many who seem to think the stage gain does not affect how the distortion products behave as both output and artifacts see the same gain. So while it seems reasonable to use low distortion stages first the other approach is to use low distortion circuits at the highest gains.

My observation is that single gain stages inside a feedback loop should work best. Yet some modeling shows otherwise!

The issue we probably are not in agreement is what is linear vs non-linear and how accurate the math is compared to reality. Obviously a reasonable step is to use all my distortion modules with the same gain and same input.

The base issue is that ninth or eleventh harmonic distortion is much worse that third or most even order versions. So it is wise to identify which combinations of gain stages and types will minimize this problem. Classic math as you mention looks at the products of the stages and you recognize the small errors due to the other non-linear components will cause what should be a small deviation from that. Experiments indicate there may be more issues, but they are still in the preliminary stage.

A good design balances all of the issues, so understanding the actual trade offs using non perfect components is only a starting point.
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Old 26th May 2011, 10:40 PM   #12474
DF96 is offline DF96  England
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Yes, people believe all sorts of things. They sometimes try to propagate their confusion. I have not seen any which claim that distortion is independent of level - maybe if I saw one of those I would simply ignore anything he said anyway!

'Using low distortion stages first' is a statement which might not have an unambiguous meaning. Given two stages with the same gain, the one with the highest non-linear coefficients in the polynomial expansion should probably be put first as here it will have the smallest signal. In addition, for polynomial transfer functions, global NFB is probably better than local NFB because the early stage has much less signal and this is likely to be more beneficial than local feedback. However, this assumes flat frequency response so not very realistic!

If an amplifier has a low dominant pole (e.g. typical SS power amp) then it also may be best to put the distortion before it if possible - then the pole will attenuate harmonics, which will partly compensate for the loss of NFB at higher frequencies. Unfortunately the typical SS amp has crossover distortion coming after the dominant pole.

I think your quest for clarity may be difficult, because you must ensure you are comparing like with like. The maths is fine for Class A, as that will have a polynomial response. Class B is more messy! A good principle to follow is that you have to understand the simple case with ideal components before you try to tackle the real world. Many people seem not to realise this.
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Old 26th May 2011, 10:58 PM   #12475
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I have cleaned things up a bit. I set the two stages to have a gain of 5. I placed a 5/1 divider on the input and between the stages. I then used stage 1 feeding stage two. I then reversed it and had stage two feed stage one. So both ways the input and output voltage of each stage was the same. I then had stage one drive stage two without the divider but with a global feedback resistor to keep the final output the same.

The results are quite a surprise! Feedback did lower the overall distortion as expected, but less feedback with stage two feeding stage one was clearly the best result!
Attached Images
File Type: jpg Match Gain One to Two.JPG (73.4 KB, 157 views)
File Type: jpg Match Gain Two to One.JPG (69.1 KB, 156 views)
File Type: jpg Feedback 5 to 1 One to Two.JPG (72.3 KB, 152 views)
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Old 26th May 2011, 10:58 PM   #12476
SY is offline SY  United States
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Quote:
Originally Posted by DF96 View Post
Given two stages with the same gain, the one with the highest non-linear coefficients in the polynomial expansion should probably be put first as here it will have the smallest signal.
You'd probably want to weight them?
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Old 26th May 2011, 11:04 PM   #12477
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And here is the big surprise. This is amplifier two feeding amplifier one with out the 5 to 1 input pad but with feedback to get the same output.

Yes this is an extreme example, but more global feedback here is worse than less local!
Attached Images
File Type: jpg Feedback 5 to 1 Two to One.JPG (72.9 KB, 146 views)

Last edited by simon7000; 26th May 2011 at 11:11 PM.
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Old 26th May 2011, 11:12 PM   #12478
DF96 is offline DF96  England
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Quote:
Originally Posted by simon7000
The results are quite a surprise! Feedback did lower the overall distortion as expected, but less feedback with stage two feeding stage one was clearly the best result!
Increasing the gain to 5 might have made the two amps more closely complementary to each other (depends on exactly how you did it), so with the same signal level there will be significant distortion cancellation. This cancellation disappears in the feedback case, as the two amps have very different signal levels. So your results are not surprising. No general conclusions can be drawn from this highly artificial situation. You are not comparing like with like.

Quote:
Originally Posted by SY
You'd probably want to weight them?
You mean multiply in the preceding gain? Yes, this makes comparison easier.

Last edited by DF96; 26th May 2011 at 11:13 PM. Reason: extra comment
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Old 26th May 2011, 11:17 PM   #12479
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Actually I made them more similar to each other and less complimentary. I am pretty sure you know which stage has less distortion now! The issue that popped up seems to be gain hogging in a global feedback situation. One stage gets run until it is very non-linear and the other gets less than it's share of gain.

Also attached is a better gain sharing version of the Two feeding One with feedback. Now Global feedback is an improvement.


BTY thanks for your enforcing the rigor of the experiment.

ES
Attached Images
File Type: jpg Equal Gain Two to One With Feedback.JPG (83.9 KB, 157 views)
File Type: jpg Other Feedback Two to One.JPG (60.0 KB, 74 views)

Last edited by simon7000; 26th May 2011 at 11:23 PM.
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Old 27th May 2011, 07:41 AM   #12480
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I think this is important. The only thing global fb does is divide the open loop distortion by the feedback factor. So, you need to look at the ol distortion in each case to decide which you like better in the open loop situation, having in the back of your mind that you can use nfb to lower the cl distortion. Not sure I make myself clear but saying that in some situations nfb gives higher distortion than in some other situations with some local fb involved (or vice versa) doesn't give you a general rule that you can apply.

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