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Design >> Analog Design >> What's the phase margin in this casde?
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Message started by dandelion on Jun 20^th, 2007, 6:11pm

Title: What's the phase margin in this casde?
Post by dandelion on Jun 20^th, 2007, 6:11pm

Hi,
Pls. take a look at the attached diagram.

My design need to provide the spec of phase margin. But for the attached diagram, what's the phase margin in this case? Is it 80 degrees?

At the point A, the phase obviously reaches -180'C while the gain is larger than one, what's the impact to the performance at thsi freq?

Thanks in advance

Title: Re: What's the phase margin in this casde?
Post by monte78 on Jun 21^st, 2007, 2:13am

Hi!

I think that your phase margin is good but I the problem is that you also need to take a look to the gain margin, that should be negative (in terms of dB). In your case, you do not have gain margin, so I think that your circuit will be unstable as if you had a poor phase margin.

Bye!

Monte

dandelion wrote on Jun 20^th, 2007, 6:11pm:

Title: Re: What's the phase margin in this casde?
Post by ACWWong on Jun 21^st, 2007, 2:48am

I would say in most usage/system circumstances your phase margin is irrelevant and reporting 80^o is not correct.

At around frequency A you are unstable, so any "stability" measures are rendered not very meaningful.

Unless your specification/system expects/requires this unstable behaviour, you should consider fixing the problem.

Title: Re: What's the phase margin in this casde?
Post by Berti on Jun 21^st, 2007, 3:44am

I am not so sure ... I think one needs to apply the extended nyquist stability
criteria. And maybe this system might even be stable..?...
But I am not so familiar with that, because usually it is enough
to check the phase-margin.

But probably somebody else has more experience.?..

Title: Re: What's the phase margin in this casde?
Post by Frank Wiedmann on Jun 21^st, 2007, 6:08am

In case of doubt (if there is more than one crossing of 180 degrees or 0 dB), you should always apply the Nyquist stability criterion (see http://en.wikipedia.org/wiki/Stability_criterion). In the case presented here, by applying this criterion, you will find that the circuit is in fact stable (if the gain remains below 0 dB for higher frequencies).

When phase margin is specified for a system, it is usually assumed that the loop gain has two significant poles and no zeros. In this case, you can derive from the phase margin the shape of the closed-loop response of the system (damping of the step response etc.). The loop gain in the example presented here does not satisfy this condition, so giving a phase margin does not make very much sense.

If you want to know how much margin your design has, you should perform some Monte-Carlo simulations (or parameter variations) on the circuit and examine if it remains stable.

Title: Re: What's the phase margin in this casde?
Post by Ken Kundert on Jun 21^st, 2007, 7:59am

One thing to be careful of in this case is slew-rate limiting. When slewing the gain of the amplifier will drop and could cause the feedback system to become unstable. I have seen this before. In my case it manifested itself as a circuit that was stable for small signals, but as soon as an abrupt change occurred in the input signal the circuit began to oscillate and would not stop. I don't know that that is what will happen in this case, but I suggest that you explore the possibility.

-Ken

Title: Re: What's the phase margin in this casde?
Post by Frank Wiedmann on Jun 21^st, 2007, 11:39pm

Thanks for pointing out this danger, Ken. To be a little more specific (for those who are not very familiar with Nyquist plots): The example presented here will become unstable if the gain decreases so that it crosses 0 dB in the frequency range where the phase is below -180 degrees.

Title: Re: What's the phase margin in this casde?
Post by aamar on Jun 22^nd, 2007, 12:48am

Hallo ,

the circuit is clear to be unstable, the range of frequencies whose phase margin is below 45 degrees will lead to oscillation.

In another way, any system that has more than one pole, has a problem at the second pole where the feedback of the system will turn to be positive and this will lead to oscillation, the solution is one of two:
1. To damp the signals at these frequencies by shifting this pole far to high frequencies where your circuit or amplifier has at least -40dB, cancelling these signals before having this positive feedback effect.
2. The second thing is to compensate this second pole, so that you bring a zero at the same frequency of the second pole to cancel its effect early before it (the second pole) brings the phase margin to critical values.

In your case at the range of frequencies below the 45 degrees you have still a gain, this means that the signal will oscillate free plus amplification, which is the unwanted case.

Best regards,

aamar

Title: Re: What's the phase margin in this casde?
Post by Frank Wiedmann on Jun 22^nd, 2007, 1:03am

aamar wrote on Jun 22^nd, 2007, 12:48am:

Hallo ,

the circuit is clear to be unstable, the range of frequencies whose phase margin is below 45 degrees will lead to oscillation.

I beg to differ. The example presented above may have ringing in the step response, but according to the Nyquist stability criterion it is stable, it will not start to oscillate by itself.

