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Design >> Analog Design >> Stability discussion
https://designers-guide.org/forum/YaBB.pl?num=1254367352

Message started by jugemu1234 on Sep 30^th, 2009, 8:22pm

Title: Stability discussion
Post by jugemu1234 on Sep 30^th, 2009, 8:22pm

Hi,

I have been discussing with my colleges on stability about the system whose AC response is such as attached picture.
Speaking of only white profile, as far as I see, this is still stable since PM is around 60 deg. However some insists on risk from the fact phase response dip at around 30dB gain. Considering Barkhausen's criteria of oscillation, system oscillates only when gain=1 and when phase becomes 180 deg. In other words, when gain is higher than 1 and when phase becomes 180deg, system does not satisfy osillation. I think this is obvious considering such as PLL phase margin which often starts 180 deg at DC.

In case I am wrong, and attached white line is dangerous somehow, how could we make sure PLL(or other loops who already reaches close to 180 deg at low freq) stable?

Thanks,

Title: Re: Stability discussion
Post by raja.cedt on Sep 30^th, 2009, 10:17pm

hi,
as many people were discussed this topic many times here , Basically bode plot works properly for all pole system and for some systems with zero also it will work...still you can find many cases where bode plot fails.After all its a special case in Nyquist plot.So always use Nyquist or root locus.

***if both magnitude and phase plot are monotonic then only bode plot will work***

Thanks,
Rajasekhar.

Title: Re: Stability discussion
Post by jugemu1234 on Sep 30^th, 2009, 10:20pm

Hi,

Agreed but in fact there is no nicer method than PM analysis via bode plot over many corners. I wish there be more straightforward Nyquist or rlocus analysis on Analog Design Environment.

Thanks,

Title: Re: Stability discussion
Post by Frank Wiedmann on Oct 1^st, 2009, 12:55am

Please see http://www.designers-guide.org/Forum/YaBB.pl?num=1182388268 for a similar discussion. And do a transient simulation of the step response to see if it satisfies your requirements.

Title: Re: Stability discussion
Post by thechopper on Oct 3^rd, 2009, 6:05pm

Hi

In addition to what Frank suggested (which I would also do if I were you), you could build a Nyquist plot by just taking the real and imaginary part of the output voltage after running a dc analysis.
In such plot you could also evaluate the PM of your system.

Regards
Tosei

Title: Re: Stability discussion
Post by jugemu1234 on Oct 4^th, 2009, 8:42am

Hi thechopper and Frank,

Thanks for your reply.

Do you have any useful tool for Nyquist analysis with good user interface? How do you usually do draw Nyquist plot form DC analysis for many corners? Did you create special SKILL/Perl for it?

Also, transient analysis would give you if it oscillates or converges, but how do you know numeric number of stability margin specifically? It can be know by ringinging magnitude but i am wonderig if it is kind of ambiguous.

Title: Re: Stability discussion
Post by buddypoor on Oct 5^th, 2009, 1:12am

jugemu1234 wrote on Sep 30^th, 2009, 8:22pm:

Hi,

Speaking of only white profile, as far as I see, this is still stable since PM is around 60 deg. However some insists on risk from the fact phase response dip at around 30dB gain. Considering Barkhausen's criteria of oscillation, system oscillates only when gain=1 and when phase becomes 180 deg. In other words, when gain is higher than 1 and when phase becomes 180deg, system does not satisfy osillation. I think this is obvious considering such as PLL phase margin which often starts 180 deg at DC.

In case I am wrong, and attached white line is dangerous somehow, how could we make sure PLL(or other loops who already reaches close to 180 deg at low freq) stable?

Thanks,

Hello jugemu1234,

I suppose, there is a deep misunderstanding on your side.
1.) Your figure does NOT show the open loop phase. Instead it shows the total phase of all loop components - without the phase inversion necessary for negative feedback.
2.) If this total phase is -180 deg and the loop gain >1, the closed loop system will NOT be stable in most cases. Instead the system will go into saturation. There are some exceptions from this rule which require the complete NYQUIST criterion to check stability, but this is - as far as I see- beyond your problem. This has been correctly emphasized by rajasekhar
3.) As far as your problem is concerned, a PM lower than 30 deg may be not sufficient, but without any doubt the system is stable.

4.) As a consequence, if the phase of the PLL loop componenets is nearly -180 deg at low frequencies , this fact is NOT dangerous at all. In opposite, it clearly reveals and prooves the negative feedback concept.

CORRECTION to 4.): Instead of "phase of PLL loop components" read "phase of loop gain" (including negative sign of the feedback loop).

