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,

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,

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

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


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).

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

you can read from slide 53...

Thanks,
rajasekhar.

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.

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.

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


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