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Design >> Analog Design >> Obtaining stability margin when "BODE plot fails"
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Message started by deba on Nov 17^th, 2016, 6:23pm

Title: Obtaining stability margin when "BODE plot fails"
Post by deba on Nov 17^th, 2016, 6:23pm

Hi All,

Sometimes the bode plots indicate a healthy gain margin(GM) and phase margin(PM) as in the attached figure. It has only one cross over but it stays flat near to 0 dB line even after cross over. The GM and PM are -6.7 dB and 78 degrees respectively, which are good. But in the step response one will see lot of ringing. It turns out that this system has very bad stability margin(SM). SM is defined as the shortest distance of the Nyquist curve to the critical (-1,0) point.

1) How does one simulate/obtain this SM from circuit simulator? As most circuit simulator only generate BODE plot.
2) There is a method of obtaining SM from closed loop output impedance. Some power electronics designs are done this way. But I haven't found any concrete material on this yet. Would appreciate if someone can point to a reference?

Title: Re: Obtaining stability margin when "BODE plot fails"
Post by sheldon on Nov 18^th, 2016, 8:49am

Deba,

This plot is not a healthy Bode plot, for example, the gain margin is
marginal. Even more it appears that there multiple poles very close to
the unity gain crossover frequency. While this circuit is not oscillating,
it is not far from oscillating. So even this result shows that issues are
expected.

Sheldon

Title: Re: Obtaining stability margin when "BODE plot fails"
Post by deba on Nov 19^th, 2016, 5:19am

Hi Sheldon,

Yes the circuit is marginally stable. The GM and PM are not the correct metrics to look for. That's I why stability margin(SM) should be looked at. Please see the link

http://www.powerguru.org/three-stability-assessment-methods-every-engineer-should-know-about/

The application note has Nyquist plot from which it measures the minimum distance to (-1,0) critical point. And they have mentioned a method of relating SM to output impedance. But there are not enough details. I want to know if someone can shed some light on this method.

Thanks

Title: Re: Obtaining stability margin when "BODE plot fails"
Post by nrk1 on Nov 21^st, 2016, 5:15am

Simulate the loop gain using stb or however else. Plot 1+loopgain (the complex quantity, not the magnitude) and find its minimum magnitude.

Title: Re: Obtaining stability margin when "BODE plot fails"
Post by deba on Nov 22^nd, 2016, 4:43am

Hi,

Thanks. Yes using stb one can obtain the minimum magnitude for 1 + loopgain(L(s)). Is there a criteria or proof on how low this value should be?

I was thinking more in terms of closed loop output impedance which is given by Zopen(s)/(1+L(s)). So for a given stability margin how much should the closed loop output impedance deviate from Zopen(s).

Thanks

Title: Re: Obtaining stability margin when "BODE plot fails"
Post by deba on Nov 24^th, 2016, 4:24am

Hi

It seems by ensuring that 1+L(s) > 0.5 is a good criteria for stabilizing the closed loop. In other words, from control theory the maximum value of sensitivity(1/(1+L)) should be limited from 1 to 2 for practical designs. A few follow up questions

1) Can one replace the GM and PM with just SM? GM and PM are just two points on the Nyquist plot. Whereas the SM is a more strict condition. Is there any loss if one closes the design using only SM?

2) Is there a relation between time domain response(settling, overshoot etc.) and the maximum sensitivity?

3) Are there any opamp designs which optimize the SM instead of GM,PM? Any reference would be helpful.

Thanks