For the circuit with an ideal OPAMP shown in the figure. $V_{\text {REF }}$ is fixed.

If $V_{\text {OUT }}=1$ volt for $V_{\text {IN }}=0.1$ volt and $V_{\text {OUT }}=6$ volt, for $V_{\text {IN }}=1 \mathrm{~V}$, where $V_{\text {OUT }}$ is measured across $R_{\mathrm{L}}$ connected at the output of this OPAMP. The value of $R_{\mathrm{F}} / R_{\text {IN }}$ is

For the transistor $M_1$ in the circuit shown in the figure, $\mu_n C_{o x}=100 \mu \mathrm{~A} / V^2$ and $\frac{W}{L}=10$, where $\mu_n$ is the mobility of electron, $C_{o x}$ is the oxide capacitance per unit area. $W$ is the width and $L$ is the length.

The channel length modulation coefficient is ignored. If the gate-to-source voltage $V_{G S}$ is 1 V to keep the transistor at the edge of saturation. Then the threshold voltage of the transistor (rounded off to one decimal place) is $\_\_\_\_$ V.

Consider the circuit with an ideal OPAMP shown in the figure.

Assuming $\left|V_{\mathrm{IN}}\right| \ll\left|V_{\mathrm{CC}}\right|$ and $\left|V_{\mathrm{REF}}\right| \ll\left|V_{\mathrm{CC}}\right|$. The condition at which $V_{\text {OUT }}$ equals to zero is

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.

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

The autocorrelation function $R_X(\tau)$ of a wide-sense stationary random process $X(t)$ is shown in the figure.

$$ \text { The average power of } X(t) \text { is ___________} $$

Consider a super heterodyne receiver tuned to 600 kHz . If the local oscillator feeds a 1000 kHz signal to the mixer. The image frequency (in integer) is $\_\_\_\_$ kHz .

A message signal having peak-to-peak value of 2 V , root mean square value of 0.1 V and bandwidth of 5 kHz is sampled and fed to a pulse code modulation (PCM) system that uses a uniform quantizer. The PCM output is transmitted over a channel that can support a maximum transmission rate of 50 kbps . Assuming that the quantization error is uniformly distributed, the maximum signal to quantization

noise ratio that can be obtained by the PCM system (rounded off to two decimal places) is $\_\_\_\_$ .

A 4 kHz sinusoidal message signal having amplitude 4 V is fed to a delta modulator (DM) operating at a sampling rate of 32 kHz . The minimum step size required to avoid slope overload noise in the DM (rounded off to two decimal places) is $\_\_\_\_$ V.

Consider a carrier signal which is amplitude modulated by a single - tone sinusoidal message signal with a modulation index of $50 \%$. If the carrier and one of the side bands are suppressed in the modulated signal, the percentage of power saved (rounded off to one decimal place) is $\_\_\_\_$

A speech signal, band limited to 4 kHz , is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range -5 V to +5 V , are subsequently quantized in an $8-$ bit uniform quantizer and then transmitted over a voice - grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB , the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is $\_\_\_\_$ kHz .

Consider a polar non-return to Zero (NRZ) waveform, using +2 V and -2 V for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4 \mathrm{~V}^2$. If the a priori probability of transmission of a binary ' 1 ' is 0.4 , the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is $\_\_\_\_$ V.

A sinusoidal message signal having root mean square value of 4 V and frequency of 1 kHz is fed to a phase modulator with phase deviation constant $2 \mathrm{rad} /$ volt. If the carrier signal is $c(t)=2 \cos \left(2 \pi 10^6 t\right)$, the maximum instantaneous frequency of the phase modulated signal (rounded off to one decimal place) is $\_\_\_\_$ Hz.

The complete Nyquist plot of the open-loop transfer function $G(s) H(s)$ of a feedback control system is shown in the figure.

If $G(s) H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is

A unity feedback system that uses proportional - integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters $K_p$ and $K_I$ The maximum value of $K_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally - stable (rounded off to three decimal places) is $\_\_\_\_$

The block diagram of a feedback control system is shown in the figure.$$ \text { The transfer function } \frac{Y(s)}{X(s)} \text { of the system is } $$

The electrical system shown in the figure converts input source current $i_s(t)$ to output voltage $\theta_O(t)$.

Current $i_L(t)$ in the inductor and voltage $\vartheta_C(t)$ across the capacitor ate taken as the state variables, both assumed to be initially equal to Zero, i.e., $i_L(0)=0$ and $\vartheta_c(0)=0$. The system is

The propagation delays of the XOR gate, AND gate and multiplexer (MUX) in the circuit shown in the figure are $4 \mathrm{~ns}, 2 \mathrm{~ns}$ and 1 ns respectively.

