GATE has on the drain current.Mathematically, the transconductance (GM) is DEFINED as:\( g_m=\frac{\partial I_{D}}{\partial V_{GS}}\)It is given the name transconductance because it gives the relationship between the input voltage and the output current.Analysis:The current for a MOSFET in saturation is given by:\({I_D} = K_n{\left( {{V_{GS}} - {V_{th}}} \right)^2}\)VGS = Gate to source voltageVth = Threshold VoltageTaking the square root of the above equation, we get:\(\sqrt{I_D} = \sqrt{K_n}{\left( {{V_{GS}} - {V_{th}}} \right)}\) ---(1)Now, the transconductance is calculated as:\( g_m=\frac{\partial I_{D}}{\partial V_{GS}}=2K_n{\left( {{V_{GS}} - {V_{th}}} \right)}\) ---(2)Evaluating (VGS - Vth) from Equation (1) and putting it in Equation (2), we get:\( g_m=2K_n.\frac{\sqrt{I_D}}{\sqrt{K_n}}\)\(g_m=2\sqrt{K_n.I_D}\)\(\therefore g_m\propto\sqrt{I_D}\)The transconductance of a MOSFET in saturation is DIRECTLY proportional to the square root of ID.