Ok, I read the later papers as soon as I could.
I will think them over a bit more but my initial impression is that your later method is indeed equivalent to Tian, as you stated.
I still need to think more about how the Tian/your method relates to Middlebrook's GFT.
Middlebrook does 3 runs of different conditions whereas you and Tian use 2.
So it seems as if the GFT has more information to separate out various components.
It provides not only loop gain but also forward transmission function.
I suspect this is important for what I want to understand.
My interest is how to optimize nested and other non-simple loop structures.
If one uses the simplistic Black-style model then the theory results are not close to reality.
So I need to include load and/or feed-forward effects.
I have not yet worked out whether I can lump these two effects into one factor.
But Middlebrook keeps them separate, so I have more options.
Best wishes
David
David,
I think that my approach is still more flexible than that of Middlebrook and certainly than that of Tian. I can pretty much get all the visibility that I need by separate analysis and piece these together to form the net response. The classic result of Numerator/(1-LoopGain) is one result only. I can discect the numerator seprately from the loop gain and explore all of the contributors. Load and loop feedback, both directions, appear as terms in factors so can be looked at separately and compared when one takes over as the other loses steam. Some of these may have embedded loops. I will look into the GFT again in a few months and will talk to you about that. A friend of mine spent a lot of time looking into GFT and has fully converted to my approach. I will bring this up w him as well. Thanks for looking into my work. Appreciate any comments you may have. Right now I am working on a paper as I mentioned before to show that the various types of feedback can be easily handled systematically using my approach. I have not seen a discussion of this in either Middlebrook or Tian--please correct me if they exist. Once I complete that then I look forward to further exploring Middlebrook.
A few years back I had a Xtal oscillator that was showing problems starting in silicon but not in simulation. Using my approach I tracked the problem down to a parasitic feedback loop through a common current source between the xtal core and the first stage of the expander. Such parasitic loops are not discussed by Middlebrook, again, to my knowledge.
Look forward to more discussions.
Regards,
Auggie
I reread Tian et al over the weekend and have some tentative comments.
It seems that Tian takes all the feed-thru and factors this into the feedback loop.
Middlebrook factors the feed-thru into a separate path.
Tian's method has trouble when there is more than one loop, he explicitly comments in the paper that multi-loop requires the use of another technique.
Middlebrook would seem to handle this better. His claim is that the two loop analysis is complete for a linear system.
The feed-thru loop can modify the transfer function independently of the feedback loop.
I suspect that's what I need.
I have previously wondered about any differences between feed-forward in the feedback loop as opposed to feed-thru in the forward path.
Maybe Middlebrook handles all this neatly, some by modification of the "Loop Gain" and some by inclusion in the feed-thru (forward bypass) path.
I will reread Middlebrook and try to clarify.
I will also reread your work, the Drive Point Impedance looks to be a useful way to analyse.
I would also be curious about your friend's conclusions from his study of Middlebrook and GFT, perhaps you can recommend to him that he join DIYaudio too. Always educational to discuss ideas.
Best wishes
David
It seems that Tian takes all the feed-thru and factors this into the feedback loop.
Middlebrook factors the feed-thru into a separate path.
Tian's method has trouble when there is more than one loop, he explicitly comments in the paper that multi-loop requires the use of another technique.
Middlebrook would seem to handle this better. His claim is that the two loop analysis is complete for a linear system.
The feed-thru loop can modify the transfer function independently of the feedback loop.
I suspect that's what I need.
I have previously wondered about any differences between feed-forward in the feedback loop as opposed to feed-thru in the forward path.
Maybe Middlebrook handles all this neatly, some by modification of the "Loop Gain" and some by inclusion in the feed-thru (forward bypass) path.
I will reread Middlebrook and try to clarify.
I will also reread your work, the Drive Point Impedance looks to be a useful way to analyse.
I would also be curious about your friend's conclusions from his study of Middlebrook and GFT, perhaps you can recommend to him that he join DIYaudio too. Always educational to discuss ideas.
