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relationship between Gain bandwidth and settling time of Opamp (Read 8022 times)
Mahesh
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relationship between Gain bandwidth and settling time of Opamp
May 13th, 2009, 1:41am
 
Hi all,

how is Gain bandwidth and settling time of an opamp related ?
Suppose the settling time is given say 6ns then what will be the gain bandwidth required by the opamp output to settle within this settling time ?
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buddypoor
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #1 - May 13th, 2009, 3:53am
 
Mahesh wrote on May 13th, 2009, 1:41am:
Hi all,
how is Gain bandwidth and settling time of an opamp related ?
Suppose the settling time is given say 6ns then what will be the gain bandwidth required by the opamp output to settle within this settling time ?


The gain-bandwidth-product GBW (transit frequency of the universal compensated opamp) does not directly influence the settling time of the closed loop step response. The relevant parameter is the phase margin (which is determind also bei the GBW). For a given opamp and a fixed GBW the margin depends on the amount of feedback resp on the closed loop gain.
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raja.cedt
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #2 - May 13th, 2009, 4:06am
 
hi Mahesh,
                 along with settling time you have to give how much error you can tolerate.
Assume you can tolerate x%age error and you have b feedback factor,now you can think like your amplifier is a first order RC circuit with UGB*b is the time constant.

Please remember the above argument holds good for well compensated amplifier.
Thanks,
rajasekhar.
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Berti
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #3 - May 13th, 2009, 6:51am
 
Buddypoor, can you please explain that to me?

Quote:
The gain-bandwidth-product GBW (transit frequency of the universal compensated opamp) does not directly influence the settling time of the closed loop step response. The relevant parameter is the phase margin...


I agree that the PM influences the settling. But once the PM is optimized I think the settling time mainly depends on the UGBW of the amplifier.

Regards
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #4 - May 14th, 2009, 12:20am
 
Mahesh wrote on May 13th, 2009, 1:41am:
Hi all,

how is Gain bandwidth and settling time of an opamp related ?
Suppose the settling time is given say 6ns then what will be the gain bandwidth required by the opamp output to settle within this settling time ?



Hi,

The phase margin and the gain-bandwidth product (computed under the appropriate loading and accounting for the correct feedback factor) will determine the timeconstant for settling. How many settling timeconstants you need depends on the accuracy you are targeting. See any standard textbook on the relationship between phase margin, unity gain bandwidth and settling timeconstant.

A very important assumption in the whole circus above is that there are no pole-zero doublets below the unity-gain bandwidth. These may not affect the phase margin much but will directly limit the settling speed and accuracy, e.g. if your unity-gain frequency is 1 MHz but you have a pole-zero doublet at 1 kHz, then the settling timeconstant will correspond to 1 kHz not to 1 MHz. This is of importance in case your trying to stretch your bandwidth or phase margin with special compensation tricks.

Best regards,

Vivek
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buddypoor
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #5 - May 17th, 2009, 8:56am
 
Berti wrote on May 13th, 2009, 6:51am:
Buddypoor, can you please explain that to me?

Quote:
The gain-bandwidth-product GBW (transit frequency of the universal compensated opamp) does not directly influence the settling time of the closed loop step response. The relevant parameter is the phase margin...


I agree that the PM influences the settling. But once the PM is optimized I think the settling time mainly depends on the UGBW of the amplifier.

Regards


Hi Berti,

I agree , my answer was a bit short and, therefore, perhaps misleading. It was my intention to make clear that you can have for a small resp. for a large GBW the same settling time. That means for my understanding: no DIRECT relationship which could be expressed by a formula.
On the other hand, when "the PM is optimzed" (your words) and if the UGBW then is modified, do you think the PM will remain constant ?
Regards
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raja.cedt
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #6 - May 17th, 2009, 11:28am
 
hi buddypoor,
1.what i feel is for any ckt you can first decide how much ugb you want for settling and then you can optimize phase margin based on ringing requirements.
2.we can get same phase margin for any ugb by adjusting poles..

i just want to know weather the above lines are correct or not

for your previous question i think you can keep your phase margin is same for set of ugb's.

Thanks,
Rajasekhar.


