An asymmetrical periodic pulse train $v_{\text {in }}$ of 10 V amplitude with on-time $T_{\mathrm{ON}}=1 \mu \mathrm{~s}$ is applied to the circuit shown in the figure. The diode $D_1$ is ideal.

The difference between the maximum voltage and minimum voltage of the output waveform $v_0$ (in integer) is $\_\_\_\_$ V.

In the circuit shown in the figure, the transistors $M_1$ and $M_2$ are operating in saturation. The channel length

modulation coefficients of both the transistors are non-zero. The transconductance of the MOSFETs $M_1$ and $M_2$ are $g_{m 1}$ and $g_{m 2}$, respectively, and the internal resistance of the MOSFETs $M_1$ and $M_2$ are $r_{01}$ and $r_{02}$ respectively.

Ignoring the body effect, the ac small signal voltage gain ( $d V_{\text {out }} / d V_{\text {in }}$ ) of the circuit is

A circuit with an ideal OPAMP is shown in the figure. A plus $V_{\text {IN }}$ of 20 ms duration is applied to the input. The capacitors are initially uncharged.

The output voltage $V_{\text {OUT }}$ of this circuit at $\tau=0^{+}$(in integer) is $\_\_\_\_$ V.

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