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Design >> Analog Design >> Phase margin in open loop and close loop
https://designers-guide.org/forum/YaBB.pl?num=1281428879

Message started by newic on Aug 10^th, 2010, 1:27am

Title: Phase margin in open loop and close loop
Post by newic on Aug 10^th, 2010, 1:27am

normally the phase margin of a close loop system like opamp, pll are analyzed in open loop rather than close loop. What is the reason behind? Is it because the open-loop phase margin is easier to be analyzed? It also shows clearly the location of poles and zeros in frequency axis.

Does it guarantee phase margin in open loop system is the same as in close loop system ?

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 10^th, 2010, 1:49am

newic wrote on Aug 10^th, 2010, 1:27am:

The parameter "phase margin" is defined only for an open-loop system.
If this margin is large enough, you can be sure that the system - after closing the loop ! - will be stable. However, be aware that this stability measure (like the gain margin) applies not to all systems.
That means - the open-loop transfer function must be stable and its gain resp. phase function must cross the zero line only once.
Otherwise, the complete Nyquist stability criterion has to be applied.

Question: What do you mean with "it shows....in the frequency axis"?
I don't understand this remark.

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 10^th, 2010, 6:09pm

Greetings,

Phase margin only has meaning for for closed loop systems.

If you read the Designer's Guide to Spectre and SPICE or the
appends on the site, you will see that in general open loop design
is not recommended and many closed loop approaches exist

http://www.designers-guide.org/Forum/YaBB.pl?num=1276870989

The reason these closed loop techniques have been developed and
are used is that the phase margin calculated from open loop
characteristics does not always match the actual closed loop phase
margin. There are assumptions in open loop analysis, for example,
that feedback factor is constant, and in real circuits these assumptions
are sometimes not satisfied.

For circuits with dynamic, periodic, operating points, there are often
alternative mathematical representations that allow closed loop
analysis of the system: phase domain modeling for PLL and state
average modeling for DC-to-DC converters.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by nobody on Aug 10^th, 2010, 6:25pm

I am with sheldon about his point of the phase margin.

Title: Re: Phase margin in open loop and close loop
Post by newic on Aug 10^th, 2010, 7:40pm

The reason i raise this question is because i see different phase margin in open loop and close loop transfer function when doing matlab analysis.

However, when people talk about phase margin, it directly refers to open loop transfer function. Analog books use open loop transfer function as well.

Is it a contradictory statement between Sheldon & buddypoor??

In the std analysis, it plots out open loop response as well but without affecting the dc bias. Do you refer this to close-loop technique?

Title: Re: Phase margin in open loop and close loop
Post by raja.cedt on Aug 10^th, 2010, 9:47pm

hello,

adding to buddypoor, as he said PM is only indicative metric of closed loop system but to measure this we need to use open loop info.

@seldon: Sir what you are saying is correct for simulation (what you mean is while finding loop gain don't open for all the reasons like dc operating point change and small signal AC impedance of the loop around the break point..it is correct) but not for theory strictly speaking it's from open loop only.

Title: Re: Phase margin in open loop and close loop
Post by newic on Aug 10^th, 2010, 10:03pm

The conclusion is to do PM analysis in open loop without affecting the dc bias / impedance etc.

How about the difference phase margins i got in the matlab by using open loop & close loop transfer function?? Is the PM of H_close invalid?

margin(H_open)
margin(H_close)

Title: Re: Phase margin in open loop and close loop
Post by raja.cedt on Aug 11^th, 2010, 12:02am

hi NEWIC,

it's quite reasonable to get difference between matlab and spice, because you are using macro models in matlab where as in spice you could take all bilateral effects of feedback.

