I started to title this on 'the solid state transformer'.

Anyhoo, how much gain can we get from the MOSFET? The simulation show 1mV in and 2 mV out. Sure doesn't sound like much does it? The text book says it has an infinite gain? So what is not so obvious?

Look a little closer at what the book says. It offers infinite CURRENT gain. With no gate current any drain current would equal infinite current gain.So in theory the gate has no current. Look at my circuit I have a 10K resistor across the input. So If we calculate power drop across the 10K input resistor and power drop across the 50Ohm load resistor we get a more meaningful number than the voltage gain of 2.

You can do the math if you are into it but I just used a calculator. 1mV and 10KOhm gives .00005uW and 2mV at 50Ohm gives .04uW. .04uW/.00005Uw = 800. So we have a power gain of 800 and the MOSFET transformed the 10K input Z to a 50Ohm output Z.

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