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HdrChopper
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #7 - May 17th, 2009, 7:50pm
 
Along Vivek's lines IŽd like to add a sort of rule of tuumb when maximizing opamps settling time:
The GBW and PM are related by the location of the second (non-dominant) pole.
If fastest settling time is desired then the optimum PM given a GBW is 76 deg. Such settling will give the fastest settling time without any ringing in the step response (critically damped system). Such PM is always achieved if f2/GBW = 3, where f2 is the second pole location.

Regards
Tosei
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Keep it simple
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Berti
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #8 - May 17th, 2009, 10:39pm
 
Hi Buddypoor,

Quote:
...if the UGBW then is modified, do you think the PM will remain constant...

Sure, you are right. But I didn't consider the actual amplifier design. I think that the thread originally started with finding the specifications and not amplifier circuit design.

Tosei,
Quote:
If fastest settling time is desired then the optimum PM given a GBW is 76 deg.

Critically damped systems don't have overshoot. But I think that a slightly lower PM (at least theoretically) results in a faster settling transient. There are some papers about that (e.g.
     
H.C. Yang D.J. Allstot , Considerations for Fast Settling Operational Amplifiers ; Transactions on Circuits and Systems ; 1990 .)

Cheers
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ndnger
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #9 - May 19th, 2009, 1:07am
 
+1 to Berti. Slight overshoot will improve the settling time.
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #10 - Jun 19th, 2009, 1:36am
 
Hi,
Well it depends on how much error u can tolerate. Based on the dynamic range, u can find out ENOB (N) of your opamp.

Now u can choose the error to be lower that this number. You can even divide the error into steady state error , decided by the open loop gain & settling error, decided by the UGB.

The relation for for a single pole, could be dominant pole compensated goes as : N*ln(2)*t = Ts

t = time-constant of opamp.
Ts = Settling time.

t = 1/ ( UGB*beta) ( beta is feedback factor )

So, if u want to settle in "Ts" time, within N bit of accuracy, better have an opamp of this "UGB"
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~VJ~
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RobG
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #11 - Jul 28th, 2009, 7:46am
 
Berti wrote on May 17th, 2009, 10:39pm:
Critically damped systems don't have overshoot. But I think that a slightly lower PM (at least theoretically) results in a faster settling transient. There are some papers about that (e.g.
     
H.C. Yang D.J. Allstot , Considerations for Fast Settling Operational Amplifiers ; Transactions on Circuits and Systems ; 1990 .)

Cheers

I believe you are correct, but it depends on what value you are trying to settle to. Go to google scholar (advanced search) and search for "opamp settling time" and you will get many papers. The classic paper is the one by BYT Kamath, RG Meyer, PR Gray, JSSC, 1974.
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andre75
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #12 - Sep 8th, 2009, 6:02pm
 
I am surprised nobody has considered slew rate yet.
Assuming a large signal step response, the settling time consists of two factors, Slewing and Linear Settling.

At the first instant, the input of your opamp will see a very large differential voltage. All current will flow through one side of the differential stage and your amplifier slews. After the output comes close to its final value, the two inputs will come closer together, at which point the opamp will enter its GBW limited settling behavior (what Asmodeus described). With a CMOS input stage, this happens approx. when the two inputs are within 50-100mV of each other (depending on the input transconductance).

Asmodeus' formula thus greatly overestimates the bandwidth needed. Its only important for the last piece of the output waveform, when the amplifier is in the linear region.
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buddypoor
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #13 - Sep 12th, 2009, 8:27am
 
The reason, we all have answered without regard to the slewing proprties of the opamp is that the original question has asked for the relation between gain-bandwidth GBW and the settling time.
And, as you probably know, the GBW product is as SMALL signal parameter (in contrary to the slew rate).
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raja.cedt
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Re: relationship between Gain bandwidth and settling time of Opamp
Reply #14 - Sep 14th, 2009, 3:30am
 
hi,
   as budypoor pointed out GBW product is small signal and slew rate is large signal parameters. For an well designed op amp slew rate will be constant and it wont change with bandwidth. This is the reason why we have not discussed SLEW rate.
 
Recently i came to know the 'if settling time is  the primary concern then dont try for 1st order response and make system slightly under damped hence in this scenario settling time calculated based on GBW is overestimated.

Thanks,
rajasekhar.  
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