Re: Hi Andy...
I don't know, to tell you the truth. As you've probably noticed, I tend to get busy during the week and often my replies are delayed. Or a thread will slip from my view if it doesn't stay near the top, as this one has. I'll have a look through the articles sometime this week and see if I can first understand your question completely, and second try to answer it. Your question is clear enough, it's just been a while since I've looked at these articles and it's a subtle point.
mikeks said:
I don't know, to tell you the truth. As you've probably noticed, I tend to get busy during the week and often my replies are delayed. Or a thread will slip from my view if it doesn't stay near the top, as this one has. I'll have a look through the articles sometime this week and see if I can first understand your question completely, and second try to answer it. Your question is clear enough, it's just been a while since I've looked at these articles and it's a subtle point.
Okay, I've looked at this some more. What Hurst calls the "loop gain" may be useful for theoretical purposes, and can take into account reverse transmission through the feedback network. But for practical purposes it's rather useless.
Consider the simple non-inverting op-amp configuration. If you use the so-called "method 1" like most people do, one of the blocks of the open-loop gain is a voltage transfer function that corresponds directly to the data sheet graph of open-loop gain vs frequency. But what if you use Hurst's "method 2"?
First you have to figure out which type of two-port parameters to use for the open-loop gain and the feedback network. At the output, the feedback loop and the amplifier output are in parallel, so the open-loop two-port parameters must have a shunt dependent current source. At the input, the feedback network and amplifier input are in series, so the open-loop two-port parameters must have a series dependent voltage source. So we end up using... h-parameters for the open-loop amplifier??? This is not practical. I want the use of block diagrams to clarify the concepts of the circuit, not obscure them. When you're done with this procedure, and combining parameters from the feedback network and forward path, you end up with only two blocks every time. But then the relationship of those blocks to reality is for all practical purposes nonexistent, except maybe for some special cases.
On the other hand, if you use "method 1", you end up with extra blocks, but those blocks mostly correspond to useful concepts in the actual circuit (like extra phase lag due to voltage division of the open-loop output impedance with a reactive load for example).
So I suspect Hurst is right according to his weird definition of "loop gain". The trouble as I see it is that he's hijacked a term that's in common use ("loop gain") to describe a concept that has little practical value. Likewise, the term that's not often used ("return ratio") he reserves for something that has great practical value. The rest of the world does not agree with his terminology it seems. Most people call "loop gain" what he calls "return ratio" and will continue to do so.
It was interesting how he used two-port analysis to cleanly deal with interactions between the feedback loop and the open-loop amplifier in "method 2" though. And I thought the article was worthwhile because it clarified for me the relationships between the blocks and the circuit parameters, including the "feedthrough" term.
As far as the TI article goes, I'd argue that the following statement regarding the inverting configuration is in error (p. 96): "The comparison also shows that the open loop gain (A) is different from the op amp open loop gain (a) for the noninverting circuit". I'd say that they are the same, but the block diagram of figure 6-1 needs an additional block at the input, an attenuation of value ZF / (ZF + ZG), to handle the inverting case.
Consider the simple non-inverting op-amp configuration. If you use the so-called "method 1" like most people do, one of the blocks of the open-loop gain is a voltage transfer function that corresponds directly to the data sheet graph of open-loop gain vs frequency. But what if you use Hurst's "method 2"?
First you have to figure out which type of two-port parameters to use for the open-loop gain and the feedback network. At the output, the feedback loop and the amplifier output are in parallel, so the open-loop two-port parameters must have a shunt dependent current source. At the input, the feedback network and amplifier input are in series, so the open-loop two-port parameters must have a series dependent voltage source. So we end up using... h-parameters for the open-loop amplifier??? This is not practical. I want the use of block diagrams to clarify the concepts of the circuit, not obscure them. When you're done with this procedure, and combining parameters from the feedback network and forward path, you end up with only two blocks every time. But then the relationship of those blocks to reality is for all practical purposes nonexistent, except maybe for some special cases.
On the other hand, if you use "method 1", you end up with extra blocks, but those blocks mostly correspond to useful concepts in the actual circuit (like extra phase lag due to voltage division of the open-loop output impedance with a reactive load for example).
So I suspect Hurst is right according to his weird definition of "loop gain". The trouble as I see it is that he's hijacked a term that's in common use ("loop gain") to describe a concept that has little practical value. Likewise, the term that's not often used ("return ratio") he reserves for something that has great practical value. The rest of the world does not agree with his terminology it seems. Most people call "loop gain" what he calls "return ratio" and will continue to do so.
It was interesting how he used two-port analysis to cleanly deal with interactions between the feedback loop and the open-loop amplifier in "method 2" though. And I thought the article was worthwhile because it clarified for me the relationships between the blocks and the circuit parameters, including the "feedthrough" term.
As far as the TI article goes, I'd argue that the following statement regarding the inverting configuration is in error (p. 96): "The comparison also shows that the open loop gain (A) is different from the op amp open loop gain (a) for the noninverting circuit". I'd say that they are the same, but the block diagram of figure 6-1 needs an additional block at the input, an attenuation of value ZF / (ZF + ZG), to handle the inverting case.
andy_c said:
The TI article is incorrect in it's definitions....what is refered to as the 'open-loop' gain, is strictly the foward path gain....
