Horror Vacui
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UGB: the frequency where the gain becomes unity GBW: the product of the 3dB bandwidth and the 3dB frequency.
In the case of a -20dB/dec roll-off the GBW will give the UGB. GBW easier to design for and it is used for an estimation for UGB. If the dominant pole of the second amp is higher than f1, than the UGB will not change. If not it would be smaller.
The math is easy, try it to work out for better understanding.
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