Title: Re: Stability discussion
Post by Mayank on Oct 5^th, 2009, 9:49pm

Hello everyone,
Nyquist Stability Criterion and Frequency Domain Analysis through Bode Plots have perturbed me also since a long time.
Can anyone please suggest me some good reading material where i can find how to apply Nyquist Stability Criterion to circuits and its comparison with Bode Plot Analysis as in how to map regions in Nyquist Plots to Bode Plots.

thanx,
Mayank.

Title: Re: Stability discussion
Post by raja.cedt on Oct 5^th, 2009, 10:27pm

hi,
i feel this presentation will give nice details regarding Nyquist plot.http://www.ee.iitm.ac.in/~nagendra/presentations/20090109vlsiconf/20090109vlsiconf.pdf

you can read from slide 53...

Thanks,
rajasekhar.

Title: Re: Stability discussion
Post by buddypoor on Oct 6^th, 2009, 1:55am

Mayank wrote on Oct 5^th, 2009, 9:49pm:

Hi Mayank,

I am afraid the above link does not work (my experience).
Instead, try this one:
http://virtual.cvut.cz/dynlabmodules/ihtml/dynlabmodules/syscontrol/node45.html

It contains something about the relationship between Nyquist and Bode.
In addition, I recommend to consult a good book on control theory which normally deal with this subject.
Regards

Title: Re: Stability discussion
Post by raja.cedt on Oct 6^th, 2009, 2:50am

hi buddypoor,
i am sorry, i forgot to tell that there you have to simply register.Any how i am uploading those slides in sendspace, here is the file
http://www.sendspace.com/file/nyinj2
And the reference you have given is very good.

Thanks,
Rajasekhar.

Title: Re: Stability discussion
Post by buddypoor on Oct 6^th, 2009, 3:34am

Hi Rajasekhar,
now i got it. Looks good. Thank you.

Title: Re: Stability discussion
Post by raja.cedt on Oct 6^th, 2009, 3:44am

hi buddypor,
i saw many times this stability discussions in many places..but no one concluded. Why don't you summaries. I am giving my conclusions here.
Bode plot will give decent results in the following cases

1.Both mag and phase plot should be monotonic
2. all pole system or system with one zero

Please correct the following and add your's also

thanks,
rajasekhar.

Title: Re: Stability discussion
Post by Mayank on Oct 6^th, 2009, 6:40am

Hi all,
Thanx everyone for helping me out with the materials.
@ Raja : I agree with your first point that Bode Plots work only on monotonic Magnitude & Phase Plots. Am not completely sure about your second point -- All pole is monotonic , Systems with only one Zero need not be monotonic i guess.

thanx,
Mayank.

Title: Re: Stability discussion
Post by buddypoor on Oct 8^th, 2009, 4:04am

raja.cedt wrote on Oct 6^th, 2009, 3:44am:

hi buddypoor, i saw many times this stability discussions in many places..but no one concluded. Why don't you summaries. I am giving my conclusions here.
Bode plot will give decent results in the following cases

1.Both mag and phase plot should be monotonic
2. all pole system or system with one zero

Please correct the following and add your's also

thanks,
rajasekhar.

Hi rajasekhar,
a final conclusion (i. e. a summary of stability criteria) cannot be done in short. I think, here in the forum we should not and cannot repeat the contents of a textbook. For my opinion, it is not so easy as you have written in your conclusion.
For example: What do you mean with "Bode plot gives results". Do you refer to the slope of the magnitude and/or the phase information ?
If yes, you only speak of the simplified Nyquist criterion which applies only under some restrictions.
However, the BODE plot can be used for a stability check also in case of poles and zeros in the RHP (instability of the open loop).
But in this case the Nyquist criterion may NOT be transferred to BODE in its simplified form. Instead, you have to count the crossings of the 180 deg-line with respect to the DIRECTIONS of these crossings.
You see, it is not as easy as you perhaps think. Sorry for that.
Finally, here is my "conclusion" (in fact: derived from other sources):
The simplified Nyquist criterion is transferred to the BODE plot in the following way:
If the function L is stable (no RHP poles) and crosses the 0 db-line only once and if the phase crosses the 180-deg-line only once, you can use the phase/gain margin as a stability criterion.
More than that, if there are no RHP zeros (i.e. L is a minimum phase system), you may use only the slope of the magnitude to evaluate stability issues.
Regards

Title: Re: Stability discussion
Post by jugemu1234 on Nov 1^st, 2009, 7:06am

Hi everyone here,

My appology for again starting discussion. I just want to discuss one more thing on stability analysis.