Title: Re: What's the phase margin in this casde?
Post by aamar on Jun 22^nd, 2007, 2:01am

:) Hallo Frank,

I accept your answers no problems, the two poles could be on the left hand side, and even the zero, but I was replying to the original question where dandelion said

"At the point A, the phase obviously reaches -180'C while the gain is larger than one, what's the impact to the performance at thsi freq?"

and I think he means the step response nothing else or at least what will happen if you applied a signal with exactly this frequency to the system.

Any how it is good to mention that the problem can have a different face if we look to it in another domain.

Thanks and best regards,

aamar

Title: Re: What's the phase margin in this casde?
Post by dandelion on Jun 22^nd, 2007, 11:57pm

Thanks for all of you for the useful replies.

Especial thanks to Frank and Ken, your replies help me more deeply understanding the stabilty of feedback systems.

Title: Re: What's the phase margin in this casde?
Post by dandelion on Jun 23^rd, 2007, 12:18am

aamar wrote on Jun 22^nd, 2007, 2:01am:

yes, just as aamar said, what I mean is i wonder if the step response or other injection will induce ring even they will not oscillate eventurally.

Here lead to my another question. In many design spec, it will always give the phase margin spec, e.g., it is needed to be larger than ~60 degrees. I want to know, here, if the phase margin >60'C is needed to guarantee the circuit will not oscillate by itsself eventuarlly?. Or 60'C is needed to guarantee good setting behavior, i.e., 60'C can have good step response which has no rings?

I found the word "stabilty" made many people puzzle.

So, would you pls. give me some commnets?

Thanks

Title: Re: What's the phase margin in this casde?
Post by Frank Wiedmann on Jun 24^th, 2007, 12:37am

If a specification of phase margin is given, this is in reality a specification for the settling behavior of the closed-loop resonse. Like I wrote in reply #4, it assumes that the loop gain has two significant poles and no zeros, even if this is not stated explicitly.

A circuit will be stable (i.e., it will not start to oscillate by itself) if the phase margin is greater than zero. However, for a small phase margin, there will be significant ringing in the step response.

Title: Re: What's the phase margin in this casde?
Post by MonteCarlo on Jun 24^th, 2007, 4:57am

Dandelion,

If you look at the openloop gain and phase of a second order PLL, you'll see a similar situation: high gain and 180 deg phase. With the zero in the right place as you have, your feedback loop will be perfectly stable.

If in doubt, check the closed loop transient response.

-Monte

Title: Re: What's the phase margin in this casde?
Post by RobG on Jun 24^th, 2007, 2:01pm

I think what dandilion is asking is will this circuit's step response be any different than the step response from a traditional two pole circuit with the same phase margin. Does anyone know? How about doublets, etc. It seems like they would come into the settling time response too.

rg

Title: Re: What's the phase margin in this casde?
Post by Frank Wiedmann on Jun 25^th, 2007, 12:37am

The step response will be different. The easiest and most precise way to determine its shape in all such cases is probably to simply perform a transient simulation of the closed-loop circuit with a step at the input and look at the result. Even seemingly small changes in the Bode plot of the loop gain can lead to significant differences in the step response, see e.g. figures 5.3 and 5.4 of http://www.elec.ucl.ac.be/enseignement/ELEC2650/chapter5.pdf.

Title: Re: What's the phase margin in this casde?
Post by Asmodeus on Jan 22^nd, 2010, 3:57am

What i feel is that the circuit is clearly unstable. At frequency around A it is unstable. Practically speaking any noise around this frequency will oscillate and won't let the circuit operate !

Title: Re: What's the phase margin in this casde?
Post by raja.cedt on Jan 22^nd, 2010, 8:27am

hi all,
seems this system has 2poles after that one zero, so how is it possible to have phase more than -180? and even if it is crossing -180 also you can't say it is unstable..strictly speaking Phase Margin applicable for all pole system, so better start using Root locus.

Thanks,
Rajasekhar.

Title: Re: What's the phase margin in this case?
Post by Frank Wiedmann on Jan 22^nd, 2010, 1:25pm

Asmodeus wrote on Jan 22^nd, 2010, 3:57am:

What i feel is that the circuit is clearly unstable. At frequency around A it is unstable. Practically speaking any noise around this frequency will oscillate and won't let the circuit operate !

I'm afraid that your feeling is misleading you here. Conditions for circuit stability can be rather non-intuitive. I would suggest that you get familiar with the Nyquist stability criterion that has already been mentioned in this thread.

If you don't believe me, build a circuit with a loop gain as shown in your favorite simulator (using ideal controlled sources etc.) and do a transient simulation. There will probably be some ringing in the step response but no self-sustained oscillation; if you simulate long enough, the output voltage will be constant at the end.