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 11^th, 2010, 1:17am

sheldon wrote on Aug 10^th, 2010, 6:09pm:

Hi Sheldon,

I agree with you, that the phase margin has a "meaning" (i.e. relevance) only for closed loop systems as open loop system cannot oscillate. However, do you DEFINE the phase margin also in a closed-loop system? This would be interesting to learn.
I like to add that I have developed a method to determine the phase margin by simulation while the loop remains closed (to be published soon in "Analog integrated circuits...") - nevertheless, I think this parameter is defined using the frequency behaviour of the open-loop system, is it not? This was and is the background for my opinion that a closed-loop system "has" no margin. (By the way: at which point within the closed-loop could such a phase difference measured resp. found by simulation?)
Regards

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 11^th, 2010, 6:48am

Greetings,

Frank Weidmann has a nice summary on this topic. Please see

http://sites.google.com/site/frankwiedmann/loopgain

Raja,

I disagree, phase margin is a measure of the stability of a closed
loop system.

Other comments,

If you idealize the system then the only component that contributes
phase shift is the open loop gain of the amplifier. Using this ideal
model you can estimate the closed loop phase margin from the phase
characteristics of the open loop. This approach is fine for performing
hand analysis to give you insight into the expected behavior of the
design and to perform a sanity check your simulation results.
However, if you are going to go to the trouble of simulating the
design, why wouldn't you perform the most accurate simulation
possible by including the effects that are difficult to include in hand
analysis?

BTW, one of the methods in the thread

http://www.designers-guide.org/Forum/YaBB.pl?num=1276870989

uses a voltage-controlled, voltage source as the feedback element
and the results for this testbench should correlate with the
open loop measurements since the system is unilateral. So can
start with this testbench to verify your open loop results and then
move to sophisticated measurement methodologies.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 11^th, 2010, 7:48am

Hi Sheldon, I am sorry, but I must resist on some definitions - in order to avoid misunderstandings.
Coming back to the original question:

newic wrote on Aug 10^th, 2010, 1:27am:

Does it guarantee phase margin in open loop system is the same as in close loop system ?

I think each circuit has only one phase margin (as long as it contains only one feedback loop). Therefore, is it the margin of the closed-loop system or of the open-loop system? Perhaps the name is not too important as it is a more or less philosophical matter.
But its DEFINITION is important: The phase margin PM is defined as phase difference between 360 deg and the actual phase of the OPEN-LOOP transfer function at the cross-over frequency. Agreed?
However, of course the amount of margin plays a role only after closing the loop.
But coming back to my question of my last posting which was not yet answered by you: : At which node and at which frequency of the closed loop do you propose to measure/simulate the PM ? Where do you define the phase difference to 360 deg?
I know the report from F. Wiedemann since a long time and he has described several methods to simulate the PM. But in all cases the PM is simulated for OPEN-LOOP conditions.
Example: Middlebrook opens the voltage and current loop, respectively, by introducing successively a voltage and a current source and, then, he combines the results.
Thus, I cannot agree that the PM is a closed-loop parameter. It is relevant only after closing the loop; but it is a parameter that belongs to the circuit configuration in which it is defined and identified: A system with feedback in an open-loop configuration.

Regards to all. Comments are welcome.

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 11^th, 2010, 11:44am

Greetings,

I think that you misunderstand the Middlebrook method. The loop
remains closed for the measurement. A signal is injected into the loop
and you measure the return ratio. If you look at the other
measurement techniques: VCVS-based, two-port, Tian's method,
in all cases the loops are closed. In some cases the signals are
injected inside the loop but this does not mean that the loop is open.

For the current measurement, the current is injected in shunt with
the loop --> loop closed
For the voltage measurement, the voltage is injected in series with
the loop --> loop closed

A phase shift of 180 degrees causes inversion and results in
oscillation so phase margin is defined relative to a 180 degree
phase shift.

You need to calculate the system transfer function, the loop gain,
and from the relationship of the gain and the phase of the loop
gain you can calculate the gain margin and phase margin.

