GATE EC 2016 Question Paper (31-Jan-2016) (Shift 1)

Consider avalanche breakdown in a silicon ${\mathrm{p}}^{+}\mathrm{n}$ junction. The n-region is uniformly doped with a donor density ${\mathrm{N}}_{\mathrm{D}}$. Assume that breakdown occurs when the magnitude of the electric field at any point in the device becomes equal to the critical field ${\mathrm{E}}_{\mathrm{crit}}$. Assume ${\mathrm{E}}_{\mathrm{crit}}$ to be independent of ${\mathrm{N}}_{\mathrm{D}}$. If the built-in voltage of the ${\mathrm{p}}^{+}\mathrm{n}$ junction is much smaller than the breakdown voltage, ${\mathrm{V}}_{\mathrm{BR}}$, the relationship between ${\mathrm{V}}_{\mathrm{BR}}$ and ${\mathrm{N}}_{\mathrm{D}}$ is given by

Consider a region of silicon devoid of electrons and holes, with an ionized donor density of ${\mathrm{N}}_{\mathrm{d}}^{+}=10^{17}\mathrm{c}{\mathrm{m}}^{-3}.$ The electric field at x = 0 is 0V/cm and the electric field at x = L is 50 kV/cm in the positive x-direction. Assume that the electric field is zero in the y and z directions at all points.



Given $\mathrm{q}=1.6\times 10^{-19}$ coulomb, ${ϵ}_{\mathrm{o}}=8.85\times 10^{-14}F/cm,{ϵ}_{\mathrm{r}}=11.7$ for silicon, the value of $\mathrm{L}(\mathrm{in}\mathrm{nm})$ is ________.

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of 𝑉${}_{\text{GS}}$ and 𝑉${}_{\text{DS}}$. Given, g${}_m$ = 0.5 𝜇A/V for 𝑉${}_{\text{DS}}$ = 50 mV and 𝑉${}_{\text{GS}}$ = 2 V,

g${}_d$ = 8 𝜇A/V for 𝑉${}_{\text{GS}}$ = 2 V and 𝑉${}_{\text{DS}}$ = 0 V,

Where ${\mathrm{g}}_{\mathrm{m}}=\frac{\partial {\mathrm{I}}_{\mathrm{D}}}{\partial {\mathrm{V}}_{\mathrm{GS}}}$ and ${\mathrm{g}}_{\mathrm{d}}=\frac{\partial {\mathrm{I}}_{\mathrm{D}}}{\partial {\mathrm{V}}_{\mathrm{DS}}}$

The threshold voltage (in volts) of the transistor is ________.

The figure shows a half-wave rectifier with a 475 𝜇F filter capacitor. The load draws a constant current 𝐼${}_{\text{O}}$ = 1 A from the rectifier. The figure also shows the input voltage 𝑉${}_{\text{i}}$, the output voltage 𝑉${}_{\text{C}}$ and the peak-to-peak voltage ripple 𝑢 on 𝑉${}_{\text{C}}$. The input voltage 𝑉${}_{\text{i}}$ is a triangle-wave with an amplitude of 10 V and a period of 1 ms.



The value of the ripple 𝑢 (in volts) is ________

In the opamp circuit shown, the Zener diodes ${\mathrm{Z}}_1$ and ${\mathrm{Z}}_2$ clamp the output voltage ${\mathrm{V}}_{\mathrm{o}}$ to $+5\mathrm{V}$ or $-5\mathrm{V}$. The switch S is initially closed and is opened at time t = 0.



The time $\mathrm{t}={\mathrm{t}}_1$ (in seconds) at which ${\mathrm{V}}_{\mathrm{o}}$ changes state is ________.