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Frank Wiedmann

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Re: negative feedback becomes positive feedback?
Reply #15 - Mar 15^th, 2013, 2:45am

Milind wrote on Mar 14^th, 2013, 11:00am:

Hi Frank,
Thank you for the links and the information. I better understand this now. After looking into this now I have another question, The nyquist plot with the gain of 1.01m encircles the +1 point in the anticlockwise direction, this says that the loop gain has a Right half plane Pole but from the derivation of the loop gain expression:

-Vo/Vi = RGm/[(1+GRGm)+sRC]

it is clear that there is no RHP pole. �So that means the creation of the RHP Pole is an artifact of applying the stb analysis in a multiple loop system without breaking all the loops. Is my interpretation correct?

Thanks,

As I already mentioned in reply #2, the result of the stb analysis is due to the fact that there are two loops in the circuit but the stb probe is only placed in one of them.

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Milind

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Re: negative feedback becomes positive feedback?
Reply #16 - Mar 15^th, 2013, 12:03pm

Frank Wiedmann wrote on Mar 15^th, 2013, 2:45am:

As I already mentioned in reply #2, the result of the stb analysis is due to the fact that there are two loops in the circuit but the stb probe is only placed in one of them.

I am sorry for beating at this but in your reply 2 you say:

Frank Wiedmann wrote on Jan 5^th, 2011, 7:27am:

... To convince yourself (or others), you can use the Nyquist stability criterion (see http://www.designers-guide.org/Forum/YaBB.pl?num=1244840188 and http://www.designers-guide.org/Forum/YaBB.pl?num=1217822985).
......

So with the nyquist showing a right half plane zero which essentitally the Bode Plot also shows, it is not convincing that the circuit is stable. For simple cases it might be easy to disregard it for complex feedback loops the only way to convince yourself and others that this case is stable is by showing a step response.

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Frank Wiedmann Community Fellow Offline Posts: 678 Munich, Germany	Re: negative feedback becomes positive feedback? Reply #17 - Mar 15^th, 2013, 4:16pm Of course, a simulation of the step response should always be the ultimate stability test. However, could you please elaborate why a right half plane zero (as opposed to a pole) of the closed-loop gain is a problem for you?
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raja.cedt

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Re: negative feedback becomes positive feedback?
Reply #18 - Mar 16^th, 2013, 11:05am

@milind: Please find the loop gain expression for frank example. You have to consider +1 encirclements...here 0 encirclements, we know already no open loop RHP hence system is stable. How did you get RHP??

@frank: Thanks for your posts on stability, they were really help full. Can you please tell me is there any way to plot nyquist plot in cadence? i am always plotting one half circle corresponding to �+ve frequency and rest i am adjusting in Matlab.

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Frank Wiedmann

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Re: negative feedback becomes positive feedback?
Reply #19 - Mar 16^th, 2013, 1:24pm

raja.cedt wrote on Mar 16^th, 2013, 11:05am:

@frank: Thanks for your posts on stability, they were really help full. Can you please tell me is there any way to plot nyquist plot in cadence? i am always plotting one half circle corresponding to �+ve frequency and rest i am adjusting in Matlab.

I just plot half of the curve (like Milind did) and imagine the other half, which is simply mirrored along the real axis.

raja.cedt wrote on Mar 16^th, 2013, 11:05am:

@milind: Please find the loop gain expression for frank example. You have to consider +1 encirclements...here 0 encirclements, we know already no open loop RHP hence system is stable. How did you get RHP??

I think that Milind is referring to the cases where gain>1m. Here we have a counterclockwise encirclement of the critical point +1. This is due to the fact that the loop gain (but not the closed-loop gain) has a right-half-plane pole, so that the circuit is open-loop unstable.

However, when the loop is closed, the circuit is stable and the right-half-plane pole of the loop gain becomes a right-half-plane zero of the closed-loop gain. This situation is described in the following quote from http://en.wikipedia.org/wiki/Nyquist_stability_criterion (where the critical point is -1):
Quote:

If the system is originally open-loop unstable, feedback is necessary to stabilize the system. Right-half-plane (RHP) poles represent that instability. For closed-loop stability of a system, the number of closed-loop roots in the right half of the s-plane must be zero. Hence, the number of counter-clockwise encirclements about -1+j0 must be equal to the number of open-loop poles in the RHP.

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raja.cedt

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Re: negative feedback becomes positive feedback?
Reply #20 - Mar 17^th, 2013, 12:03pm

Hello Frank,
yes i agree about the critical point - when you plot for -loop gain, but here i have plotted loop gain(i follow this not have confusion).

@ Milind ,
when egain is less than 1 system stable (0 encirclements, 0 open loop RHP so 0 closed loop RHP).

When egain>1 system unstable (1 encirclements, 0 open loop RHP so 1 closed loop RHP)

Please correct me if am wrong.

Thanks,
Raj.

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Frank Wiedmann

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Re: negative feedback becomes positive feedback?
Reply #21 - Mar 18^th, 2013, 2:35am

You are wrong. The closed-loop circuit is stable for all values of the gain variable. This can very easily be seen from the simulation results of the second version of the circuit. Here, the loop gain probe Vprobe is in a different place so that it cuts both loops, but the circuit itself remains unchanged. For this second version, the loop gain is practically identical for all values of the gain variable and shows that the circuit is stable.

Looking at the first version of the circuit, we can explain the behavior in the following way:

For gain<1m, the loop gain has no right-half-plane pole and the closed-loop circuit is stable because in the Nyquist plot, there is no clockwise encirclement of the crictical point.
For gain>1m, the loop gain has one right-half-plane pole and the closed-loop circuit is stable because in the Nyquist plot, there is one counterclockwise encirclement of the critical point (as described in the quote from Wikipedia in my last response).

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Milind

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Re: negative feedback becomes positive feedback?
Reply #22 - Mar 18^th, 2013, 11:02am

Frank Wiedmann wrote on Mar 15^th, 2013, 4:16pm:

Of course, a simulation of the step response should always be the ultimate stability test. However, could you please elaborate why a right half plane zero (as opposed to a pole) of the closed-loop gain is a problem for you?

Hi Frank,
Yes that is not a problem, I was thinking about the open loop gain.
Thank you for the discussion.

Regards,
Milind

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