# Consider an n-channel MOSFET having width W, length L and electron mobility in the channel is µn and capacitance per unit area is C_ox. If gate to source voltage V_GS = 0.7V, drain to sour voltage V_DS = 0.2 V, µ_nC._ox = 120µA/V, threshold voltage V_T = 0.4V and (W/L) = 60. Calculate the transconductance gm in mA/V

Consider an n-channel MOSFET having width W, length L and electron mobility in the channel is µn and capacitance per unit area is C_ox. If gate to source voltage V_GS = 0.7V, drain to sour voltage V_DS = 0.2 V, µ_nC._ox = 120µA/V, threshold voltage V_T = 0.4V and (W/L) = 60. Calculate the transconductance gm in mA/V

### Right Answer is: 1.44 mA

#### SOLUTION

Given

VGS =0.7
VDS = 0.2
VTh = 0.4V
VDS < VGS – VTh = 0.7 – 0.4 = 0.3

Linear (Ohmic) Region   –   with VGS > Vthreshold and VDS < VGS the transistor is in its constant resistance region behaving as a voltage-controlled resistance whose resistive value is determined by the gate voltage, VGS 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,

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

Cox is the gate oxide capacitance in F/cm2

WN is the width of the NMOS transistor

LN is the length of the NMOS transistor

VTN is the threshold voltage of the NMOS transistor

Now for transconductance gm diffrentiate the above equation by VGS

gm = δID/δVGS = μN.Cox.VDS.[W/L]

=120 × 10–6 × 60 × 0.2

= 1.44 mA

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