does the higher GBW mean faster settling time?

[renwl]

does the higher GBW mean faster settling time? why?
thanks!

 

[bastos4321]

does the higher GBW mean faster settling time? why?
thanks!

Usually yes, but depends also on the slew-rate.

V(t)=c + k.e^(-t.gbw) this for a unity gain configuration.

so if you have a higher gbw you will have a fast response. If your gain is higher than one the expoent will be -t.gbw/gain.

For low speed applications you can be limitated by the slew-rate and not by the gbw.

Bastos

 

[leg1234]

It is uaually right
For first order system (dominate pole)
A
G(s)=---------- open loop
(s/a+1)
a*A
Gcl(s)=-------------- close loop
(s+a*A+a)

step reponse ~ (1-exp(-a*At)) setting time is highly depended on the GBW=a*A

However, it does not correct for standard 2nd order system.
(Wd^2)/(1-Tau^2)
Gcl(s)=---------------------------------------- close loop
s^2+2*Tau*s+(Wd^2)/(1-Tau^2)

step reponse= 1-exp(-Tau*t)*(cos(Wd*t)+Tau/Wd*sin(Wd*t))

with the GBW increases, the system may keep getting oscillation.

 

[renwl]

I have seen a paper.
it says that it's butterworth response when the phase margin is larger than 65 deg. and it has overshooting when the phase margin is less than 65deg. it doesn't mention the the GBW. why?

if not consider the slew rate, can I improve the settling time when I increase the driving ability in the last stage?
thanks

 

[pixel]

if not consider the slew rate, can I improve the settling time when I increase the driving ability in the last stage?
thanks

Sometimes you can improve it by GBW, assuming same stability.. but it is not always straightforward. Generally for higher GBW you need higher current, Bipolars increase gain by ~I, while mos~√I, (which means not too much). Also increasing current you can decrease output resistances, and also you need larger components, which means slightly higher capacitance...... Then comes stability...
Limitation factor can be high recovery time, when some components due to large amplitude are cut-off and need additional time to turn-on again..
Also you can have zero-pole doublet around cut-off freq which can significantly degrade settling time, while bandwidth and stability are good ...
So, you can imporove settling time increasing GBW until you reach some of the previous problems...

 

[femtopiconano]

Usually yes, but depends also on the slew-rate.

V(t)=c + k.e^(-t.gbw) this for a unity gain configuration.

so if you have a higher gbw you will have a fast response. If your gain is higher than one the expoent will be -t.gbw/gain.

For low speed applications you can be limitated by the slew-rate and not by the gbw.

Bastos

In switched cap design, what does k depend on ? The slew-rate :?:

BTW, do you have a paper or better a tutorial on that relation ?

 

[jonashat]

Check the Johns and Martin book, it has a nice discussion about linear settling of amplifiers.

But to answer renwl question, yes, in general if you have a higher GBW you'll have a faster settling time provided that maintain the same feedback factor.

You can simply think of it as follows:

tau = 1/w3db = 1/(F.wt)

where w3db is the -3dB frequency of the closed loop system, F is the feedback factor and wt is the unity gain frequency of the open loop system (usually equal to the amplifier's wt if your feedback doesn't limit the loop frequency response)