SOLUTION

Given

V_GS =0.7
V_DS = 0.2
V_Th = 0.4V
V_DS < V_GS – V_Th = 0.7 – 0.4 = 0.3

Linear (Ohmic) Region   –   with V_GS > V_threshold and V_DS < V_GS the transistor is in its constant resistance region behaving as a voltage-controlled resistance whose resistive value is determined by the gate voltage, V_GS level.

The magnitude of current increases linearly with increasing drain voltage till a particular drain voltage determined by the following relations –

VGS ≥ Vth

VDS < VGS – Vth

For Linear region

${I_D} = \dfrac{{{\mu _n}{C_{ox}}{W_N}}}{{{L_N}}}\left[ {\left( {{V_{GS}} – {V_{TN}}} \right){V_{DS}} – \dfrac{{V_{DS}^2}}{2}} \right]$

where,

μ_N is the mobility of electrons in the drain-source channel in cm²/Vsec

C_ox is the gate oxide capacitance in F/cm²

W_N is the width of the NMOS transistor

L_N is the length of the NMOS transistor

V_TN is the threshold voltage of the NMOS transistor

Now for transconductance gm diffrentiate the above equation by V_GS

g_m = δI_D/δV_GS = μ_N.C_ox.V_DS.[W/L]

=120 × 10^–6 × 60 × 0.2

= 1.44 mA