If the later definition is used instead, then indeed the foward path gain of the inverting configuration is different from that of the non-inverting arrangement.
It would appear that it is this difference that moves Hurst to implicitly suggest that the loop-gain of the inverting topology is also different from that of the inverting arrangement...
This from my perspective is untrue, as loop-gain is by definition obtained with independent sources set to zero, which confirms the prediction in equations 6-18 and 6-19 on pg 97 here:
http://focus.ti.com/lit/an/slod006b/slod006b.pdf
..that loopgain for both topologies is identical.....
The feedfoward path presented from input to output by the feedback network with foward-path dependent sources set to zero, only affects the closed loop transfer function in the presence of an independent input source, (as shown in the numerator of 6-18)....But this is not present when loop gain is determined (denominator of 6-18).....and thus cannot be factored into the loop gain function.
Therefore, the magnitude of the return ratio of an arbitrary feedback system, (regardless of topology), with indepedent sources set to zero, is indeed equal to the magnitude of loop-transmission, provided the ratio of foward to return impedances at the test point is infinite for a voltage test source, and conversely for an independant current test source.
This is contrary to Hurst....
This is contrary to Hurst....
I looked at this a bit more in light of your comments. I played around a bit with the non-inverting op-amp configuration using h-parameters for the op-amp and feedback network. If you're interested, try deriving the un-numbered equation between (13) and (14) in his transactions on education paper. For this circuit, the return ratio is computed by injecting a current source into the h21A position and going through the usual motions. In this case, h21A is the h21 of just the open-loop amplifier by itself. Hurst implicitly defines the loop gain as the return ratio of the unilateralized circuit. The unilateralized circuit combines h21A and h21B into a single source. To find the loop gain, this combined source is replaced with an independent source and the return ratio calculated in the usual way. You end up with different formulas which end up being the same if h21A >> h21B. In practice, h21A is huge, being AV(ol) * Zin(ol) / Zout(ol), so numerically the two formulas are almost identical in this particular case (ol = "open loop"). I don't know of a good way to describe this in terms of some general principles though. It's just a bunch of algrbra. To me, once non-unilateral behavior gets into the picture, it gets hard to interpret.
There's a nifty loop gain probe in the LTSpice users' group that uses a formula by Tian for loop gain that takes into account non-unilateral behavior. It's described in the article below. I'd love to get a hold of it.
Michael Tian, V. Visvanathan, Jeffrey Hantgan, and Kenneth Kundert, "Striving for Small-Signal Stability", IEEE Circuits and Devices Magazine, vol. 17, no. 1, pp. 31-41, January 2001.
There's a nifty loop gain probe in the LTSpice users' group that uses a formula by Tian for loop gain that takes into account non-unilateral behavior. It's described in the article below. I'd love to get a hold of it.
Michael Tian, V. Visvanathan, Jeffrey Hantgan, and Kenneth Kundert, "Striving for Small-Signal Stability", IEEE Circuits and Devices Magazine, vol. 17, no. 1, pp. 31-41, January 2001.
for bode plotting
this schematic appeared in EDN about a month ago -- instead of using a transformer in the feedback loop (of an SMPS or Linear Power Supply) an op-amp is used --
http://www.reed-electronics.com/ednmag/contents/images/91604di.pdf
in one of Nat Semi's articles on LDO regulator design they suggest an audio transformer., the EDN article points out that an opamp of suitable bandwidth is cheaper.
this schematic appeared in EDN about a month ago -- instead of using a transformer in the feedback loop (of an SMPS or Linear Power Supply) an op-amp is used --
An externally hosted image should be here but it was not working when we last tested it.
http://www.reed-electronics.com/ednmag/contents/images/91604di.pdf
in one of Nat Semi's articles on LDO regulator design they suggest an audio transformer., the EDN article points out that an opamp of suitable bandwidth is cheaper.
andy_c said:
Hi Andy..
He does indeed.....but then again, so does everyone.....except that Hurst asserts that, If RR and AF are to be equal, fig 1b has to be reduced to fig 1a here:
http://www.ece.ucdavis.edu/~hurst/papers/ExactSimFB,CAS91.pdf
Infact i reckon his fig. 1b does not need to be reduced to fig 1a, as the non-unidirectionality modeled by d in fig 1b affects Acl, but has no effect on return ratio, H, as the later is determined with d disabled.......
In other words, the inner sections of Hurst's Fig. 1b correspond exactly to his Fig1a.....which all that is required....making RR=AF
Note that the paper above was submitted for publication in 1990...
In the paper below, which he submitted four years later, Hurst appears to backtrack from his earlier position:
http://www.ece.ucdavis.edu/~hurst/papers/FullyDiffRR,CAS.pdf
In the second sentence of section 3 of the later, he states, without qualification:
Note that the references given were cited as incorrect by Hurst in his earlier submissions....
