GATE 2014 - Syllabus for Electronics and Communication Engineering

Engineering Mathematics

Linear Algebra:

Matrix Algebra, Systems of linear equations, Eigen values and eigen vectors.

Calculus:

Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series. Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green's theorems.

Differential equations:

First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy's and Euler's equations, Initial and boundary value problems, Partial Differential Equations and variable separable method.

Complex variables:

Analytic functions, Cauchy's integral theorem and integral formula, Taylor's and Laurent' series, Residue theorem, solution integrals.

Probability and Statistics:

Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis.

Numerical Methods:

Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

Transform Theory:

Fourier transform, Laplace transform, Z-transform.

Electronics and Communication Engineering

Networks:

Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices. Solution methods: nodal and mesh analysis. Network theorems: superposition, Thevenin and Norton's maximum power transfer, Wye-Delta transformation. Steady state sinusoidal analysis using phasors. Linear constant coefficient differential equations; time domain analysis of simple RLC circuits, Solution of network equations using Laplace transform: frequency domain analysis of RLC circuits. 2-port network parameters: driving point and transfer functions. State equations for networks.

Electronic Devices:

Energy bands in silicon, intrinsic and extrinsic silicon. Carrier transport in silicon: diffusion current, drift current, mobility, and resistivity. Generation and recombination of carriers. p-n junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET, LED, p-I-n and avalanche photo diode, Basics of LASERs. Device technology: integrated circuits fabrication process, oxidation, diffusion, ion implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.

 

Analog Circuits:

Small Signal Equivalent circuits of diodes, BJTs, MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier. Biasing and bias stability of transistor and FET amplifiers. Amplifiers: single-and multi-stage, differential and operational, feedback, and power. Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal oscillators; criterion for oscillation; single-transistor and op-amp configurations. Function generators and wave-shaping circuits, 555 Timers. Power supplies.

Digital circuits:

Boolean algebra, minimization of Boolean functions; logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs and PLAs. Sequential circuits: latches and flip-flops, counters and shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories. Microprocessor(8085): architecture, programming, memory and I/O interfacing.

Signals and Systems:

Definitions and properties of Laplace transform, continuous-time and discrete-time Fourier series, continuous-time and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling theorem. Linear Time-Invariant (LTI) Systems: definitions and properties; causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay. Signal transmission through LTI systems.

Control Systems:

Basic control system components; block diagrammatic description, reduction of block diagrams. Open loop and closed loop (feedback) systems and stability analysis of these systems. Signal flow graphs and their use in determining transfer functions of systems; transient and steady state analysis of LTI control systems and frequency response. Tools and techniques for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and Nyquist plots. Control system compensators: elements of lead and lag compensation, elements of Proportional-Integral-Derivative (PID) control. State variable representation and solution of state equation of LTI control systems.

Communications:

Random signals and noise: probability, random variables, probability density function, autocorrelation, power spectral density. Analog communication systems: amplitude and angle modulation and demodulation systems, spectral analysis of these operations, superheterodyne receivers; elements of hardware, realizations of analog communication systems; signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise conditions. Fundamentals of information theory and channel capacity theorem. Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes: amplitude, phase and frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers, bandwidth consideration and probability of error calculations for these schemes. Basics of TDMA, FDMA and CDMA and GSM.

Electromagnetics:

Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems, Maxwell's equations: differential and integral forms. Wave equation, Poynting vector. Plane waves: propagation through various media; reflection and refraction; phase and group velocity; skin depth. Transmission lines: characteristic impedance; impedance transformation; Smith chart; impedance matching; S parameters, pulse excitation. Waveguides: modes in rectangular waveguides; boundary conditions; cut-off frequencies; dispersion relations. Basics of propagation in dielectric waveguide and optical fibers. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.

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Answer key with complete solutions of test form no. 555QJ4

 

Click here to download question paper

 

Technical knowledge section

 

101)  Ans (C)

Clouds have low thermal conductivity.It will not allow heat to escape easily.