Best wishes
David
Again, I have not fully gone into Tian nor Middlebrook as neither sets up the process completely for me to follow easily. My approach is fundamental from the start so that I can examine validity at any point. Want to fix that (Tian and Middlebrook questions) and take time to explore both later. Tian's result is the same as mine so can talk to that. However I produce more than just the loop gain function. The numerator needs to be defined specifically with the loop gain to produce the full transfer relation. In my approach I generate the numerator and the loop gain, combine these algebraically to generate the transfer function, and simultaneously do a closed loop simulation (analysis for simple ckts) and show complete agreement.
The math for what you are distinguising as 'feedforward in the feedback "net"' where I changed it to 'net', compared to that of the direct through amp 'feed-thru' is identical. The paths are symetric in the (math) transfer relations and the system smoothely passes from one to the other as dominance changes. As the amp gain drops and the feed-forward path impedance perhaps decreases (capacitive shunt path for example) you see the effect in the factors involved--a system zero appears. It is strictly a matter of dominance. The forward loop path in the loop gain analysis is also fully symetric to the reverse loop path in the math domain and the larger of the two in magnitude at a given frequency dominates. We call the path through the amp 'forward' by convention and perhaps that is part of the problem. Nomenclature.
I handle internal loops transparently. These collapse and modify appropriate factors in the transfer function adding detail to the flow graph. You can see this in the LDO designs where the Miller compensation internal loop is absorbed in the appropriate factors and terms in the analysis--in simulation and in hand analysis. Another example is in my 2012 and again in my 2013 paper for the Mid West Symposium on Circuits and Systems where I specifically add a large gate-to-drain capacitor (internal loop) AND a resonator shunt to the output to show their effects in the effects to ckt responses. I see no problem w multiple loops in this sense. Now if I want to focus on these internal loops, then my final Tian-like result needs to be enhanced. This can be done systematically again by adding texture to the graph exposing the effects of internal nodes specifically. This is generally not needed and I mostly allow all internal loops to collapse naturally in the process. I plan to include part of this discussion in my next paper but would like to continue this dialog w you and others to help me formulate the paper better. I will likely add more developed notes to my website as I go as well.
And I will be seeing my friend, Don Patterson, in the next few weeks to discuss much of this. He will be a co-author in the coming paper. Will invite him to join these discussions. Don contacted me about 15 years ago and we have had on-goning discussions since. I am still learning how to navigate this forum (DIY) myself and only stumbled into this conversation which I much appreciate.
Please take a step back and apply my dpi/sfg approach to very simple circuits such as I do in my papers to remove circuit complexity from the process. Even two loop passive nets reveal aspects of the process nicely. Analysis of the standard bandgap circuit with two external loops, one positive and the other negative feedback loops, plus internal amp compensation is another example of multiple loop systems. Then move onto my Z-method for specific loop gain analysis. The dpi/sfg results will be in the classic feedback form but this is only math and not valid for loop gain representation. Mostly the results will be close enough that this distinction is not needed BUT you will eventually find a circuit where the difference may be important. RF applications perhaps?
Thanks again for the discussion. As I do not see others responding, we may consider moving this discussion elsewhere... Coments?
Best Regards,
Auggie
Thanks for the note on interest. Glad it is more than just Dave and me talking to each other.
Regards,
Auggie
Yes, I think this is the heart of the issue.
Tian (and you, presumably, but I know Tian better so that will be my reference)
absorbs the forward transmission thru the feedback network into the controlled source.
And similarly the reverse transmission thru the controlled source can be absorbed into the feedback network*.
This leads to an "pseudo" loop gain that is useful but I do not think it reflects the physical reality of the circuit.
If the controlled source is inactive then the "pseudo" loop gain will be zero.
In reality the feed-forward thru the feed-back net will still exist.
This is the behavior that Middlebrook's extra path can model but I don't see that Tian does.
In practical circuit simulation it probably doesn't make much difference but I want to clarify the concepts because I want to understand nested loops better and I can find very little useful information on this.
Best wishes
David
*Ed Cherry also proposes this in the reference in posted.
I hope to discuss this with him as soon as his personal affairs allow.
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Let's define terms as we go. I look at the fbk system as having a gain block and a feedback net. There is 'forward' and 'reverse' transmission both through the gain block and the feedback net. So forward and reverse transmission exist in real systems more than one may think--bi-directional aspects of gain block, fbk net, active elements.
