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So I studied the gain cascode amplifier as follows, enter image description here

I understand that the gain for this circuit is approximately -(gmro)^2

Now, here is a different circuit using the cascode amplifier but instead of a standard current source, we use a PMOS current mirror. enter image description here

Now, I am told that the gain for this circuit is just gmro, no square. Why is that? I mean clearly all we did was replace a standard current source with a PMOS current mirror? Shouldn't the gain for this circuit also be -(gmro)^2?

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It's to do with the ro of the current mirror M4. Cascode amplifiers need very large load resistors to get the theoretical gain that you quote. With a MOS current mirror the output resistance drops to r0. The solution is to use a cascode current mirror.

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