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Design >> Analog Design >> negative feedback becomes positive feedback?
https://designers-guide.org/forum/YaBB.pl?num=1294178255

Message started by sapphire on Jan 4^th, 2011, 1:57pm

Title: negative feedback becomes positive feedback?
Post by sapphire on Jan 4^th, 2011, 1:57pm

Hi,

I am simulating the AC response of a unity-gain feedback amplifier using Spectre stb analysis. It works fine for most corners. But for some corners such as slow-fast(t=-40,125; vdda=2.05), the loop phase suddenly change to 0 degree at DC (it's supposed to be 180 degree). That means positive feedback! It's so werid. Is it a problem of spectre or a problem of the circuit? The simulation includes post-layout extraction.

Thanks
Sapphire

Title: Re: negative feedback becomes positive feedback?
Post by ssahl on Jan 4^th, 2011, 11:01pm

Hi Sappire!

How does the phase curve looks like when the frequency increases from 0Hz. Does it increase up to +90deg, flats out and then falls of again towards 0deg and beyond that? In such case your circuit is stable, if the phase margin at the real 0dB crossing is sufficiant.

It is hard to have an explaination of the behavoural without looking at the circuit.

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on Jan 5^th, 2011, 7:27am

This behavior usually is due to some asymmetry in a differential circuit. In your case, this asymmetry probably comes from the post-layout extraction. I have also seen this behavior during mismatch Monte Carlo analysis.

The attached pdf file shows a simple circuit that duplicates this behavior. It models an amplifier with some coupling from the output to the positive input. Depending on the amount of coupling, you get either 180 degrees or 0 degrees at low frequencies.

Like ssahl already mentioned, this behavior usually does not indicate a stability problem. 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).

In my example circuit, the strange behavior is due to the fact that there is a second loop in the circuit that does not include the stb probe Vprobe. If I redraw the circuit so that Vprobe is part of both loops (see the second circuit in the attached pdf file), the strange behavior disappears.

Title: Re: negative feedback becomes positive feedback?
Post by sapphire on Jan 5^th, 2011, 12:55pm

Hi Frank,

Your plots look exactly the same as mine. Do you know why asymmetry in layout would causes this strange behavior? Is it a bug in spectre stb analysis?

Thanks,
Sapphire

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on Jan 5^th, 2011, 3:25pm

No, it's not a bug in stb analysis. It's an artifact due to the fact that there are other loops in the circuit that do not include the stb probe. If you take my example circuits and do a detailed analysis with Spectre (or on paper), you will see how this can happen. Please see http://www.designers-guide.org/Forum/YaBB.pl?num=1201763532 for the limitations of stb analysis with respect to multiple loops.

Here's how you can analyze my example circuit: Because the impedance looking forward from Vprobe (into the controlling pin of Gota) is infinite, the loop gain is equal to the voltage loop gain in this case. The voltage loop gain is the ratio V(outp)/V(inn) when Vprobe is the only active independent source in the circuit. So, you can set Vin to 0V and Vprobe (DC and AC amplitudes) to 1V and do dc and ac analyses. If you annotate the DC node voltages to the circuit, you will quickly see why you get different positive and negative values for the DC loop gain when you vary the gain of the controlled source Ep.

Title: Re: negative feedback becomes positive feedback?
Post by Milind on Mar 11^th, 2013, 1:11pm

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).

Hi Frank,
I saw your post and example and found it very informative. Thanks. I don't understand though is why would the nyquist plot give any different result? Do you mean generate the loopgain data from something other than stb analysis? Or use the same stb analysis data to generate the nyquist plot?

Thanks

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on Mar 11^th, 2013, 2:05pm

If you do Nyquist plots of the loop gain data shown (which were generated by stb analysis), they will all indicate that the circuit is stable.

Title: Re: negative feedback becomes positive feedback?
Post by Milind on Mar 11^th, 2013, 5:15pm

Here are the plots I got. I plotted the loop gain in the real vs Imag plot and in 1 graph the real part is positive and in the other it is negative. If drawn for negative frequencies 1 of them will go around -1. What am I doing wrong?

Thanks.

Title: Re: negative feedback becomes positive feedback?
Post by Milind on Mar 11^th, 2013, 5:15pm

This is the second graph

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on Mar 12^th, 2013, 1:36am

Please note the following two points:

The loop gain as calculated by the stb analysis uses a slightly unusual sign convention (see http://www.designers-guide.org/Forum/YaBB.pl?num=1124688329). So, you either need to turn the Nyquist plot by 180 degrees or look at the encirclements of +1.

The Nyquist Stability Criterion looks at clockwise encirclements of the critical point (see http://en.wikipedia.org/wiki/Nyquist_stability_criterion).

Title: Re: negative feedback becomes positive feedback?
Post by Milind 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,

Title: Re: negative feedback becomes positive feedback?
Post by raja.cedt on Mar 14^th, 2013, 1:38pm

hello milind,

1. Nyquist criterion says closed loop RHP-open loop RHP=clockwise encirclement, So if you know about open loop RHP, number of encirclement's then you could comment on stability. But here you don't know about your open loop then you can't determine stability.

2. You have ignored few parasitic's like cgd which creates RHP zero and many like this. What is your circuits.

Thanks,
Raj.

Title: Re: negative feedback becomes positive feedback?
Post by raja.cedt on Mar 14^th, 2013, 1:38pm

hello milind,

1. Nyquist criterion says closed loop[b] RHP-open loop RHP=clockwise encirclement[/b], So if you know about open loop RHP, number of encirclement's then you could comment on stability. But here you don't know about your open loop then you can't determine stability.

2. You have ignored few parasitic's like cgd which creates RHP zero and many like this. What is your circuits.

Thanks,
Raj.

Title: Re: negative feedback becomes positive feedback?
Post by raja.cedt on Mar 14^th, 2013, 1:39pm

hello milind,

1. Nyquist criterion says closed loop RHP-open loop RHP=clockwise encirclement, So if you know about open loop RHP, number of encirclement's then you could comment on stability. But here you don't know about your open loop then you can't determine stability.

2. You have ignored few parasitic's like cgd which creates RHP zero and many like this. What is your circuits.

Thanks,
Raj.

Title: Re: negative feedback becomes positive feedback?
Post by Milind on Mar 14^th, 2013, 4:15pm

raja.cedt wrote on Mar 14^th, 2013, 1:39pm:

Hi Raj,
I am just analyzing and simulating the circuit given by Frank in the earlier post. That does not have any parasitics it is a simple single pole circuit. I derived its loop gain based on the stb setup shown in the pdf which produces the problem of 0 phase at DC.
Since my nyquist plot is encircling +1 which is equivalent to encircling -1 if I correct for the sign by stb analysis, that means an anticlockwise encirclement of the -1 point which in turn means my contour in the s plane contains a pole. Since my contour encircles the Right Half s-Plane that leads me to conclude that I have a pole in the right half plane.

Milind

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on Mar 15^th, 2013, 2:45am

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

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.

Title: Re: negative feedback becomes positive feedback?
Post by Milind on 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.

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann 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?

Title: Re: negative feedback becomes positive feedback?
Post by raja.cedt 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??

@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.

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on 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:

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.

Title: Re: negative feedback becomes positive feedback?
Post by raja.cedt on 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.

Title: Re: negative feedback becomes positive feedback?
Post by Frank Wiedmann on 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).

Title: Re: negative feedback becomes positive feedback?
Post by Milind on Mar 18^th, 2013, 11:02am

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

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

Regards,
Milind