... 'good' zeros... don't decrease Loop Gain or increase load... so have a less evil effect on THD.
Bob Cordell points out the evils (to do with RF immunity) of using a cap across the feedback resistor in his book.
Not just less evil, but can be used to help actually reduce THD.
I understand concerns about RFI but I am inclined to make the feedback network the best feedback network and deal with RFI with RFI filters and the like. Don't compromise the primary function of the feedback network for a problem that should be properly dealt with elsewhere.
I have really started to think a few air cored RF inductors are an excellent idea.
Best wishes
David
Another useful zero is obtained by decoupling the VAS emitter resistor that Michael despises. Guru Zan points out that the effect of this is more subtle ... but its certainly worth trying if you have a VAS emitter resistor for other reasons ... or even if you haven't
If you have a VAS emitter resistor anyway then a capacitor helps to neutralise the effect of the RHP "bad" zero and is recommended.
What I haven't yet worked out is whether it is possible to create a useful LHP zero.
No point to add an emitter resistor unnecessarily just so you can cancel it out and be back where you started. This is indeed a bit subtle.
Even Cherry didn't have a simple way to explain it. I am not sure how it varies dependent on the VAS/TIS details and the load presented by the OPS.
No helpful input from any experts on this, so far, but I live in hope.
Best wishes
David.
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Thanks JPV. I have read that section, and I am afraid I do not agree with Sansen; I much prefer Solomon's analysis of the two stage Miller compensated amplifier as a voltage amplifier and not an OTA.
It is instructive that other respected authorities such as Grey, Hurst, Lewis and Meyer in their book "Analysis and Design of Analog Integrated Circuits" don't refer to the OTA in this context at all.
Finally, below are links to what I understand to be an OTA:
LM13600/LM13700
http://users.ece.gatech.edu/~lanterma/sdiy/datasheets/ota/ca3080apnote.pdf
Nothing at all to do with two stage miller compensated amplifiers, I think you'll agree.
You have not read the references I gave you. Browzing a preview in Amazone and reading a single page available on the subject and then commenting that you are in disagrement with one of the most respected person in the field without digging further is not serious

You come up with the 3080 dating from the sixties as a reference 🙂
There is a saying in french that must exist in English:
Il n'est pire aveugle que celui qui ne veut pas voir
Il n'est de pire sourd que celui qui ne veut pas entendre
there is no worse ( blind/deft) person who do not want to see/hear
Dave Zan
an interesting experiment about non minimum phase would be:
try to bring GBW much lower than second pole by increasing Cmiller and decreasing Cload of second stage. this will also decrease the zero with respect to second pole.
If now you connect the Miller OTA 🙂eek🙂 with a lot of feedback ( 100%) , the closed loop pole will be near the gbw and hopefully the zero will be at 2 to 3 times this frequency ( hoping it is stable).
Then we have a system ( closed loop) with a positive zero not far from its first pole in frequency. A step function injected at the input should show a response starting in the wrong direction ( negative) or at least very much depressed with respect to the response of the system without zero.
H(s) = (s/z+1)/D(s) where z is negative to make a postive zero.
Then H(s) = 1/D(s) + 1/z s/D(s)
The first term is the transfer function without zero giving you the step response from which you substract the derivative ( second term) of the step response. If pole and zero are not to far apart, a dip should be seen at the beginning of the step response.
Perhaps not relevant to audio amplifiers but interesting to see a temporal aspect of non minimum phase
an interesting experiment about non minimum phase would be:
try to bring GBW much lower than second pole by increasing Cmiller and decreasing Cload of second stage. this will also decrease the zero with respect to second pole.
If now you connect the Miller OTA 🙂eek🙂 with a lot of feedback ( 100%) , the closed loop pole will be near the gbw and hopefully the zero will be at 2 to 3 times this frequency ( hoping it is stable).
Then we have a system ( closed loop) with a positive zero not far from its first pole in frequency. A step function injected at the input should show a response starting in the wrong direction ( negative) or at least very much depressed with respect to the response of the system without zero.
H(s) = (s/z+1)/D(s) where z is negative to make a postive zero.
Then H(s) = 1/D(s) + 1/z s/D(s)
The first term is the transfer function without zero giving you the step response from which you substract the derivative ( second term) of the step response. If pole and zero are not to far apart, a dip should be seen at the beginning of the step response.
Perhaps not relevant to audio amplifiers but interesting to see a temporal aspect of non minimum phase
And now ifyou put a resistor in serie with Cmiller, the dip should dispear ( providing everything remains stable
You have not read the references I gave you...