Ive got attached AC profile which looks little weird to me. It looks phase goes backward even on 2nd pole around 150k Hz. According to the PM definition "phase margin to (+/-)180deg at gain 1", can we say PM=150deg in this case? I am not intending to say herein that PM is all about I need to know, indeed I need to run transient as well.

Title: Re: Stability discussion
Post by buddypoor on Nov 1^st, 2009, 10:13am

Hi jugemu1234,

At first, the stability margin certainly will NOT be app. 150 deg.
Just the opposite is true: The rapid increase of the phase function around 150 kHz indicates stability problems (worst case: instability!).
The reason is as follows: The concept of phase margin is applicable only in case of a loop gain function which has no zeros and which is a minimum phase system - and the increase around 150 kHz looks like a zero influence. (By the way: I assume you have shown us the loop gain, did you?)
More than that - you cannot trust the results of an ac analysis alone, because even in case of instability you can get a curve which looks more or less good.
Regards

Addendum/Correction: Because of the rapid phase increase it is more likely that the whole system is unstable.

Title: Re: Stability discussion
Post by Mayank on Nov 1^st, 2009, 9:11pm

Hi BuddyPoor,
Could you please elaborate on your statement,
Quote:

More than that - you cannot trust the results of an ac analysis alone, because even in case of instability you can get a curve which looks more or less good.

It would be very helpful, if you could show some example so that we can be careful in future..

regards,
mayank.

Title: Re: Stability discussion
Post by raja.cedt on Nov 1^st, 2009, 9:25pm

@ maynk: i guess what he wants you say is even in case instability also you will get pretty nice ac wave form, so don't believe bode plots in case both magnitude and phase plots are monotonic.

@jugemu1234:hi man in your ac plot i saw sudden change in phase by almost 180..this is some times common mistake. How did you open the loop because if your both L and C are small then at resonance frequency you could see this type of weird behavior, so first you increase L and C and see whether you are getting same rapid change at that point.

Thanks,
rajasekhar..

Title: Re: Stability discussion
Post by Mayank on Nov 1^st, 2009, 10:09pm

Yeah,
i got buddy's point raja...But it would have be helpful if some1 could post an example of ac analysis showing normal behaviour while it's otherwise...And What could possible be the reason that poles & zeros of Bode plots FOR MONOTONIC minimum phase functions shows stablitiy while ckt goes unstable ??

thanx,
mayank.

Title: Re: Stability discussion
Post by buddypoor on Nov 1^st, 2009, 11:47pm

Mayank wrote on Nov 1^st, 2009, 10:09pm:

Hi MAYANK !
1) For example, when you by mistake connects the feedback line to the non-inverting opamp input (that means: positive feedback) the result of the ac analysis looks normal. That is because the program does find an operating point (which you also can calculate by hand, but it is unstable). However, the program does not know that it will be unstable because it does not take care about noise and power switch-on.

As another example, take a non-compensated opamp and use 100% feedback. The opamp in reality will be unstable. But you will see that the result of ac analysis - as far as the magnitude is concerned !! - looks normal. However, the phase will exhibit a rapid increase - as in your case!! This is an indication for instability !

2.) The answer to your second question cannot be given in short here in the forum. Please refer to the complete NYQUIST stability criterion. In this context, you should realize that the stability check in the BODE plot is nothing else than a transfer of the NYQUIST criterion from the complex plane to the simpler BODE plot. And according to NYQUIST the parameter called "phase margin" indicates stability/instability not for all kinds of functions. Description and explanation of this criterion can be found in books on control theory.
Regards

Title: Re: Stability discussion
Post by jugemu1234 on Nov 2^nd, 2009, 2:08am

Hi raja and guys here,

Thanks for info first of all.
It is not simple L&C on feedback path to set up open loop in my case. But I change it back to L&C components, no change on ac response though.

Title: Re: Stability discussion
Post by raja.cedt on Nov 2^nd, 2009, 2:20am

hi,
thanks for your quick cheek.I wounder how you are getting 180 phase change at one point..the reason could be some complex pole, but how in open loop you get complex pole? any how i donno much may be some senior person should help us..have you done transient simulation?

Thanks,
rajasekhar.

Title: Re: Stability discussion
Post by buddypoor on Nov 2^nd, 2009, 2:23am

jugemu1234, does this mean that your FIRST graph (BODE- plot) was the result of this simple RC circuit ?

If yes, I am sure that the models of your passive components R resp. C include parasitic parts which cause deviation from the normal first order response.

But - independent from that - what is the circuit for your complete feedback loop ?

