A MOSFET with λ = 0.01 V−1 is biased in the saturation region at ID =

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A MOSFET with λ = 0.01 V−1 is biased in the saturation region at ID = 0.5 mA. If VGS and VDS remain constant, what are the new values of ID and ro if the channel length L is doubled?

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A MOSFET with λ = 0.01 V−1 is biased in the saturation region at ID = 0.5 mA. If VGS and VDS remain constant, what are the new values of ID and ro if the channel length L is doubled?

Explanation & Steps

Drain current of NMOS transistor in saturation region, considering channel length modulation can be denoted as:

$I_D=\frac{{\mu}_nC_{ox}}{2}*\frac{W}{L}*(V_{GS}-V_{tn})^2(1+\lambda V_{DS})$

Where:

ID = Drain current of NMOS transistor.

$\mu_n$ = Electron mobility.

Cox = Oxide capacitance per unit area.

W, L = Width and length of NMOS transistor.

VGS = Gate-to-source voltage.

VDS = Drain-to-source voltage.

Vtn = Threshold voltage of NMOS transistor.

$\lambda$ = Channel length modulation parameter of NMOS transistor.

From the given equation effect of length on drain current can be calculated while keeping other parameters constant. New drain current can be further used to determine new value output resistance of NMOS transistor in saturation region.