Settling time of opam at different closed loop gain

[Junus2012]

Hello,

Why when we simulate the settling time of the operational amplifier we usually do it at unity gain connection ? while theoretical analyses shows that settling time increases when the closed loop gain increases as shown below

tau = A(closed loop)/GBW*ß

where ß is the feedback factor

 

[FvM]

You'll analyze the settling time at the intended operation condition of the OP, which may be unity gain or different.

Because the settling time depends also on the phase margin, your formula isn't generally correct.

 

[Junus2012]

Dear FvM

that was my point, settling time has to be simulated at the intended operation, however, it looks like always given in the data sheet with G=1, as the same setting to simulate the slew rate..

the equation which I shoed before is an approximation of the amplifier to a simple first-order system, assuming all poles are clearly and safely pushed beyond the GBW. This derivation was given by Behzad Razavi

Nevertheless, your point is also important, you mentioned about the phase margin which was ignored in that expression, maybe this is the reason why simulating the settling time in unity feedback connection as phase margin is worst here

Thank you

 

[sutapanaki]

Stability of the opamp is worst when it is connected in a unity gain configuration. Then the loop gain crosses 0db at the UGBW which means closest to whatever non-dominant poles are there.

 

[Junus2012]

Stability of the opamp is worst when it is connected in a unity gain configuration. Then the loop gain crosses 0db at the UGBW which means closest to whatever non-dominant poles are there.

Sure it is the stability worst at unity gain cross point, but the settling here is not worst if we ignore the phase margin, then settling time increases and becomes worse as we increase the closed-loop gain, I am still assuming the first-order system and well safe phase margin like >=60

 

[sutapanaki]

First order system will have PM=90 or close there. PM=60deg is already a good 2nd order system with non-dominant pole about 2x away from the GBW. Yes, settling will be worse for higher closed loop gains. Or you can pump more current so that you increase the GBW and still get the settling that you want.

 

[Junus2012]

First order system will have PM=90 or close there. PM=60deg is already a good 2nd order system with non-dominant pole about 2x away from the GBW. Yes, settling will be worse for higher closed loop gains. Or you can pump more current so that you increase the GBW and still get the settling that you want.

Yes right, for phase margin less than 90, for example, PM = 60, it is well compensated second-order system,

May be for simplicity, designers are still approximating the model to first order for step response calculation

In the same time for ac small-signal analyses the well-compensated opamp is still functioning as 1st order until unity gain cross point

am I right in this discreption ?

 

[sutapanaki]

From magnitude point of view yes, because the magnitude fall with -20d/dec at least until the unity cross-over frequency. But phase reveals the deception.