Title: Re: Stability discussion
Post by jugemu1234 on Nov 2^nd, 2009, 2:49am

Hi,

Pls find attached. This is simplified model of whole loop and how I made it open loop. "ACBLK" indicates the circuit I had attached previously. The very first Bode of this thread is not coming from this circuit but the picture attached yesterday (on which I noted 150 PM) is derived with this open loop. And AC source is on Vref.

Thanks,

buddypoor wrote on Nov 2^nd, 2009, 2:23am:

Title: Re: Stability discussion
Post by buddypoor on Nov 2^nd, 2009, 3:13am

jugemu1234, I don´t understand the meaning and the relevance of the ACBLK as it is a simple RC circuit (and no LC which is to be used for loop gain simulation).
Nevertheless, I suggest you the following: Forget any artificial block like ACBLK and put instead an ac source of 1 volt BETWEEN the pos. input of the opamp (node B) and the resistive voltage divider (node A)
The, perform an ac simulation. The loop gain (magnitude and phase) is the RATIO of both node voltages v(A)/v(B).
This simplified operation is always possible if you find a point in the loop where a small source resistance is connected to a high input resistor (as is the case in front of your opamp input).

Title: Re: Stability discussion
Post by Mayank on Nov 2^nd, 2009, 9:48pm

Hi,
Buddy, thanx for your reply....
Jugemu, I agree with buddy that if you want to measure your open Loop Gain response, why are you placing an extra LC ckt in between...Do the normal return ratio analysis by breaking the loop at resistive divider node & givng an ac signal to +ve node of opamp & measuring the tf upto the loop-breaking point...I guess that should do...

You can also place an i-probe available in spectre b/w resistive divider node & +ve opamp i/p and do a stb analysis to obtain LG response...

--Mayank.

Title: Re: Stability discussion
Post by raja.cedt on Nov 9^th, 2009, 1:31am

hi mayank,
i feel return ratio method is only for hand calculation..not for simulation..if you want to simulate you have to middlebrooke method..

Thanks,
rajasekhar.

Title: Re: Stability discussion
Post by Mayank on Nov 9^th, 2009, 2:45am

Hello raja,
Yeah, return ratio method is for hand-calculation....My second suggestion refers to middlebrook method only....
Placing an i-probe or a CMDM probe provided in analogLib of spectre virtuoso is an element for middlebrook FB analysis...
My point is to avoid placing a LC filter,which imitates simulation conditions for return ratio analysis,(instead do a hand calculation by return ratio method) & use the middlebrook method for simulation, (which places baluns/ideal transformers and does a stability analysis).
Instead spectre + virtuoso makes life easy by providing an iprobe/ cmdm probe cellview which you can directly place in your schematic and do the stb analysis on it.....There you get your LG without placing any L,C ckt inside your schematic.....

--Mayank

Title: Re: Stability discussion
Post by raja.cedt on Nov 9^th, 2009, 5:07am

hi mayank,
i got what you are saying...in your reply you stated that for doing middlebroke no need to use any balen,TF....just find Av and Ai and do some post processing....

Thanks,
Rajasekhar.

Title: Re: Stability discussion
Post by Mayank on Nov 9^th, 2009, 11:01am

Hi raja,
MiddleBrook requires you to calculate Av and Ai...Using these probes in your schematic....you dont need to perform any processing....just place an iprobe in your schematic....choose stb analysis from ADE....select the probe as the probe instance...and run a stb analysis over deisred freq. range...It automatically gives you the Loop Gain Bode Plots...No post processing required...faster analysis...
[ I agree with Jerry here....Best Design Tool -> Capable designers :P ]

--Mayank.

Title: Re: Stability discussion
Post by buddypoor on Nov 10^th, 2009, 12:53am

Hi Mayank,

I cannot comment on ADS capabilities (stb analysis) as I am not familiar with this program.
However, in order to avoid problems and misunderstandings, just one hint: The phase margin concept within the frame of the BODE plot gives correct results only if the NYQUIST criterion in its simplified form with its restrictions is applicable.
Thanks
LvW

Title: Re: Stability discussion
Post by Andrew Beckett on Nov 15^th, 2009, 12:12am

Note that it is spectre that is providing stb analysis within ADE (Analog Design Environment) (not ADS which is a simulator from Agilent; that may well also have a stb analysis, but I can't answer that).

Regards,

Andrew

Title: Re: Stability discussion
Post by Mayank on Nov 15^th, 2009, 2:38am

Hi,
I was referring to Analog Design Environment ADE from Cadence....Guess buddy mistook it as Agilent's ADS, but simulator's name wasnt his point....So didnt correct...
Anyways, Thanx for the correction Sir....

regards,
Mayank