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Design >> Analog Design >> Gain Margin
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Message started by raja.cedt on Jun 7^th, 2009, 12:44am

Title: Gain Margin
Post by raja.cedt on Jun 7^th, 2009, 12:44am

hi,
can any body please tell what is the significance of gain margin? I know about phase margin significance like ringing and peaking..i didn't see in any text about this?

Thanks,
rajasekhar.

Title: Re: Gain Margin
Post by buddypoor on Jun 7^th, 2009, 1:57am

Hi, rajasekhar

It´s very simple.
At the frequency where the loop gain is unity: The phase margin is the amount of phase to be introduced into the loop in order to get a total phase of 360 deg. (which is the oscillation condition regarding the phase)

At the frequency where the loop phase is 360 deg.: The gain margin is the amount of gain to be introduced into the loop to get a total gain of unity (osc. condition for gain).
(Comment: In the Nyquist diagram the critical phase is 180 deg instead of 360 deg. because the neg. feedback sign is not included).

Title: Re: Gain Margin
Post by raja.cedt on Jun 7^th, 2009, 2:48am

hi buddypoor,
tx for your ans but what i am asking whats the impact of less gain margin on step response?

Thanks,
Rajasekhar.

Title: Re: Gain Margin
Post by sheldon on Jun 7^th, 2009, 4:50am

Raja,

The same effect of insufficient gain margin is the same as
not having enough phase margin. They are two measurements
with two different reference points of the same thing, how close
you are to oscillation. Phase margin tells you how close you
are in phase and gain margin tells you how close you are in
gain.

Best Regards,

Sheldon

Title: Re: Gain Margin
Post by aaron_do on Jun 7^th, 2009, 9:21am

Hi,

the gain margin tells you (in common cases) how much gain headroom you have before your system will become unstable. i.e suppose you have a simple system where your gain margin is 10 dB. If you were to increase your feedback factor by 10 dB your system would become unstable.

cheers,
Aaron

Title: Re: Gain Margin
Post by raja.cedt on Jun 7^th, 2009, 1:36pm

hi all,
thanks for your reply,lastly i want to know what is the reasonable value of gain margin like 60 deg phase margin is good and above is good from stability point of view but slow.
As Sheldon said phase margin and gain margin are same indications means if PM is high means GM is also good but i think other way around is wrong because even though you have less PM there may be some poles beyond UGB which can give high GM, so now oscillation condition for magnitude is not satisfied and it may not oscillate.

thanks,
Rajasekhar.

Title: Re: Gain Margin
Post by buddypoor on Jun 7^th, 2009, 10:35pm

raja.cedt wrote on Jun 7^th, 2009, 1:36pm:

......................
As Sheldon said phase margin and gain margin are same indications means if PM is high means GM is also good but i think other way around is wrong because even though you have less PM there may be some poles beyond UGB which can give high GM, so now oscillation condition for magnitude is not satisfied and it may not oscillate.
............

I don´t think it is so simple. You can have a good PM and at the same time a rather small GM and VICE VERSA ! More than that, the simple rule that a PM of 60 deg ensures a good step response is true only for a simple 2nd order system.
In addition of PM and GM there is 3rd margin called "vector margin" which is something like a combination of PM and GM - it is equivalent to the minimum distance between the nyquist curve and the critical point "-1".

Title: Re: Gain Margin
Post by raja.cedt on Jun 7^th, 2009, 11:25pm

hi buddypoor,
i am very happy to see your answer with a new interesting term (vector margin), but if you have time can you please direct me a good reference regarding Vector margin or give little introduction about that.

thanks,
Rajasekhar.

Title: Re: Gain Margin
Post by vivkr on Jun 8^th, 2009, 4:12am

Hi,

I don't believe that there is a magic number for gain margin (GM) in any textbook which tells you how much GM you need to get a certain kind of settling pattern for a second order system. However, you may try to derive that and call this GM_min.

That being said, you need the same sort of rules for defining GM as for PM, i.e. GM should be large enough that despite all expected variations (process, supply voltage, temperature, signal level etc.), it is still sufficient to achieve GM_min.

Regards,

Vivek

raja.cedt wrote on Jun 7^th, 2009, 1:36pm:

Title: Re: Gain Margin
Post by Frank Wiedmann on Jun 8^th, 2009, 4:23am

And in any case, you should always do a transient simulation of the step response, which will tell you the final truth. Also examine the effect of variations (as mentioned by Vivek) on the step response.

Title: Re: Gain Margin
Post by buddypoor on Jun 8^th, 2009, 4:25am

raja.cedt wrote on Jun 7^th, 2009, 11:25pm:

Hi Rajasekhar,
please find some information on the enclosed pdf- document.
Regards

Title: Re: Gain Margin
Post by bharat on Jul 24^th, 2009, 3:32am

As responded in the earlier posts PM and GM both are two different measurement of same thing i.e. instability of the system.

From PM alone one can decisively say that whether the system has potential threat of instability or not but on seeing GM it is not so.
If PM = 35 deg, the condition of oscillation is at the border
(considering the Supply, Voltage & Temperature variations).

But if GM is <5dB or so, Can we still say that the system may potentially go to instability?

Even if GM is <5dB but PM is 92 deg (say), there is no real threat of instability because though the pole is outside UGB but very close to UGB (which may be causing low GM), 92 deg of PM is good enough to take care even if the pole comes inside the UGB in different Voltage, Process and Temperature conditions

So from PM alone one comment about the stability of the system BUT from GM alone it is hard to make same comment.

Thanks

Title: Re: Gain Margin
Post by aaron_do on Jul 24^th, 2009, 7:34am

Hi Bharat,

if you have a GM of 5 dB, and your DC loop gain drops by 5 dB without any change in the pole positions, then I believe your system will be unstable. So in that respect GM does tell you how close you are to instability. Correct me if i'm wrong.

cheers,
Aaron

Title: Re: Gain Margin
Post by ray_wang on Jul 24^th, 2009, 9:42am

In my opinion, phase margin is more important since it is calculated at GBW. Those poles and zeros that affect transfer function below GBW also have impact on settling. Gain margin is calculated beyond GBW and poles and zeros there have little impact on settling, but still affect transfer function.
We want to know the impact on settling, therefore, PM can be viewed a direct index of poles and zeros that has such impact. As for GM, some outband poles and zeros might affect it but not settling, making it less meaningful.
As a extreme case, I once designed a feedforward opamp which gives PM of 30 but no GM below GBW*10! The phase shift returns from 150 to 120 above GBW and begins to drop beyond GBW*10.

Title: Re: Gain Margin
Post by skywalker_1 on Aug 1^st, 2009, 12:00am

In other words, I always consider gain margin for some unknown effect of zeros after 2nd pole.
But this effect is visible in transient simulation.