Amplifier stability question,

[ljy4468]

Hi,

In huijsing's opamp book,

it says 'For a minimum phase margin of 60, the unity gain frequency wt of the amplifier must be at least a factor two lower than the secondary pole p1.'

It seems right in simulation,
but how can I prove that????

 

[LvW]

Hi,

In huijsing's opamp book,

it says 'For a minimum phase margin of 60, the unity gain frequency wt of the amplifier must be at least a factor two lower than the secondary pole p1.'
It seems right in simulation,
but how can I prove that????

If you really want to prove it, you can do it
1.) via simulation
2.) by calculating the second order transfer function based on the opamp poles (po and p1) and its phase response.

But - is it important to recalculate ? It´s your time.
regards

 

[safwatonline]

phase @ wt =180-tan-1(wt/wp1)-tan-1(wt/wp2)

for wt>>wp1 tan-1(wt/wp1)=tan-1(inf)=90
PM = phase(w=wt)=180-90- tan-1(wt/wp2)
PM = 90-tan-1(wt/wp2)=tan-1(wp2/wt)

for wp2=2wt >> PM=63.4deg

 

[sutapanaki]

Another explanation which is a bit more intuitive is the following. Assume the dominant and 1st non-dominant poles of the loop-gain are well spaced apart so that the phase can reach almost -90deg before the non-dominant pole starts influencing it again. We all know that a single pole phase starts dropping down at around 0.1Fp, then at the pole frequency it is at -45deg below it's initial value and at -90 deg for 10Fp and beyond i.e. 45deg/dec. If we want the phase of the loop-gain of the amplifier to be at -120deg for Ft i.e. 60deg of phase margin and also 30deg below the -90deg initial phase contributed by the dominant pole, that would mean Ft/(0.1Fp1)=30/45=0.67dec. Equivalently, this is Ft/(0.1Fp1)=4.6 as a ratio and consequently Fp1/Ft=2.17.
This is kind of a crude calculation and only valid if the two poles are well separated but it gives the idea.

 

[ljy4468]

Thanks all, I got it.