a question about GBW and BW

[IC_fly]

I want to ask a question about GBW and BW.
I have a questions: If feedback coefficient β is 1 (buffer) for cases and input signal frequency for 1MHz ( ignored SR of problem), hope the precision of output signal is high (1 per thousand). So we should design loop gain as 1000 around at 1MHz for, however,we couldn’t simply design GBW as 1MHz (at 1MHz , loop gain only 1), eventually design out of amplifier put GBW far away from 1MHz(1GHz) . But build time is determined by the GBW,so someone tell me just GBW=1MHz is OK.
So there are two ways to design this op amp :
1.BW > 1MHz, DC Gain > 1000,
GBW > 1 GHz
2.GBW(loop gain) > 1 MHz
Who can tell me witch one is right?:x

 

[erikl]

Your no. 1 is the correct one: (non-)accuracy = closed_loop_gain / open_loop_gain

If you need an (non-)accuracy ≦ 1‰ = 1e-3 , you'll need an open_loop_gain = 1/(non-)accuracy = 1e3 = 1000 ≙ 60dB for a closed_loop_gain=1 buffer at the operating frequency (op_frequency = 1 MHz in your case).

GBW = open_loop_gain * op_frequency = 1000 * 1MHz = 1GHz

 

[FvM]

The required excess bandwidth for "1 per thousand output signal precision" will however depend on the nature of the error you want to supress. The factor 1000 is correct e.g. for non-linearities. If it's linear frequency dependent gain, less overhead is needed.

 

[IC_fly]

Thank you！！

 

[checkmate]

You have to get your terminology right first.

Assume you start off with an ideal single-pole opamp with open loop DC gain of 1000, and open loop -3dB frequency of 1kHz.
This gives you a gain bandwidth product of 1MHz.

You take this opamp, configure it with unity beta and you get a closed loop DC gain of 1, and closed loop -3dB frequency of 1MHz.
You inject a 1MHz input signal, and you get a -3dB (ie half) output signal.

You want error at less than 1%? You find the frequency in which closed loop gain is -0.087dB.
If you look at the closed loop gain curve, you will see that at 0.1MHz, the gain is already pretty darned close to 0dB.

With the same reasoning, for error less than 1% at 1MHz, an opamp supporting 10MHz GBWP is pretty darned close to be able to do the job.

 

[IC_fly]

At first，thank you very much. But i think error at less than 1% need GBW=100MHz because [loop_gain /(loop_gain +1)]=0.99.
loop_gain=100 and -3dB frequency is 1MHz,so GBW =100MHz
And what i want is 0.1% ,so GBW=1GHz.