If all the inputs $P, Q, R, S$ and $T$ are applied simultaneously and held constant, the maximum propagation delay of the circuit is

A digital transmission system uses a $(7,4)$ systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-code word pairs in this code ( $m_i ; c_i$ ). Where $c_i$ is the codeword corresponding to the $i^{\text {th }}$ message $m_i$, are known to be $(1100 ; 0101100),(1110 ; 001 1110)$ and $(0110 ; 1000110)$, then which of the following is a valid codeword in this code?

Addressing of a $32 K \times 16$ memory is realized using a single decoder. The minimum number of AND gates required for the decoder is :

An 8-bit unipolar (all analog output values are positive) digital-to-analog converter (DAC) has a full-scale voltage range from 0 V to 7.68 V . If the digital input code is 10010110 (the leftmost bit is MSB). Then the analog output voltage of the DAC (rounded off to one decimal place) is

$\_\_\_\_$ V.

The propagation delay of the exclusive-OR (XOR) gate in the circuit in the figure is 3 ns . The propagation delay of all the flip-flops is assumed to be Zero. The clock (Clk) frequency provided to the circuit is 500 MHz .

Starting from the initial value of the flip-flop outputs $Q_2 Q_1 Q_0=111$ with $D_2=1$, the minimum number of triggering clock edges after which the flip-flop outputs $Q_2 Q_1 Q_0$ becomes 100 (in integer) is $\_\_\_\_$

Consider a rectangular coordinate system $(x, y, z)$ with unit vectors $a_x, a_y$ and $a_z$. A plane wave traveling in the region $z \geq 0$ with electric field vector $E=10 \cos \left(2 \times 10^8 t+\beta z\right) a_y$ is incident normally on the plane at $z=0$, where $\beta$ is the phase constant. The region $z \geq 0$ is in free space and the region $z<0$ is filled with a lossless medium (permittivity $\varepsilon=\varepsilon_0$ permeability $\mu=4 \mu_0$, where $\varepsilon_0=8.85 \times 10^{-12} \mathrm{F} / \mathrm{m}$ and $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ ). The value of the reflection coefficient is

The impedance matching Network shown in figure is to match a lossless line having characteristic impedance $Z_o= 50 \Omega$ with a load impedance $Z_L$. A quarter - Wave line having a characteristic impedance $Z_1=75 \Omega$ is connected to $Z_L$. Two stubs having characteristic impedance of $75 \Omega$ each are connected to this quarter - wave line. One is a short - circuited (S.C) stub of length $0.25 \lambda$ connected across PQ and the other one in an open - Circuted (O.C) stub of length 0.5 $\lambda$ connected across RS.

The impedance matching is achieved when the real part of $Z_L$ is

The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48 respectively. The critical propagation angle. Which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is $\_\_\_\_$ degree.

An antenna with a directive gain of 6 dB is radiating a total power of 16 kw . The amplitude of the electric field in free space at a distance of 8 km from the antenna in the direction of 6 dB gain(rounded off to three decimal places is$\_\_\_\_$ $\mathrm{V} / \mathrm{m}$.

A standard air-filled rectangular waveguide with dimensions $a=8 \mathrm{~cm}, b=4 \mathrm{~cm}$, operates at 3.4 GHz . For the dominant mode of wave propagation, the phase velocity of the signal is $v_p$. The value (rounded off to two decimal places) of $v_p / c$, where $c$ denotes the velocity of light, is $\_\_\_\_$ .

The vector function $F(r) = -x \hat{i} + y \hat{j}$ is defined over a circular arc C shown in the figure,

The line integral of $\int\limits_{C} \mathbf{F(r)} \cdot d\mathbf{r}$ is

A silicon $P-N$ junction is shown in the figure. The doping in the $P$ region is $5 \times 10^{16} \mathrm{~cm}^3$ and doping in the $N$ region is $10 \times 10^{-16} \mathrm{~cm}^{-3}$. The parameters given are

Built-in voltage $\left(\phi_{b i}\right)=0.8 \mathrm{~V}$

Electro charge $(q)=1.6 \times 10^{-19} \mathrm{C}$

Vacuum permittivity of silicon $\left(\varepsilon_{s i}\right)=12$

The magnitude of reverse bias voltage that would completely deplete one of the two regions ( $P$ or $N$ ) prior to the other (rounded off to one decimal place) is $\_\_\_\_$ V.

