Consider an ideal long channel nMOSFET (enhancement-mode) with gate length 10 $$\mu$$m and width 100 $$\mu$$m. The product of electron mobility ($$\mu$$_n) and oxide capacitance per unit area (C_ox) is $$\mu$$_nC_ox = 1 mA/V². The threshold voltage of the transistor is 1 V. For a gate-to-source voltage V_GS = [2 $$-$$ sin(2t)] V and drain-to source voltage V_DS = 1 V (substrate connected to the source), the maximum value of the drain-to-source current is ___________.

Consider the circuit shown with an ideal long channel nMOSFET (enhancement mode, substrate is connected to the source). The transistor is appropriately biased in the saturation region with V_GG and V_DD such that it acts as a linear amplifier. v_i is the small-signal ac input voltage. v_A and v_B represent the small-signal voltages at the nodes A and B, respectively. The value of $${{{v_A}} \over {{v_B}}}$$ is __________ (rounded off to one decimal place).

For an $n$-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity ( $\partial V_T / \partial\left|V_{B S}\right|$ ) is found to be $50 \mathrm{mV} / \mathrm{V}$ at a substrate voltage $\left|V_{B S}\right|=2 \mathrm{~V}$, where $V_T$ is the threshold voltage of the MOSFET. Assume that, $\left|V_{B S}\right| \gg 2 \phi_B$, where $q \phi_B$ is the separation between the Femi energy level $E_F$ and the intrinsic level $E_i$ in the bulk. Parameters given are

Electron charge $(q)=1.6 \times 10^{-9} \mathrm{C}$

Vacuum permittivity $\left(\varepsilon_o\right)=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}$

Relative permittivity of silicon $\left(\varepsilon_{S i}\right)=12$

Relative permittivity of oxide $\left(\varepsilon_{o x}\right)=4$

The doping concentration of the substrate is

Using the incremental low frequency small - signal model of the MOS device, the Norton equivalent resistance of the following circuit is