Discussion
Why is a field effect transistor's transconductance lower than a bipolar device's at the same current?
Answer: A
An exponential characteristic is far steeper than a square-law one, so a bipolar device gives about forty millisiemens per milliamp while a field effect device gives a few. The absence of gate current is the reason for the high input impedance, not the low transconductance. Channel resistance and capacitance affect other things. One difference in the underlying law produces the family's central trade: enormous input impedance bought with much less gain per milliamp.
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