GATE ECE 2016 PYQ

The figure shows a half-wave rectifier with a 475 F filter capacitor. The load draws a constant current from the rectifier. The figure also shows the input voltage , the output voltage and the peak-to

The diodes D1 and D2 in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in

In the circuit shown in the figure, transistor M1 is in saturation and has transconductance = 0.01 siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation to be ze

In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in kHz) at the output pin 3 is __________

Consider the constant current source shown in the figure below. Let represent the current gain of the transistor. The load current through 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 V, then breakdown oc

Which one of the following statements is correct about an ac-coupled common-emitter amplifier operating in the mid-band region?

The following signal of peak voltage 8 V is applied to the non-inverting terminal of an ideal opamp. The transistor has = 0.7 V, =100; = 1.5 V, = 10 V and - = -10 V. The number of times the LED glows

For the circuit shown in the figure, and . If the input , then the overall voltage gain ( ) of the circuit is __________

In the circuit shown in the figure, the channel length modulation of all transistors is non-zero ( 0). Also, all transistors operate in saturation and have negligible body effect. The ac small signal

A p-i-n photodiode of responsivity 0.8A/W is connected to the inverting input of an ideal opamp as shown in the figure, +Vcc = 15 V, -Vcc = -15V, Load resistor = 10 k . If 10 W of power is incident on

An opamp has a finite open loop voltage gain of 100. Its input offset voltage is modeled as shown in the circuit below. The amplifier is ideal in all other respects. is 25 mV. The output voltage (in m

An ideal opamp has voltage sources connected to the non-inverting input and connected to the inverting input as shown in the figure below (+ = 15 volt,- = -15 volt). The voltages are 1, -1/2, 1/3, -1/

The Ebers-Moll model of a BJT is valid

Resistor in the circuit below has been adjusted so that = 1 mA. The bipolar transistors Q1 and Q2 are perfectly matched and have very high current gain, so their base currents are negligible. The supp

Consider the circuit shown in the figure. Assuming = 0.7 volt, the value of the dc voltage (in volt) is __________

Consider the oscillator circuit shown in the figure. The function of the network (shown in dotted lines) consisting of the 100 k resistor in series with the two diodes connected

What is the voltage in the following circuit?

In the opamp circuit shown, the Zener diodes Z1 and Z2 clamp the output voltage to +5 V or -5 V. The switch S is initially closed and is opened at time t=0. The time t= (in seconds) at which changes s

Assume that the diode in the figure has = 0.7 V, but is otherwise ideal. The magnitude of the current (in mA) is equal to ________

Consider a discrete memoryless source with alphabet and respective probabilities of occurrence . The entropy of the source (in bits) is _______

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density Watt per Hz. If information at the rate of 52 kbps is to be t

Consider a random process X(t) = 3V(t) - 8, where V(t) is a zero mean stationary random process with autocorrelation . The power in X(t) is ________

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is

The block diagram of a frequency synthesizer consisting of a Phase Locked Loop (PLL) and a divide-by-N counter (comprising 2 , 4, 8, 16 outputs) is sketched below. The synthesizer is excited with a 5

An antenna pointing in a certain direction has a noise temperature of 50 K. The ambient temperature is 290 K. The antenna is connected to a pre-amplifier that has a noise figure of 2 dB and an availab

An analog baseband signal, bandlimited to 100 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities p1 = p4 = 0.125 and p2

For a superheterodyne receiver, the intermediate frequency is 15 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequen

A binary baseband digital communication system employs the signal for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be

A binary communication system makes use of the symbols "zero" and "one". There are channel errors. Consider the following events: : a "zero" is transmitted : a "one" is transmitted : a "zero" is recei

An ideal band-pass channel 500Hz - 2000Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosi

Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) req

An information source generates a binary sequence can take one of the two possible values -1 and +1 with equal probability and are statistically independent and identically distributed. This sequence

A speech signal is sampled at 8 kHz and encoded into PCM format using 8 bits/sample. The PCM data is transmitted through a baseband channel via 4-level PAM. The minimum bandwidth (in kHz) required for

The bit error probability of a memoryless binary symmetric channel is . If bits are sent over this channel, then the probability that not more than one bit will be in error is __________

A superheterodyne receiver operates in the frequency range of 58 MHz - 68 MHz. The intermediate frequency and local oscillator frequency are chosen such that . It is required that the image frequencie

A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is , then the autocorrelation function of the output Y(t) is equa

