GATE EC 2016 Question Paper (31-Jan-2016) (Shift 2)

The direct form structure of an FIR (finite impulse response) filter is shown in the figure.



The filter can be used to approximate a

The injected excess electron concentration profile in the base region of an $npn$ BJT, biased in the active region, is linear, as shown in the figure. If the area of the emitter-base junction is $0.001{\text{cm}}^2$, ${\mu }_n=800{\text{cm}}^2/(\text{V-s})$ in the base region and depletion layer widths are negligible, then the collector current $I_C$ (in mA) at room temperature is ___________

(Given: thermal voltage $V_T=26\text{mV}$ at room temperature, electronic charge $q=1.6\times 10^{-19}\text{C}$)

Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials X (of thickness $t_1=1\text{nm}$ and dielectric constant ${\epsilon }_1=4$) and Y (of thickness $t_2=3\text{nm}$ and dielectric constant ${\epsilon }_2=20$). The capacitor in Figure II has only insulator material X of thickness $t_{Eq}$. If the capacitors are of equal capacitance, then the value of $t_{Eq}$ (in nm) is ______________

The I-V characteristics of the zener diodes D1 and D2 are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from $0$ to $100\text{V}$, then breakdown occurs in

For the circuit shown in the figure, $R_1=R_2=R_3=1\Omega$, $L=1\mu H$ and $C=1\mu F$. If the input $V_{in}=\cos (10^{6}t)$, then the overall voltage gain $(V_{out}/V_{in})$ of the circuit is ______________