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17th April 2013, 09:59 AM  #11 
diyAudio Member
Join Date: Sep 2012

One more example
Here is a further example of Bob's demonstration amplifier (page 63 of his book), now with
two nested Miller compensation loops. The unity gain crossovers again are around 400 kHz. This is achieved without compensation capacitors in global feedback loop or over the LTP degeneration resistors. Thus, as Bob points out in his book and is also my experience, the danger of grainy sound due to highfrequency overloading is reduced. Simulated THD at 10kHz is 1.7ppm at 1V rms into 4ohm, 3.7 ppm at 10V into 4ohm (readings from the .four command). See also fft10k1V.png and fft10k10V.png. The Bode diagrams of all loops in globalloop.png, nestedloop1.png, and nestedloop2.png look like in a text book. A rough estimation of the VAS loop behaviour is depicted in loopvas.png. It is not that ideal, but the phase margin still appears to be larger than 60 degree. OPS quiescent current is about 50 mA, i.e. total supply current is lower than 100mA. There is a problem with all loops (as in Bob's original amplifier, too), if the load capacity C8 is set to e.g. 10nF, and the load resistor R20 to 1K. Then the series resonance between L2 and C8 remarkably reduces the phase margins, see seriesresonance.png. Unfortunately, the effect does not vanish with higher OPS quiescent current. Probably, only faster output transistors can cure that. Behaviour during turning on and off and clipping is considered in the next post. Matze doublenestedmiller.png fft10k1V.png fft10k10V.png globalloop.png nestedloop1.png nestedloop2.png loopvas.png seriesresonance.png 
17th April 2013, 10:07 AM  #12 
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Join Date: Sep 2012

Clipping and turning on/off
Clipping behaviour is not nice, see clipping.png. At least, the amplifier remains stable. Do not yet know what happens if one includes short circuit prevention in the OPS.
Probably it would be best to add some circuitry to prevent clipping at all. I also had a look on behaviour during turn on and off. In the simulations, main supply voltages are turned on after one second, and turned off after 5 seconds. In noclamp.png, one sees output excursions to both supply voltages on turn on, but no highfrequency oscillations relating to only conditional stability. In clamppos.png, Q28 together with D8 and D9 restricts the positive voltage at the Vbe multiplyer, so that only around 300mV can appear at the output. For that, one would need additional circuitry in place of the PWL voltage source V3 which turns Q28 off after 1.5 seconds. The high negative voltage can be supressed by delayed biasing of Q16 due to R41/C17, see clampboth.png. ================================ I think that nested Miller compensation may be a valuable ingredient to build good amplifiers. Audio amplifier construction should not neglect techniques routinely applied in operational amplifiers. Are there any comments? ================================ Matze clipping.png noclamp.png clamppos.png clampboth.png 
17th April 2013, 01:02 PM  #13 
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Join Date: Aug 2009

Nice try!
The outer Miller loop gets feedback directly from output stage so that it can achieve very low THD. That's the same idea as TMC. BTW, did you sort out the Math 
17th April 2013, 03:27 PM  #14  
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Join Date: Sep 2012

Quote:
thank you for the comments. I aggree that the approach lies somewhere between "our" TMC approach and the conventional nested Miller compensation. As in the former, all but the most inner loop (around VAS) include the output stage, thus increasing the NFB around VAS and OPS. From the latter stems the idea of recursive application of the compensation scheme, the difference being that in OPAs all "right end sides" of the Miller capacitors are connected to the same point, usually the output. Doing the Math certainly would be a good undertaking. May be it could bring more justification and better dimensioning rules than the simple explanation that I tried to give in "matzesamp.pdf" in post #1. To my defense I can only say that this rather informal approach is along the lines of Johan Huijsings OPA book, which provides a very clear but accessible explanation of all this stuff  except of course the tricks with the additional zero. A mathematical treatment could bring a better understanding especially of the transient behaviour. To be honest, I'm also a bit suspicious whether these nice 90 degree phase margins and 20dB per decade rolloffs really mean that the whole circuit will (at least in principle) behave like a simple topology with firstorder characteristics. From my breadboard amplifier (post #1), where I strechted the whole idea as far as possible, I only can say that the square wave response looks as nice on the oscilloscope as in the simulation. BR, Matze 

20th April 2013, 08:33 PM  #15 
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Join Date: Sep 2012

