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# What is the correct frequency to determine Phase Margin

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#### diarmuid

##### Full Member level 2
Hello all,

My question is best illustrated with the below example I am seeing for my system:

At the GBW, the phase response is 55deg from the 180deg pt. This would imply a phase margin (PM) of 55deg.

However: At a frequency < GBW, my phase response dips to 40deg (LHP zero present).

=> Is the PM = 55deg or 40deg?

I see by definition PM is measured at GBW implying PM = 55deg. If so, can someone please explain the rationale behind
PM not being 40deg for this scenario i.e. why would the 40deg frequency not cause more ringing?

Also, gain margin (GM). Is GM really that useful?

In going from open loop to closed loop stability analysis, it seems that PM bridges the two i.e. dampening
ratio is related to PM (PM/100 ~ zeta for some cases).

If this is completely true, what really is the use of GM? Should one even bother calculating it?

Thanks,

Diarmuid

At a frequency < GBW, my phase response dips to 40deg (LHP zero present).
... i.e. why would the 40deg frequency not cause more ringing?

Right: If you set the amplifier's closed loop gain to that gain < GBW where you find this 40° PM dip, the amplifier will show more ringing around that frequency.

Also, gain margin (GM). Is GM really that useful?

I think so: it shows you the min. closed loop gain which you may set in order to still have a stable system. At any lower set closed loop gain it will be unstable, i.e. oscillating.

Perhaps this tutorial may be helpful.

diarmuid

### diarmuid

Points: 2
Thanks. After a day with the system, yes I would redefine PM:

PM = 180 - the minimum phase between 0 -> GBW.

Only for a 2 pole system where any zero's or higher order poles occur at > 10xGBW should the following definition be used:

PM = 180 - the phase at GBW.

As for GM, yes I agree. A system can have good PM (> 60deg) but poor GM (>-10dB) and still show substantial ringing.

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