Does small signal parameter gm for a MOSFET equal 1 gm 2IdV

Does small signal parameter gm for a MOSFET equal:

1. gm = (2*Id)/(Vgs-Vt)

or

2. gm = kn(Vgs-Vt)

Solution

the formula for transconductance in mosfet is

g_m = 2*i_d / (vgs-vt)

a simple expression that highlights the dependence of gm on the DC drain current, we neglect the (usually) small error in writing:g_m = 2*i_d / (vgs-vt)

the drain current as a function of the gate-source voltage, so that the slope can be identified with the transconductance