Probably, it will be necessary. I'm not sure about possible higherorder characteristics and others refer to Bode's results that seem to forbid firstorder behaviour with increased amount of feedback.
On the other hand, simulating the amplifier and looking at both frequnecy responses and transient squarewave responses (also at internal nodes), one does not see any overshoots in the wrong direction or any ringing. For my simple understanding, this altogether would point to firstorder behaviour. So I will have to look into the text books. This is the system under study from post #7: http://www.diyaudio.com/forums/attac...ationfig3.gif My plan is to first recap the transfer function for a closed loop of a miller integrator and a preceeding transconductance stage (standard OPA theory). Then I have to include an additional pole/zero (the nested Miller cap with zeroproviding resistor) in the originally resistive feedback path, giving a modified closedloop transfer function. Finally, this block should be included into the next outer loop with additional transconductance stage and resistive feedback network. If one can show that the closedloop transfer function of this outer block has firstorder characteristics (of course given the poles / zeros are placed properly), then the work is done. This certainly sounds too simple. What do you think? Is this the right way? Best regards, Matze 
21st April 2013, 08:57 AM  #16 
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Join Date: Sep 2012

Mathematics for firstorder behaviour
In the text below, one sees that each additional feedback loop with nested Miller compensation and additional zero leads to a new firstorder transfer function that is theoretically the same as the old function without the additional loop. This, of course, only holds true, if component and transconductance values are exactly matched. Otherwise, polezero pairs are created.
From my simulation examples, e.g. post #11, with not at all perfectly matched values, one can follow that this is not a too great problem. All loops still exhibit a nice gain slope of 20 dB per decade. Matze nmcfirstorder.pdf 
21st April 2013, 01:29 PM  #17  
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Join Date: Aug 2009

Quote:
It will be different cases which depends on whether the outer loop includes output stage or not. 1. If not, the outer loop must maintain the same loop gain bandwidth as you desired, not the inner loop. It is not good idea you put a Zero in the outer loop. It will worse the Gain Margin. I guess with out that Zero, it will remain stable. You will get a super VAS with very HIGH DC gain, and very low output impedance. 2. If outer loop includes output stage, the inner loop should maintain loop gain bandwidth. What I would do is put a EF right in front of VAS. In order to maintain the same as loop gain bandwidth, I would put a 100nF capacitor to the base and emitter of that EF. (That will bypass that EF at high frequency). So far, you will find the loop gain is pretty much a 2 pole compensation. I believe you will get there. The final step is put outer miller capacitor to the base pin of the EF and the output of Output Stage. The idea is to come up a 2 pole compensation so that you can use the extra gain to compensate with the outer Miller loop. You will get 2pole performance and 1pole like frequency response. I haven't tested yet. Hope that will work. Last edited by jxdking; 21st April 2013 at 01:52 PM. 

21st April 2013, 03:55 PM  #18  
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Join Date: Sep 2012

Hi jxdking,
thank you for reading and commenting the ideas. First, I have to clarify that in the small math derivation, the most outer global feedback loop was skipped. As it is assumed to be purely resistive, it will not change des system characteristcs in question. For a closedloop system, the calculated transfer function G(s) would equal the loop gain (in the closed loop) times feedback ratio. If we assume for simplicity a feedback ratio of one, unity gain crossover would be at 1/(2 pi R C). For that, the first transconductance stage just had to be thought as a stage with differential input, one serving as "real" input and the second connected to the output b(s). Quote:
Summing up, both the  in the math skipped  global feedback path and the feedback path with capacitor plus resistor are connected to the OPS output, creating the desired NFB (see also my examples with Bob's demonstration amplifiers and the implemented and bicely operating breadbord schematic from post #1). The stability margin penalty from including the OPS into these loops is not considered in the math, since we also do not consider it when discussing e.g. the TPC compensation scheme with its secondorder characteristic. In this case, only the slopes created by the feedback network around the VAS are discussed, the additional lowpass of the OPS is assumed to be high enough in frequency as to not remarkably change the picture. (Building an amplifier with a unity gain crossover just in the vicinity of the dominating OPS lowpass frequency probably is only feasible if one has a very well defined load impedance.) Quote:
Quote:
Quote:
I'm wondering about the loop one can open when inserting a probe between OPS output and "righthand sides" of all feedback paths (except VAS) glued together. This topic is also discussed in the thread on Dadod's TTTMC. I'm still convinced that it has no physical relevance, as it is the sum of all feedback paths, but not the feedback path important for any single loop starting "earlier" in the amplifier. Is there anybody who can comment on this last issue? Thanks and best regards, Matze 

21st April 2013, 05:31 PM  #19 
diyAudio Member
Join Date: Nov 2010

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 cancelled and the result will be first order behaviour.
This is also the assumption behind Cherry's Nested Dif. Feedback Loops. 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. More on the outer loop issue when it is not bedtime here! You could try a PM to JCX. Just his area, when he feels inclined to comment. Best wishes David 
21st April 2013, 06:21 PM  #20  
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Join Date: Feb 2003
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Quote:
Last edited by jcx; 21st April 2013 at 06:45 PM. 

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