On the contrary, I have Sansen's book " Analog Design Essentials", and I do not doubt his credentials, but similarly I don't doubt the credentials of the authorities who don't hold his views, such Hurst, Grey, meyer, Solomon, e.t.c.
I am squarely in the camp of those authorities who don't call a two stage Miller compensated amplifier an OTA, and, just like them, I am entitled to this position.😎
It is also quite clear from the references I provided, that the two stage Miller compensated amplifier was not historically what was refered to as an OTA, so I am not persuaded by Sansen:
http://www.uni-bonn.de/~uzs159/ota3080.html
http://users.ece.gatech.edu/~lanterma/sdiy/datasheets/ota/ca3080apnote.pdf
And, no, the 3080 is not from the sixties.

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You stated
This is incorrect. Amplifiers are not minimum phase.
Usually this is not relevant and they are practically minimum phase.
But for some reasonable amplifiers, not just implausible "straw man" examples, the non minimum phase has a practical impact. In particular it reduces the GM.
I posted evidence here -
http://www.diyaudio.com/forums/soli...lls-power-amplifier-book-369.html#post3546769
Asked you again here -
http://www.diyaudio.com/forums/soli...lls-power-amplifier-book-370.html#post3546905
And here -
http://www.diyaudio.com/forums/soli...lls-power-amplifier-book-372.html#post3547381
And then, after Mike commented that he missed it, reposted it here -
http://www.diyaudio.com/forums/soli...lls-power-amplifier-book-373.html#post3547703
So your statement above is remarkable, to put it politely.
The Spice ASC has been checked against the real amplifier.
It is not perfect, but it is better evidence than other simulations I have seen in DIY audio, mainly due to the work of Toni and Richard Lee to confirm the models and study normally overlooked parasitics.
Dave, it is hopeless. You quoted 4 or 5 times the same thing which, to start with, is an amplifier that has a some 47 degrees phase margin. Try to bias the output towards the rails, and note the phase margin going to 20-25 degrees. For anything else but simulation purposes, that's in my book a pathological design.
Secondly, you posted a simulation result, and a link to a schematic and the LTSpice file. You also mentioned "I haven't worked out the details", so please do, mention clearly what changes you did in the original schematics, what models you are using, and then maybe somebody will pick up, replicate the results, and draw it's own conclusions. Meantime, your example doesn't prove that "audio amplifiers are non-minimum phase system", but only that "all amplifiers have RHP zeroes".
Third, a 3-4dB reduction (out of 14-15dB) in the gain margin @7-8MHz doesn't make an audio amplifier non-minimum phase. Following your logic, all amplifiers are non-minimum phase, simply because all active devices have some sort of Miller feedback (be it Cob, Cgd, etc...). I've posted myself an example of an common emitter stage that has a relevant RHP zero. Is this relevant for audio? If you follow the example you will easily reach the conclusion that it is not.
Fourth, I quoted published material that clearly shows the relationship between the transconductance and the RHP zero positioning. And I've mentioned that there are cases (cmos op amps) where the RHP zero cannot be ignored. Are these audio amplifiers? Usually not, but for completely different reasons than their non-minimum phase behavior.
Perhaps you are missing the relevance of the non-minimum phase property in audio? This property essentially says that there are no ways to adjust the gain and phase separately. The corollary of this is that the only way to increase an audio amplifier loop gain at HF, while still keeping the audio amplifier stable, is to add N LHP poles to the loop gain, and N-1 LHP zeroes to bring the gain back to 20dB/decade at ULGF (where N=1 for Miller compensation, N=2 for TPC and TMC and N=3 for Cherry's NDFL). That's about it, and every attempt to go beyond this rule of thumb comes to the price of stability margins. Anything with N>3 is, from a practical perspective, irrelevant (at least because it would require fraction of pF precision), although I'm sure even a N=10 can be made to work in the simulator. IC design, that's a different story, but then again, we are talking about discrete audio here, isn't it?
Hi
The link is excellent. I found and read it a few years back and re-read it when reminded by Michael's post. Thanks to him for that because it was helpful to read it second time. So you probably need to read it a few times too😉
RHP zeros are practically never desirable in an amplifier so it is worth the effort to eliminate them. In a conventional amplifier the only one is likely to be caused by the VAS aka TIS. Usually not a problem because it is above any frequency of interest.
It is possible for a particular combination of reasonable component choices to result in the RHP zero frequency to be sufficiently low to affect the stability a little. This can occur if the LTP emitter resistors are fairly low (to reduce noise probably) compared to the VAS/TIS emitter resistor (used for over-current protection, often).
