Electrical Engineering: Microelectronics: Assuming a MOSFET circuit is operating in the saturation/active region, if gm = 3.2 mA/V at ID = 120 uA, then what is gm when ID = 820 uA?

Question

Electrical Engineering: Microelectronics: Assuming a MOSFET circuit is operating in the saturation/active region, if gm = 3.2 mA/V at ID = 120 uA, then what is gm  when ID = 820 uA?

anonymous · Answer

In saturation, the current in MOSFET can be described as, 
$$Id=uCox/2*(Vgs-Vth)^2 *W/L$$. gm is derivative of Id w.r.t Vgs. In this situation , u r using same device for both cases. Hence mobility( u) , Cox , W and L must be same, use relation $$gm=\sqrt{2*u*Cox*W/L*Id}$$ to calculate gm when ID=820uA.

Can u please tell me what do u mean by active region in MOSFET. This term is mainly used in BJT .