A bar of silicon is doped with boron concentration of $10^{16} \mathrm{cm}^{-3}$ and assumed to be fully ionized. It is exposed to light such that electron-hole pairs are generated throughout the volume of the bar at the rate of $10^{20} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$. If the recombination lifetime is $100 \mu \mathrm{~s}$, intrinsic carrier concentration of silicon is $10^{10} \mathrm{~cm}^{-3}$ and assuming $100 \%$ ionization of boron, then the approximate product of steady-state electron and hole concentrations due to this light exposure is

The energy band diagram of a $p$-type semiconductor bar of length $L$ under equilibrium condition (i.e., the Fermi energy level $E_F$ is constant) is shown in the figure. The valance band $E_V$ is sloped since doping is non-uniform along the bar. The different between the energy levels of the valence band at the two edges of the bar is $\Delta$.

If the charge of an electron is $q$, then the magnitude of the electric field developed inside the semiconductor bar is

The content of the registers are $R_1=25 \mathrm{H}, R_2=30 \mathrm{H}$ and $R_3 =40 \mathrm{H}$. The following machine instructions are executed.

$$ \begin{aligned} & \operatorname{PUSH}\left\{R_1\right\} \\ & \operatorname{PUSH}\left\{R_2\right\} \\ & \operatorname{PUSH}\left\{R_3\right\} \\ & \operatorname{POP}\left\{R_1\right\} \\ & \operatorname{POP}\left\{R_2\right\} \\ & \operatorname{POP}\left\{R_3\right\} \end{aligned} $$

After execution, the content of registers $R_1, R_2, R_3$ are

Consider the circuit shown in the figure.

The current I flowing through the 7$$\Omega$$ resistor between P and Q (rounded off to one decimal place) is ______ A

The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time $t=0$.

Initially, when the switch is open, the capacitor is discharged, and the ammeter reads zero ampere. After the switch is closed, the ammeter reading keeps fluctuating for some time till it settles to a final steady value. The maximum ammeter reading that one will observe after the switch is closed (rounded off to two decimal places) is $\_\_\_\_$ A.

$$ \text { Consider the two-port network shown in the figure. } $$

The admittance parameters, in siemens are

The switch in the circuit in the figure is in position $P$ for a long time and then moved to position $Q$ at time $t=0$

The value of $\frac{d v(t)}{d t}$ at $t=0^{+}$is

In the circuit shown in the figure, the switch is closed at time $t=0$, while the capacitor is initially charges to -5 V (i.e., $\left(\theta_C(0)=-5 \mathrm{~V}\right)$.

The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is $\_\_\_\_$ ms .

Consider a real-valued base-band signal $x(t)$. band limited to 10 kHz . The Nyquist rate for the signal $y(t)=x(t) \times \left(1+\frac{t}{2}\right)$ is

Consider the signals $x[n]=2^{n-1} u[-n+2]$ and $y[n]=2^{-n+2} u[n+1]$, where $u[n]$ is the unit step sequence. Let $X\left(e^{j \omega}\right)$ and $Y\left(e^{j \omega}\right)$ be the discrete-time Fourier transform of $x[n]$ and $y[n]$, respectively. The value of the integral

$$ \frac{1}{2 \pi} \int_o^{2 \pi} X\left(e^{j \omega}\right) Y\left(e^{-j \omega}\right) d \omega $$

(round off to one decimal place) is $\_\_\_\_$

For a unit step input $u[n]$, a discreate-time $L T I$ system produces an output signal $(2 \delta[n+1]+\delta[n]+\delta[n-1])$. Let $y[n]$ be the output of the system for an input $\left(\left(\frac{1}{2}\right)^n u[n]\right)$.

The value of $y[0]$ is The value of $y[0]$ is $\_\_\_\_$

The exponential Fourier series representation of a continu-ous-time periodic signal $X(t)$ is defined as

$$ x(t)=\sum\limits_{k=-\infty}^{\infty} a_k e^{j k w_0 t} $$

Where $\omega_0$ is the fundamental angular frequency of $x(t)$ and the coefficients of the series are $a_k$. The following information is given about $x(t)$ and $a_k$.

I. $x(t)$ is real and even, having a fundamental period of 6

II. The average value of $x(t)$ is 2

III. $a_k=\left\{\begin{array}{c}k, 1 \leq k \leq 3 \\ 0, k>3\end{array}\right.$

The average power of the signal $x(t)$ (rounded off one decimal place) is $\_\_\_\_$