If your circuit is unconventional then normal rules-of-thumb won't help. But I doubt a RHP at >3GHz will hurt.😉
Best wishes
David
Hi Dave,
I seem to recall that the RHP zero for a VAS with 100pF Cdom and running at about 10mA with degeneration somewhere on the order of 25 ohms lies at about 60MHz. The RHP zero is there, but not causing a lot of damage. It is easy to remove with a small resistor in series with Cdom. That small resistor, if sized correctly, can provide a normal zero with will give a little bit of leading phase that is actually helpful. But we never want to over-do it with this resistor.
Cheers,
Bob
If you have a VAS emitter resistor anyway then a capacitor helps to neutralise the effect of the RHP "bad" zero and is recommended.
What I haven't yet worked out is whether it is possible to create a useful LHP zero.
No point to add an emitter resistor unnecessarily just so you can cancel it out and be back where you started. This is indeed a bit subtle.
Even Cherry didn't have a simple way to explain it. I am not sure how it varies dependent on the VAS/TIS details and the load presented by the OPS.
No helpful input from any experts on this, so far, but I live in hope.
Best wishes
David.
The emitter resistor plays an important role in setting, and stabilizing, the VAS standing current. Without it, you are likely to have an unbalanced LTP.
Not just less evil, but can be used to help actually reduce THD.
I understand concerns about RFI but I am inclined to make the feedback network the best feedback network and deal with RFI with RFI filters and the like. Don't compromise the primary function of the feedback network for a problem that should be properly dealt with elsewhere.
I have really started to think a few air cored RF inductors are an excellent idea.
Best wishes
David
You can claw back some gain and phase margin using this technique. However, if the cap is too large, you actually make things worse. I did lots of sims on this and eventually concluded m e-Amp was better served without it. RFI is a concern also.
If you have a VAS emitter resistor anyway then a capacitor helps to neutralise the effect of the RHP "bad" zero and is recommended.
I am not sure this is true. From my simulations the TIS's emitter resistor and shunt capacitor only seem to affect singularities in the TIS's minor loop transmission and not in its forward path frequency response which contains the positive zero.
What I haven't yet worked out is whether it is possible to create a useful LHP zero.
You can create a negative zero by placing a lead capacitor in the feedback network. Note that, contrary to Cordell, this does not compromise RF susceptability if a properly designed Thiel network is used at the amplifier output. Note also that this phase lead capacitor does not have any effect on THD because its action occurs well outside the audio band.
Alternatively, the TIS's positive zero can be made to migrate to the LHP by using an appropriately sized resistor in series with the Miller compensation capacitor. Note that if the resistor is too large, then it may increase the unity loop gain frequency, which, taken together with non-dominant sigularities, may again compromise stability margins.
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The Japanese approach as it was taught to me is simpler even than that . Fix problem not blame . Approach the challenge as a team and over come them.This is really Quality Management 101.
Perhaps the biggest factor in the rise to dominance of Japanese manufacturing in the 50s & 60s was their adoption of these methods and more importantly, their understanding of these issues. The statistical tools were taught to EVERYONE at a very early age in school.
My experience is that Japanese engineers are always quite surprised to find the rare decadent Western engineer who understood these concepts ..... while the chap who sweeps the floor in a Japanese factory certainly would 🙄
One of my most satisfying experiences was explaining the bell (Gaussian) curve to my Shop Floor Supervisors & Charge Hands and realising they instantly grasped the implications with regard to the parts they had to work with ... and also as a measure of the quality of their own work.
On the other hand, I know Quality Assurance Managers who could quote AQLS, six-sigma and other pedantic stuff in their sleep ... but who didn't have a clue about the implications of a flat top or slanting distribution. You try not to buy from these people as you also wouldn't buy 5% parts from people who supplied you with 'flat top' 1% parts. (Kindhornman's double peaked distribution 😱)
I hope the situation has changed for Western manufacture.
Harry, there will be people in Bristol U who teach this, probably in Manufacturing Technology or something. It will be under Statistical Process Control. Sadly, understanding the concepts as they relate to real life is far more important than being able to do the maths. Many of my Supervisors and Charge Hands didn't finish High School.
There are simple techniques to get around the maths .. but the 'real life' understanding is paramount ... as the pseudo gurus here so clearly demonstrate. 🙂
_______________
Kindhornman, some manufacturing methods are more amenable to process control than others. NPO ceramics do have quite small variance and can probably be pushed towards a nominal. Alas, there is no demand so no incentive for the makers.
