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Analog Enthusiast
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India
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Both the circuits might be producing equal voltages. But the looking in DC incremental impedance should be different for both circuits. In fact the first one would have 2/gm and the second one would have 1/gm. This means that if we had a capacitance in the output node, the first one would halve half the bandwidth of the second one. Probably we can see the 2x current in the second one as a reason to get this extra bandwidth. In Bandgap you might be more worried about the feedback amplifier's poles than this pole though.
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