A discrete memoryless source has an alphabet with corresponding probabilities . The minimum required average codeword length in bits to represent this source for error-free reconstruction is ________

The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal . The value of the modulation index is __________

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral den

A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as and H(s)=1, respectively. If the variable parameter K is real

The open-loop transfer function of a unity-feedback control system is given by For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is____________

For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as . The steady state error due to a unit step input is

The asymptotic Bode phase plot of , with k and both positive, is shown below. The value of is ________

A second-order linear time-invariant system is described by the following state equations where are the two state variables and u(t) denotes the input. If the output c(t) = , then the system is

In the feedback system shown below The positive value of k for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is ________

In the feedback system shown below . The step response of the closed-loop system should have minimum settling time and have no overshoot. The required value of gain k to achieve this is ________

The open-loop transfer function of a unity-feedback control system is The value of K at the breakaway point of the feedback control system's root-locus plot is ________

Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh?s Table of the system characteristic equation.

The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

The number and direction of encirclements around the point -1+j0 in the complex plane by the Nyquist plot of is

The response of the system to the unit step input u(t) is y(t). The value of at t= is _________

The transfer function of a linear time invariant system is given by The number of zeros in the right half of the s-plane is ________

Identify the circuit below.

Assume that all the digital gates in the circuit shown in the figure are ideal, the resistor R= 10 k and the supply voltage is 5 V. The D flip-flops D1, D2, D3, D4 and D5 are initialized with logic va

The functionality implemented by the circuit below is

The minimum number of 2-input NAND gates required to implement a 2-input XOR gate is

For the circuit shown in the figure, the delay of the bubbled NAND gate is 2 ns and that of the counter is assumed to be zero. If the clock (Clk) frequency is 1 GHz, then the counter behaves as a

In an N bit flash ADC, the analog voltage is fed simultaneously to comparators. The output of the comparators is then encoded to a binary format using digital circuits. Assume that the analog voltage

A 4:1 multiplexer is to be used for generating the output carry of a full adder. A and B are the bits to be added while is the input carry and is the output carry. A and B are to be used as the select

Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is

Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst case charge and discharge times for driving a load capacitor C. This design is to be converted to that of

The logic functionality realized by the circuit shown below is

The output of the combinational circuit given below is

The state transition diagram for a finite state machine with states A, B and C, and binary inputs X, Y and Z, is shown in the figure. Which one of the following statements is correct?

For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are 2 ns, 1.5 ns and 1 ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instan

A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 150 and is aligned for maximum directional radiation and reception to a target 1 km away havi

Faraday's law of electromagnetic induction is mathematically described by which one of the following equations?

The propagation constant of a lossy transmission line is and its characteristic impedance is at rad . The values of the line constants L, C,R, G are, respectively,

A microwave circuit consisting of lossless transmission lines is shown in the figure. The plot shows the magnitude of the input reflection coefficient as a function of frequency f. The phase velocity

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is E when the plate separation is d. The capacitor is then isolated electr

Consider the charge profile shown in the figure. The resultant potential distribution is best described by

Consider an air-filled rectangular waveguide with dimensions a = 2.286 cm and b = 1.016 cm. The increasing order of the cut-off frequencies for different modes is

A uniform and constant magnetic field exists in the direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity . Given that B, m, q, and ar

A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness t and relative permittiv

The current density in a medium is given by The total current and the average current density flowing through the portion of a spherical surface r = 0.8 m, are given, respectively, by

Light from free space is incident at an angle to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are , respectively. The maximum value of (in

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as , where the propagation constant is a function of the angular frequency . Assume that a

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20 nC/ , -4 nC/ and , respectively. The value of required to ensure that the electric flux density at r

A positive charge q is placed at x= 0 between two infinite metal plates placed at x =-d and at x = +d respectively. The metal plates lie in the yz plane. The charge is at rest at t = 0, when a voltage

The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power . The solar cell has an area of and a fill factor of 0.7. The maximum efficiency (in %) of the

A voltage is applied across a MOS capacitor with metal gate and p-type silicon substrate at T=300 K. The inversion carrier density (in number of carriers per unit area) for is . For , the inversion ca

Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials X (of thickness nm and dielectric constant = 4) and Y (of thickness nm and dielectric constant

Consider a silicon sample at T = 300 K, with a uniform donor density illuminated uniformly such that the optical generation rate is throughout the sample. The incident radiation is turned off at t = 0