But think of how polystyrene caps are made and you'll not be surprised that 1% film caps will often be selected from a large batch.
My knowledge is 20 yrs old so 21st century tech may be a lot better. Certainly, resistors (at least through hole ones) are much improved from da Jurassic carbon sticks.
_______________
ABSOLUTE NONSENSE! Your circuit can't possibly work unless you call it by the correct TLA. [deleted : 2 pgs of references supporting my definitive 8 pg explanation of why my TLA is right nyah! NYAH! while yours is rubbish]
En u spul 'mater' rong 2! 😱
The emitter resistor plays an important role in setting, and stabilizing, the VAS standing current. Without it, you are likely to have an unbalanced LTP.
I suspect this is true only in the case of the fully complementary TIS with complementary LTPs.
With the ordinary Thompson topology taught by Self the TIS current source defines quiescent current and not the TIS's emitter resistor.
Alternatively, the TIS's positive zero can be made to migrate to the LHP by using an appropriately sized resistor in series with the Miller compensation capacitor. Note that if the resistor is too large, then it may increase the unity loop gain frequency, which, taken together with non-dominant sigularities, may again compromise stability margins.
In the case of your schematic you can remove the 100pF
loading the VAS/TIS (or is it VATIS ?) and simply increase
its buffer output Z by increasing its emitter resistance
from 250r to 1k.
The value of the buffer's emitter resistor was selected so as to makes the buffer's current draw roughly equal to the current drawn by the current mirror so as to minimise current imbalance in the LTP.
Making relatively small (was it 250R?) has no effect on the characteristics of the TIS.
Making relatively small (was it 250R?) has no effect on the characteristics of the TIS.
Zero error is zero effective input signal gives zero output. We colloqially (sp?) say that we want to drive the error to zero, but that implicitly assumes infinite gain. Once you figure in the gain, it should be: drive the error to Vout/OLG.
Edit: we may have a semantic issue here: I use 'error' as the effective input signal of the amp, i.e Vin-Vfeedback.
jan
This may be true for an inverting amplifier. 100% FB with infinite gain would wipe the signal out completely. But I can't see this with the non inverting mode. Simulate with an ideal op amp and see what happens. With no attenuation at the non inverting input the lowest the gain can go is unity no matter how much feedback.
Cheers,
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The value of the buffer's emitter resistor was selected so as to makes the buffer's current draw roughly equal to the current drawn by the current mirror so as to minimise current imbalance in the LTP.
Making relatively small (was it 250R?) has no effect on the characteristics of the TIS.
Frequency response with 250r and 1k buffer output load.
100pF VAS/TIS loading is absent when simulating with 1k.
Attachments
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I suspect this is true only in the case of the fully complementary TIS with complementary LTPs.
With the ordinary Thompson topology taught by Self the TIS current source defines quiescent current and not the TIS's emitter resistor.
Yes, but who in their right mind would design an amplifier like that?
I started what I called Quality Meetings in our factory before I knew what Quality Circles were. I did it cos 'senior management' would argue & blame each other for problems to no useful purpose ... like our semantic/pedantic discussions.The Japanese approach as it was taught to me is simpler even than that . Fix problem not blame . Approach the challenge as a team and over come them.
Much later, when I first got a book on Quality Circles, I was so shocked that I went to the park and read it from cover to cover.
It described EXACTLY the problems & successes we achieved ... and also the opposition from 'senior management'. These dinosaurs where opposed to my Quality Meetings even when there was clear evidence that they resulted in substantial gains in productivity, quality & morale.
The SPC (which I didn't know was called SPC at the time) was part of this initiative. My Quality Meetings/Circles were teams. Senior Management weren't.
If this sounds like I'm prejudiced against Western Management .. that's cos I am. 🙂
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The emitter resistor plays an important role in ... the VAS ... current. Without it, you are likely to have an unbalanced LTP.
I suspect this is true only in the case of the fully complementary TIS with complementary LTPs.
With the ordinary Thompson topology taught by Self the TIS current source defines quiescent current and not the TIS's emitter resistor.
Yes, it depends on the details of the VAS/TIS. I have looked at fully complementary for myself, the test amp was more or less "blameless".
Also depends on whether you use a EF in front of the VAS. I have posted a bit on this in Toni's thread.
I wanted to study effect of VAS emitter resistor with minimum assumptions about the rest of the circuit.
Then we can discuss the implications, if any, on the VAS/TIS.
Best wishes
David
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