He makes no such claim throughout this last paper, and perhaps most significantly, he makes no reference at all to his earlier submissions below on the issue:
http://www.ece.ucdavis.edu/~hurst/papers/ExactSimFB,CAS91.pdf
http://www.ece.ucdavis.edu/~hurst/papers/Compare2FbApproaches,EDU.pdf
I need to find this....
Striving for small-signal stability
Tian, M. Visvanathan, V. Hantgan, J. Kundert, K.
Cadence Design Syst. Inc., San Jose, CA;
This paper appears in: Circuits and Devices Magazine, IEEE
Publication Date: Jan 2001
On page(s): 31-41
Volume: 17, Issue: 1
ISSN: 8755-3996
References Cited: 9
CODEN: ICDMEN
Anyone..please??
Striving for small-signal stability
Tian, M. Visvanathan, V. Hantgan, J. Kundert, K.
Cadence Design Syst. Inc., San Jose, CA;
This paper appears in: Circuits and Devices Magazine, IEEE
Publication Date: Jan 2001
On page(s): 31-41
Volume: 17, Issue: 1
ISSN: 8755-3996
References Cited: 9
CODEN: ICDMEN
Anyone..please??
andy_c said:
http://www.diyaudio.com/forums/showthread.php?postid=632038#post632038
I have had a long hard look at Tian...by comparing his method to Rosenstark's extension of Middlebrook's approach....
In order to establish whether bilateral transmission through the loop affects loop transmission, it seems to me that the ideal candidate for such an investigation would be the miller-compensation loop,where gross feedfoward transmission introduces an RHP zero in the foward path transfer function of an amp. so compensated...
If Tian is right, then minor loop-transmission determined using Rosenstark should be VERY different from that obtained using his (Tian's) method....
In fact the results are virtually identical...
...which seems to suggest, (as i have indicated elsewhere), that foward transmission does not affect loop-transmission....
Thoughts welcome...
mikeks said:
I'm not familiar with Rosenstark's method. Do you have the paper by chance?
Yes, that circuit would seem to demonstrate the issue of reverse transmission through the feedback network. But how to cleanly separate this effect from the reverse transmission of the amplifier forward path? At first glance, a simple candidate for purely hand-done analysis might be a simple single-transistor CE amp with Miller capacitor Cdom. But all reverse transmission of the forward path (say, y12 of just the CE amp) is due to Ccb in this configuration. This makes it indistinguishable from an amplifier with a unilateral forward path and Miller capacitor Cdom+Ccb. So such a circuit might tend to obscure differences between two loop gain computation techniques that are only subtly different from each other. I'm just thinking out loud - I haven't tried the comparison you did.
Hmm, you got me there. I wasn't aware of this RHP zero (which is bad news if true, unless it's at a very high frequency). When I get some time this weekend, I'll play around with some of these ideas with a good old pencil and paper.
If Tian is right, then minor loop-transmission determined using Rosenstark should be VERY different from that obtained using his (Tian's) method....
In fact the results are virtually identical...
You haven't shown the circuit diagram, so I'm puzzled at this point as to how you're able to analyze in situ the loop gain of the inner Miller loop in the presence of global feedback. I tried this a while back with the Middlebrook technique using subcircuit replication, and the global feedback seemed to foil my attempt at analyzing the loop gain of the Miller loop by itself. Your results look exactly as I would expect from a hand calculation of the loop gain of the minor loop - just the result I was trying for earlier with no success.
There's a lot of potential for confusion with terminology here. As an RF guy, I'm used to "forward" meaning "the desired way" and "reverse" meaning "the undesired way". But I think by "forward", you're referring to the transfer function of the feedback network from amplifier input to output, the reverse of the ideal way. Suppose the amplifier were unilateral. It seems reasonable that in this case, your "forward" transmission of the feedback network wouldn't affect the loop gain at all, since by the unilateral assumption of the amplifier, the signal couldn't propagate backwards all the way around the loop. I could see it creating a feedforward leakage term though. But suppose the amplifier portion were not unilateral. Take an extreme case where its reverse transmission were larger than its forward transmission, say y12=10*y21. Seems like there would have to be some effect on the loop gain, don't you think?
Of course, all this is just intuitiion and speculation. Also, I'm using the term "loop gain" as a synonym for "return ratio" rather than Hurst's non-intuitive definition (hijacking as far as I'm concerned) of the term "loop gain". I'll have a more detailed look when I get some more time. After working 10 hours a day writing code, I get burned out on problem solving. I really need to look at Tian's paper in more detail too.
AAAHHHH..
It would appear i was right after all...
http://www.ee.bgu.ac.il/~paperno/Negative_feedback.pdf
It would appear i was right after all...
http://www.ee.bgu.ac.il/~paperno/Negative_feedback.pdf
andy_c said:
RHP zero usually at sufficiently high freqs. that it can be ignored for typical TIS transadmittance....
Unless...(for some perverse 'subjective reason')......... one selects a MOSFET TIS....whose low gm will require that the RHP zero be compensated for....; resistor in series with Cdom should do the trick...
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