Each method of measuring the loop gain: Middlebrook, Tian, VCVS,
two-port places different requirements on where the signal is injected
and the measurements are made.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by Frank Wiedmann on Aug 12^th, 2010, 1:25am

I have the impression that your disagreement is just about words and not about the facts. Perhaps you can both agree on the following statement which avoids the terms open-loop and closed-loop:

The stability of a circuit that contains a loop is determined by the loop gain, which is the (negative) gain around the loop. Stability criteria like phase margin, gain margin or the Nyquist stability criterion must be applied to the loop gain. Loop gain is best simulated by one of the methods developed by Middlebrook or Tian.

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 12^th, 2010, 1:26am

Hello SHELDON,
Thanks for your answer. Sorry, but I am afraid that you are mistaken.

I think that you misunderstand the Middlebrook method.

I don't think so. Please, look at the attached pdf-file. I have tried to explain the background of Middlebrooks method using a simple example - and I think I have shown that it is, indeed, an open-loop simulation. But, that's no surprise. It's only logical - the gain of an open loop cannot be determined in a closed-loop configuration. That would be a contradiction!

The loop remains closed for the measurement. A signal is injected into the loop and you measure the return ratio.

No, that`s not the case. In principle, it is impossible to simulate the loop gain when the loop remains closed! It is evident that the loop gain is identical to a ratio of two voltages - an output voltage caused by an input voltage. That means, you need two ac decoupled nodes for injection of the input and measurement of the output - whereby the output voltage must be caused only by the gain of the open loop!
That is the reason I have asked you twice: How and where do you intend to inject such a voltage into a closed loop?

If you look at the other measurement techniques: VCVS-based, two-port, Tian's method, in all cases the loops are closed.
In some cases the signals are injected inside the loop but this does not mean that the loop is open.

The answer is given in the attachement. Perhaps the loops look as they were closed - but they aren't.

A phase shift of 180 degrees causes inversion and results in
oscillation so phase margin is defined relative to a 180 degree
phase shift.

No, speaking of the loop gain the PM is defined relative to zero resp. 360 deg. The margin is defined relative to 180 deg only if you speak about the simple product of all loop elements - i.e. without consideration of the inversion due to negative feedback (as it is often done in control systems). However, the term loop gain must include the minus sign. Thus, the reference to 360 deg.

You need to calculate the system transfer function,

For which purpose? It is not needed for loop gain determination. More than that, it is not possible to derive an expression for the loop gain from the closed-loop transfer function without knowing the contribution of the amplifier in advance.

Each method of measuring the loop gain: Middlebrook, Tian, VCVS,
two-port places different requirements on where the signal is injected
and the measurements are made.

Yes, no doubt about it. Otherwise, all these methods would be more or less identical. However, all are open-loop based. Maybe, its not easy to realize by simple visual inspection (as in case of Middlebrook).
__________________

Sorry, for the long answer.
But I think - in particular for beginners, who may follow this discussion - it is important to
(a) know the exact definitions of the parameters and
(b) their meanings and
(c) how they can be measured/simulated.

Greetings, regards. Comments are welcome.

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 12^th, 2010, 1:47am

Frank Wiedmann wrote on Aug 12^th, 2010, 1:25am:

I have the impression that your disagreement is just about words and not about the facts. Perhaps you can both agree on the following statement which avoids the terms open-loop and closed-loop:
.

Thank you, Frank, for your proposal. However, having in mind the original question

"Does it guarantee phase margin in open loop system is the same as in close loop system?"

I don't think that it is just a disagreement about words. It was my intention to make clear that there are not two but only one parameter called "phase margin" and that is defined for open-loop conditions.
However, it's effect is important only for closed-loop operation. But that was not the question.
Regards
Lutz

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 1:59am

Attachment 1: Voltage Loop Gain Testbench

Title: Re: Phase margin in open loop and close loop
Post by Frank Wiedmann on Aug 12^th, 2010, 2:06am

Phase margin only makes sense with respect to the loop gain of the circuit (and so indeed is only one parameter). For simple circuits like your example, the loop gain can be simulated by physically opening the loop. In general, however, it will be difficult to apply the correct operating points and impedances at the opening, so that the methods developed by Middlebrook or Tian are recommended. If the voltage and current sources inserted by these methods correspond to an "opening" of the loop is probably more of a philosophical question.

