What will be the gain of circuit 1) We dont include channel length modulation? 2) we include channel length modulation? If we include channel length modulation will the gain be 1? as vds should remain constant as current source is ideal so increase in vg should have increase in vs and same increase in vd? Moreover why we bias at constant current then if vgs cannot be changed? How will gmvgs current increment gets generated?
The ideal current source in the source path has an infinite internal source resistance Ri. Hence, you have a circuit with a an infinite large feedback resistor (because every resistor in the source path provides negative feedback).
This can be seen for evaluating the gain formula with feedback (gm: transconductance):
A=Rc/[(1/gm) + Ri)]
In case you want to consider channel length modulation we have Rc||ro instead of Rc only.
This means: Gain A=0 for Ri approachung infinity.
The current of dependent source all goes through Ro, and by KCL at point A, the small signal current through RL will be zero, hence vout=0*RL=0V, so no amplification at all and gain will be 0.