MOSFET amplifier mid-point bias
The properties of MOSFETs vary a lot making this setup very unpredictable meaning, the DC level at the output will vary over almost everything including temperature. So even if you would know the Vgs you need and apply it, the output DC level would drift away due to temperature changes.

Also, due to the voltage gain of the circuit a small change in Vgs will result in a much larger change at the output.

All in all, this is not going to work very well.

What you need is either DC feedback or calibration.

This is what I mean with a calibration setup:







simulate this circuit &ndash; Schematic created using CircuitLab

You (or a program) would measure the DC voltage at the output and then adjust Vcal such that the output reaches the desired DC voltage.

This is cumbersome, is there a more easy way?

Yes there is:







simulate this circuit

Here the opamp compares the reference voltage of Vdd/2 (made by R3 and R4) with a filtered version (removing the signal, R5 and C2 do this) of the output voltage. That is the same as the DC level. The output controls the DC voltage at the NMOS's gate and makes it such that Vout(DC) = Vref = Vdd/2

This is what circuit designers call DC-feedback.

Should you not use the - input of the opamp for the output voltage?

No, I purposely used the + input of the opamp to sense the output voltage as there is already an inversion in the loop because of the NMOS circuit.