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 2:27am

Comment,

Please review the attachment, it shows the testbenches and the
results for measuring the loop gain of an amplifier using Middlebrook's
method. In addition, the dc sweep results and the transient results
for the current mode testbench are shown. The testbenches are closed
loop testbenches and the parameter of interest is the loop gain of the closed
loop system.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 2:28am

Part II

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 2:28am

Part III

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 12^th, 2010, 3:13am

Hi Sheldon,

thank you for the simulation results you have sent.
However, they contain not really some new information for me.
Therefore, I have problems to consider these graphs as an answer to my extensively described opinion.
Moreover, I am a bit confused cause I don't know what to do or how to comment the graphs.
For my opinion, the best way to discuss a technical matter is to ask and to answer questions.
Therefore, what is your comment to my last posting and the attachement? Anything wrong?

By the way, may I direct your attention to Tian`s & Kundert's paper (that, more or less is an extension of Middlebrook's method)?
It contains several times the phrase "broken loop".
Examples:
page 31, right columne, line 5
page 33, right columne, line 5 to 8 in "Null Double-Injection Technique"
page 34, right columne, line 7 below eq. (13) and line 8 above eq. (14)
_______________
Kind regards
Lutz

Title: Re: Phase margin in open loop and close loop
Post by aaron_do on Aug 12^th, 2010, 3:20am

Hi,

from the schematic it seems that vf = vn + vac, where vac is the ac voltage that has been inserted into the closed loop system. So I personally can't see how you can simulate loop gain like this. I'm definitely going to try it myself however, and if I'm wrong then thanks for the info.

btw did you simply run an AC analysis? Also how do the results compare with stb analysis. I don't have access to my workstation at the moment but i'll check it up later.

cheers,
Aaron

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 8:06am

Buddypoor,

Guess I need to invoke Occam's Razor

Your "open loop" testbench is basically the closed loop testbench with
the loop broken. It implicitly assumes that the loop is closed since the
input voltage source is tuned to force the amplifier output to the
appropriate voltage. Both testbenches give the same results, see the
attachment. As implemented this testbench can not be used for corner
analysis, parametric sweeps, Monte Carlo analysis, ... because the
input voltage needs to be manually tuned. The good news is that both
testbenches produce the same results.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by sheldon on Aug 12^th, 2010, 8:09am

Additional comment:

The current "open loop" testbench is difficult to use because of the
manual tuning required to set the dc operating point. Attached is a
modified version of the testbench that has a stable dc operating point.
It uses analysis dependent to close the loop for the dc operating point
calculation and to open the loop for the loop gain simulation.

Best Regards,

Sheldon

Title: Re: Phase margin in open loop and close loop
Post by buddypoor on Aug 12^th, 2010, 8:51am

Hi Sheldon,

Thanks for the reply, however I didn't get everything, as for example

Your "open loop" testbench is basically the closed loop testbench with
the loop broken.

Maybe, the reason is my limited knowledge of your language.

It implicitly assumes that the loop is closed since the
input voltage source is tuned to force the amplifier output to the
appropriate voltage., ...
.................
because the
input voltage needs to be manually tuned.

No, there is no need to tune any voltage manually. Both schemes ( I didn't invite them!) do not require any "tuning". But - I am aware that the second "test bench" in my former pdf attachement does not work properly for real opamps. It was used only to demonstrate that the first scheme (simplified Middlebrook) produces exact the same input/output voltages resp. the same ratio as the "classical and robust" open-loop method.
Anyway, thanks for the discussion.

Remember the original question if there are two phase margins (open resp. closed loop): I think, at least this question has been clarified.
It would be interesting to hear from the forum member who has posted the question if he is satisfied now.
Thank you and regards
Lutz

Title: Re: Phase margin in open loop and close loop
Post by newic on Aug 12^th, 2010, 9:17pm

Very impressive discussion.
I really learn a lot from this forum.
Thank you very much :)