Discussion
Why does a differential pair make a good multiplier element?
Answer: D
The transconductance is proportional to the tail current, so a signal applied differentially is multiplied by whatever the tail current is made to represent - which is the basis of the Gilbert cell and of every analogue multiplier and balanced mixer. Offset, input impedance and output arrangement are not what makes it work. A stage whose gain is set by a current is a multiplier waiting to be used, and recognising that turns one circuit into a whole family. The shared properties explain why these belong to one family, and the differences explain why more than one exists.
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