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Feedback and Stability (Read 16087 times)
hchanda
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Feedback and Stability
Nov 14th, 2006, 11:24am
 
Hi all,

I know that there are several discussions on the feedback and stability. I went through all the discussions and searched alot in google.
But still I do not understand the following (fundemental stuff)

1. When studying the stability (not using spectre), if we want to break the loop and perform an AC analysis , where should we break the loop.
I have seen in many papers and discussion saying that we should break the loop at high impedance node. Is it applicable for any feedback systems (like in oscillators)?

2. When we have multiple loops in a circuit, how to evaluate the stability of the circuit?  How do you decide which loop is critical  and affect more?

Please let me know if you have any good books/papers (introductory) on the above topics.
I appreciate all of your precious time.

Thanks in advance,
ch
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Frank Wiedmann
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Re: Feedback and Stability
Reply #1 - Nov 15th, 2006, 1:01pm
 
You have probably already seen the thread at http://www.designers-guide.org/Forum/YaBB.pl?num=1155668476;start=all. The article mentioned in reply #28 describes the method used by Spectre and is one of the best treatments of loop gain I have seen so far. In reply #12, there is a link to an implementation of Spectre's method in another Spice simulator.

It is generally not a good idea to break the loop because of the difficulties in getting the operating points and the impedances at the breaking point right. However, for a simplified analysis, you can also use the loop gain definitions Gv and Gi according to http://www.spectrum-soft.com/news/spring97/loopgain.shtm. They will always tell you correctly if a circuit is stable, although you will get different values for phase margin and gain margin than with Spectre's method and the loop gain will also vary depending on the position of the probe, unlike with Spectre's method.

Gv and Gi can be used because they fulfill equation (3) of the article mentioned above. You can find a derivation of this equation in section 4.4 of Bode's book, which is reference 1 of the article. For the circuit of figure 7 of the article, the determinant Δ is k1+k3+Ye+Yf. For the loop gain defined in the article, we have x=k1+k3. If you do the math, you will find that for Gv, you get x=k1+Ye and for Gi, you get x=k1+Yf. So, Gv gives results close to Spectre's method if k3 and Ye are small with respect to k1 and Yf, and Gi gives results close to Spectre's method if k3 and Yf are small with respect to k1 and Ye. In other words, you will get best results if there is no significant backward transmission and the impedance looking forward is much larger than the impedance looking backward (use Gv in this case) or vice versa (use Gi in that case).

For multiple loops, first look if you can find a wire that breaks all loops and perform a stability analysis at this point if it exists. If such a wire does not exist, the rigorous method calls for disabling all loops and then activating them one by one, plotting a Nyquist diagram in each case. This is described in section 8.8 of Bode's book. In Bode's words: "If a circuit is stable when all its tubes have their normal gains, the total number of clockwise and counterclockwise encirclements of the critical point must be equal to each other in the series of Nyquist diagrams for the individual tubes obtained by beginning with all tubes dead and restoring the tubes successively in any order to their normal gains." In practice, if the loops are not dependent on each other, you can often get away with examining each loop separately.
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hchanda
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Re: Feedback and Stability
Reply #2 - Nov 15th, 2006, 9:55pm
 
Hi Frank,

Thank you very much for the response. Could you please explain how the impedance seen at different nodes is related to breaking of the loop? Also I could not follow you statement quoted below

"you will get best results if there is no significant backward transmission and the impedance looking forward is much larger than the impedance looking backward (use Gv in this case) or vice versa (use Gi in that case)."

Thank you very much for your time.

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Frank Wiedmann
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Re: Feedback and Stability
Reply #3 - Nov 15th, 2006, 11:24pm
 
Please refer to figure 7 of the article and to my mathematical formulation in the sentence before the one you quoted (which is the more exact one anyway). Although you do not actually break the loop for doing the analysis, you look at the impedances you would see if you broke the wire at the given point. As you can see in figure 7, Ye is the admittance (reciprocal of impedance) looking forward and Yf is the admittance looking backward.
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hchanda
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Re: Feedback and Stability
Reply #4 - Nov 16th, 2006, 8:15am
 
Hi Frank,

Thank you very much for the response.

I am unable to correlate the equations or figure numbers(like figure7 in below quoted text) that you are explaining to the article you have mentioned above.

"Please refer to figure 7 of the article and to my mathematical formulation in the sentence before the one you quoted (which is the more exact one anyway). Although you do not actually break the loop for doing the analysis, you look at the impedances you would see if you broke the wire at the given point. As you can see in figure 7, Ye is the admittance (reciprocal of impedance) looking forward and Yf is the admittance looking backward."

Can you please let me know what you meant by " Although you do not actually break the loop for doing the analysis, you look at the impedances you would see if you broke the wire at the given point."

Just to get clear understanding,

1. With the classical method, that is by breaking the loop , adding a low pass filter, the poles/zeroes shift at very high frquencies because of the filter(how low pass filter affects the AC results, can you provide me an example). That is the reason we are going with other methods (spectre stability and Middlebrook). But If I do not care about the response at such an high frequencies, I am still OK to use classical method. So if I were to use classical method and if I have a signle feedback loop it does not matter where I break the loop right? (as long as I have correct DC operating point).

2. If I would like to go with Spectre stability and if I have a single feedback loop, I can place the probe anywhere in the loop right? Do we need to take care of placing it at high impedance node ?  For example http://www.designers-guide.org/Forum/YaBB.pl?num=1155668476;start=all, in this forum reply#21, Grosser have tried placing probes at output of op-amp and at the positive input of op-amp. So If I performs spectre stability analysis by placing the probe once at the output of op-amp and another time at the positive input of op-amp, Will I get the same loop gain response?

Once again I appreciate alot for all your help.

hc

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Frank Wiedmann
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Re: Feedback and Stability
Reply #5 - Nov 16th, 2006, 1:17pm
 
I don't really understand your problem. Are you trying to tell me that you cannot find figure 7 in the article mentioned in reply #28 (i.e., http://www.kenkundert.com/docs/cd2001-01.pdf )? Looking at this figure should make pretty clear what I meant by my explanations.

Regarding your questions:

1. I strongly advise against using the "classical" method of breaking the loop you describe, because it is much more complicated and error-prone than any of the other methods described here. However, if you insist on using this method, it might indeed be preferable to use a high-impedance node because you will probably disturb the impedances less by inserting the filter.

2. Like I already briefly mentioned above, the loop gain calculated by Spectre's method is independent of the position of the probe in the loop (and also of its orientation).
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hchanda
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Re: Feedback and Stability
Reply #6 - Nov 16th, 2006, 1:38pm
 
Frank, I was referring to this article http://www.spectrum-soft.com/news/spring97/loopgain.shtm and I was not able to correlate.  Thank you very much for your guidance. I am not going to use the classical method but I wanted get a clear understanding on its disadvantages. Thanks once again.
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