The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in

The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all re

Consider a silicon p-n junction with a uniform acceptor doping concentration of on the pside and a uniform donor doping concentration of on the n-side. No external voltage is applied to the diode. Giv

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 i

Consider avalanche breakdown in a silicon junction. The n-region is uniformly doped with a donor density . Assume that breakdown occurs when the magnitude of the electric field at any point in the dev

Consider an n-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-tosource voltage of 1.8V. Assume that , , the threshold voltage is 0.3V, and the channel length modulation

Consider a region of silicon devoid of electrons and holes, with an ionized donor density of . The electric field at x= 0 is 0 V/cm and the electric field at x=L is 50 kV/cm in the positive x directio

Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET): P: As channel length reduces, OFF-state current increases. Q: As channel length reduces, output resi

A small percentage of impurity is added to an intrinsic semiconductor at 300 K. Which one of the following statements is true for the energy band diagram shown in the following figure?

A long-channel NMOS transistor is biased in the linear region with =50 mV and is used as a resistance. Which one of the following statements is NOT correct?

Consider a long-channel NMOS transistor with source and body connected together. Assume that the electron mobility is independent of and . Given, , , where and The threshold voltage (in volts) of the

The figure below shows the doping distribution in a p-type semiconductor in log scale. The magnitude of the electric field (in kV/cm) in the semiconductor due to non uniform doping is _________

In an 8085 system, a PUSH operation requires more clock cycles than a POP operation. Which one of the following options is the correct reason for this?

An 8 Kbyte ROM with an active low Chip Select input ( ) is to be used in an 8085 microprocessor based system. The ROM should occupy the address range 1000H to 2FFFH. The address lines are designated a

In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and

In the figure shown, the current i (in ampere) is __________

In the circuit shown in the figure, the magnitude of the current (in amperes) through is ___

Consider a two-port network with the transmission matrix: . If the network is reciprocal, then

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor R is __________

In the circuit shown below, is a constant voltage source and is a constant current load. The value of that maximizes the power absorbed by the constant current load is

The z-parameter matrix for the two-port network shown is

the RLC circuit shown in the figure, the input voltage is given by The output voltage is

Assume that the circuit in the figure has reached the steady state before time when the 3 resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at is__________

The switch has been in position 1 for a long time and abruptly changes to position 2 at t=0. If time t is in seconds, the capacitor voltage (in volts) for is given by

The switch S in the circuit shown has been closed for a long time. It is opened at time t=0 and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. T

The z-parameter matrix for the two-port network shown is where the entries are in . Suppose . Then the value of (in ) equals ________

In the given circuit, each resistor has a value equal to 1 . What is the equivalent resistance across the terminals a and b?

An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that , and , and that the diode is ideal. RMS current (in mA) through the diode is ________

The figure shows an RLC circuit with a sinusoidal current source. At resonance, the ratio | |/| |, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is

Consider the signal , where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t)=x(2t+ 5) is

A continuous-time speech signal is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real time using the radix-2

Consider the sequence , where u[n] denotes the unit-step sequence and 0 |a| |b| 1. The region of convergence (ROC) of the z-transform of x[n] is

The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal , , then the ROC of its z-transform is represented by

Consider the signal . If is the discrete-time Fourier transform of x[n], then is equal to _________

If the signal with * denoting the convolution operation, then x(t) is equal to

Which one of the following is a property of the solutions to the Laplace equation: ?

Which one of the following is an eigen function of the class of all continuous-time, linear, timeinvariant systems (u(t) denotes the unit-step function)?

The energy of the signal is ________

A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff

A discrete-time signal has z-transform X(z). If X(z)=X(-z) is the z-transform of another signal y[n], then

A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period . In which one of the following cases is the sampled signal periodic?

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time re

A signal is the input to an LTI system with the transfer function . If denotes the coefficient in the exponential Fourier series of the output signal, then is equal to

The Discrete Fourier Transform (DFT) of the 4-point sequence x[n]={ x[0],x[1],x[2],x[3] } = {3,2,3,4} is X[k]={ X[0],X[1],X[2],X[3] } = {12,2j,0,-2j}. If is the DFT of the 12-point sequence ={3,0,0,2,

The Laplace transform of the causal periodic square wave of period T shown in the figure below is

The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form , where . The

A continuous-time filter with transfer function is converted to a discretetime filter with transfer function so that the impulse response of the continuous-time filter, sampled at 2 Hz, is identical a