Something has occurred to me, and I was wondering if anyone knew more about this. Could a CMOS logic inverter, like a 4049, be used as a very high gain amplifier if it were properly biased? I figured that the DC offset should be set at just about half the supply voltage, so that the gate was always between a '1' and a '0'.
I am not sure if the gate would behave linearly in that region, or if thermal noise might cause it to reach a valid logic state and not amplify the signal, but if it would work, it might be a cheap way to make an amplifier for long wave or AM radio.