A number of fbk loops exist in the ckt that may never be identified so when you talk about multi-loop ckts, at some level ALL fbk ckts are multi-loop. An mos transistor will have gate-drain cap coupling for example, adding an internal loop. An amp block may have reverse transmission in addition to the dominant forward path, another internal loop. Add resistive supply and ground lines and you add feedback paths...
For me, the controlled source is not the focus and further it is NOT the controlled source of an active element in the design. It comes about from where I choose to look at the circuit--as an effective port.
Not clear what you mean about a pseudo loop gain. My approach to loop gain is to find the impedance looking into a single node. This leads to a clear distinction in signals-- those that loop the circuit (cross-currents) and those that are shunted to ground (self-currents). Loop gain is then the negative of the ratio of the summ of the cross-currents to the sum of the self-currents. As for your psuedo loop gain going to zero 'when the controlled source is inactive', yes, that is exactly what should happen. Loop gain is different than system transfer function and transmission through the fbk net will still exist as you say and appear in the proper formulation of the transfer function.
Tian gives the loop gain. The system transfer function still needs the numerator function and this numerator function will contain the path that you are looking for that Middlebrook specifically adds while my Z-method explicitly accounts for. How does Tian handle the numerator? H=Num/(1-LG)
We will need to get specific soon. Can you sketch a simple inverting gain stage and formulate your questions from there. Best to use simple amp two-port model and passive fbk net to keep analysis to hand calculations.
Regards,
Auggie
Yes, that's about the way I see it too, but most analyses assume a simple loop.
So I want to find the simplest way that still accurately handles the complexity you mention.
I have mostly looked to Bode for my methods, so I tend to think in terms of controlled sources.
Also Tian has distinctly different "loop" and "controlled source" techniques and that has influenced my attempts at a synthesis.
I will look more closely at the differences between Tian's results and yours.
The similarity may have lead me to miss important differences.
Yes, I was just at the point where I think I need to do some simple examples.
I will sketch them and post as soon as I can.
Best wishes
David
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Bode and his co-workers did a lot of hand analysis so kept models simple. This led to Middlebrook's observation that you cannot bench measure loop gain as you cannot separate currents in the active device controlled source externally. Stepping back and looking at the controlled source from a two-port perspective, this separation is done in the composite and is now feasable as this effective controlled source now contains more than just the active element gm--it contains internal feedback/feedforward effects as well. The additional paths are now seen to be part of the loop transmission in addition to the active element's transconductance. Once you extend the concept of controlled source the problems that you see go away.
The simplest feedback circuit that I could come up w is in my 2013 paper using a single transistor amplifier. I added gate-drain capacitance to enhance the 'internal device feedback' effect for discussion. The resonant load added additional effects. Once this circuit is understood, the single transistor can be replaced with a general amp two port model and the analysis is the same as for the single device. The model absorbs all the additional complexity and SPICE performs the math in the simulation. Take a look at that circuit to start with.
--Auggie
Hi
Are you ready for a bit more discussion now?
I noticed in one of your papers a reference to Mason's rule for a gain calculation.
The particular calculation in the paper only needs the simple Black formula but the reference was a timely reminder to re-study Mason's work.
I re-read the technical note he published to summarize his thesis and that inspired me to acquire a copy of the thesis itself.
Lots of work there, in the meantime I have a few comments.
Mason has an important result that essentially restates Bode's work.
That is, that if there is one node that can be split to break all feedback then the system is effectively a one loop system, he calls this "index of one".
He then draws the general index one system, after simplification to essentials.
This looks to me to be equivalent to Middlebrook's GFT formulation.
Perhaps this addresses your concern (expressed in #15) where you didn't consider it was developed from first principles?
Best wishes
David
As I re-read the earlier posts to find the reference, I noticed one of my prior posts was not correct.
In #17 I questioned whether Tian was incomplete in the way it handled the reverse transmission.
In fact the issue is whether Tian is incomplete because it does not consider null (forward) transmission.
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Dave,
Yes and No. I want to discuss this further BUT have found an error in my and in Tian's result. Am still working on resolving this but essentially we have a result that is wrong in the internal details but correct in external results. This means that results internal to the model are subject to misinterpretation while external results are correct. The external transfer function is correct while results looking at internal resposes are comprimised. Please bear with me while I unravel this. Perhaps I too need to look into Mason's thesis. Not familiar with 'index of one' definition. I think that we will converge soon to a final result that may indeed be consistent w Middlebrook. Thanks for your comments and questions as they have caused me to look more closely at my own work. Am very greatful for this.
Best Regards,
Auggie
Yes and No. I want to discuss this further BUT have found an error in my and in Tian's result. Am still working on resolving this but essentially we have a result that is wrong in the internal details but correct in external results. This means that results internal to the model are subject to misinterpretation while external results are correct. The external transfer function is correct while results looking at internal resposes are comprimised. Please bear with me while I unravel this. Perhaps I too need to look into Mason's thesis. Not familiar with 'index of one' definition. I think that we will converge soon to a final result that may indeed be consistent w Middlebrook. Thanks for your comments and questions as they have caused me to look more closely at my own work. Am very greatful for this.
Best Regards,
Auggie
I expressed myself a bit unclearly, the actual thesis is a lot of work and I have just started on it, my comments "in the meantime" refer to the Technical Report 153 that he wrote to summarize and disseminate his research results.
It is excellent, well worth close study, best of all it's public domain and available >HERE<, so we can have a common reference, save cut-and-paste.
The picture I referred to is 17a on p12.
Nice to learn that the discussion has been helpful to you, it has certainly made me think about it.
More soon.
Best wishes
David
I have reread Bode and now understand a bit better the essential equivalence of Bode, Mason and Middlebrook.
I think the essential issue is what Middlebrook calls the "null loop gain", but I find it difficult to relate his conceptual view and nomenclature to Tian's.
However, I note the GFT method has three runs compared to Tian's two, the third pass is essentially to determine the null loop gain.
Simply on basic maths, number of equations should equal number of unknowns, I don't see how a two run system can be complete.
While that is not much to report for 2 weeks, the study has lead me to very satisfactory results in related work, nice consolation.
Best wishes
David
Dave,
I am looking into Mason and Middlebrook now. Still not a fan of Middlebrook and his GFT. Mason shows some math that I have been playing with--basically, a transfer function can be modified to maintain 'external' equivalency but internal results are not consistent. Sounds like your two weeks have been more productive than mine... However, I see that my approach as well as Tien's results have some math manipulations that need to be better defined. Not ready for more than that at this time. I see what I need to do just not liking it much. Middlebrook may provide an answer. I think in the end I will converge w Bode so will look more into his work next.
Regards,
Auggie
I am looking into Mason and Middlebrook now. Still not a fan of Middlebrook and his GFT. Mason shows some math that I have been playing with--basically, a transfer function can be modified to maintain 'external' equivalency but internal results are not consistent. Sounds like your two weeks have been more productive than mine... However, I see that my approach as well as Tien's results have some math manipulations that need to be better defined. Not ready for more than that at this time. I see what I need to do just not liking it much. Middlebrook may provide an answer. I think in the end I will converge w Bode so will look more into his work next.
Regards,
Auggie
I have reread some of Bode and was reminded of a question I have had for a while.
Most of Bode's work is expressed in terms of matrix determinants.
For instance the Return Ratio is expressed as the ratio of circuit matrix determinants under different conditions.
What is the physical interpretation of these determinants?
Usually I try to understand by dimensional analysis, in other words - examination of the units.
The units would seem to be admittance^2 in the nodal formulation.
That doesn't really help me, and in fact most of his work is done in immittance, which is even less specific.
This is why I try to reformulate in terms of Mason or Middlebrook, where I can see what happens.
Any lurkers on the thread are welcome to jump in too at this point
Best wishes
David
Correction, actually units are = admittance^n for circuit with n nodes, not much clearer but at least some advance to have it correct.
David
I don't know of a direct physical interpretation of the determinants. For me it's pure algebraic.
You can interpret the result. The matrix is build from node or mesh equations. To solve for a transfer function Cramers rule is used and from here comes the determinants.
Wai-Kai Chen in 'Active Network Analysis' gives a physical interpretation of the Return Ratio / Difference after it's definition with cofactors.
Josef
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