 

102)  Ans (B)

P_x = P_Total ( n_x / n_Total )where
P_x = partial pressure of gas x
P_Total = total pressure of all gases
n_x = number of moles of gas x
n_Total = number of moles of all gases
P_hydrogen = P_Total ( n_hydrogen / n_Total )
P_helium = P_Total ( n_helium / n_Total )
P_hydrogen / P_helium  = n_hydrogen  /  n_helium
                                                = 2 / 4 = 0.5

103)  Ans (C)

Consider an electron moving from north to south on the plane of a paper. Electric field direction is downwards, which means positive charge is above plane of paper and negative is below it. Since electron always moves towards positive, its direction will be upward.

104)   Ans (B)

 E=q/(4πεr²)

Ratio for r,2r,3r will be  1: (1/4) : (1/9) which is 36 : 9 : 4

105)   Ans (C)

Topic - optics

Distance between slits , y = nλd/D

n – maxima number; λ – wavelength ; d – distance of slits from screen; D - distance between slits

106)  Ans (C)

Frequency cannot change with medium

107)  Ans(B)

KE = (3/2)KT

KE depends only on temperature

108) Ans(B)

109) Ans(D)

110) Ans(C)

X_c = 1/(2πfc)

5 = 1/(2π*50*C) ; find C and Solve for X_c  at 200Hz

111) Ans(not in choices)

Topic – Doppler effect

For source moving towards observer, f’ = v/v-v_s   * f

For source moving away from observer, f’ = v/v+v_s   * f

112) Ans(D)

Topic – torsion pendulum

Couple per unit twist C = ½ πnr⁴ / l

Where r –radius of rod ; l- length of rod ; n- rigidity modulus

113) Ans (A)

114) Ans (D)

Mean life = 1/ (decay constant)

115) Ans(C)

F_m = 5KHz

BW = 2 *5 =10 KHz

Number of stations = 100/10 =10

116) Ans(C)

β = α / 1-α

117) Ans(D)

The signals are first passed through filters which only allow through frequencies up to 15 kHz. The L and R signals are then added to produce a sum signal and subtracted one from the other to produce a difference signal. The sum is essentially a monophonic signal which is what we would send for playing through a single loudspeaker. The difference signal is used to DSBSC modulate a 38 kHz sinewave.The DSBSC output is added to the sum (mono) signal and the combination is sent on the transmitter's FM modulator. A monophonic receiver can now ignore the stereo information simply by using a filter after its FM demodulator to block everything above 15 kHz. A stereo receiver has to have an additional circuit after the FM demodulator which can detect and demodulate the DSBSC wave.

118) Ans(B)

Local oscillator frequency F_o  = f + f_IF

119)  Ans(C)

Magnification=Focal length of the Objective/Focal length of the Eyepiece

120) Ans (C)

Dielectric constant = ε / ε₀

121) Ans(B)

Area of B-H loop gives energy dissipated on reversing magnetic field.

In 50Hz cycles magnetisation changes @ 50 times/sec. In 1 hour it changes 60*60*50 times

Energy dissipated = 10*60*60*50

122) Ans(B)

Efficiency = output power/input power = I²R/VI =  5² * 10 / 200 * 5

123) Ans(C)

Topic - Thomson effect

Heat released/absorbed , H = σ Q Δθ

Q – charge, σ – Thomson coefficient, Δθ – temperature difference

124) Ans(A)

125) Ans(D)

Stoneman transmission bridge is used in telephone communication (at central offices) to separate voice path from signal path (used for ring tone, dial tone, busy etc) and battery.

126) Ans(C)

Grade of service of a telephone system = number of blocked calls  / total number of calls

127) Ans(B)

128) Ans(B)

AM range 535KHz – 1635KHz

129) Ans(D)

130) Ans(D)

 %Modulation = V_m / V_c   * 100  

131) Ans(B)

132) Ans(A)

Mixer gives sum and difference frequencies at the output.

133) Ans(A)

Microwave range

134) Ans(D)

135) Ans(A)

Ratio detector provides inbuilt  AGC mechanism

136) Ans(D)

137) Ans(C)

138) Ans(C)

139) Ans(D)

140) Ans(C)

f_s = 2f =200 Hz

141) Ans(B)

142) Ans(C)

Preemphasis – boosting higher frequencies

143) Ans(C)

144) Ans(D)

All others are light emitters

145) Ans(B)

146) Ans(C)

R=G=0 for lossless line

147) Ans(B)

Compressor –expandor.

On compression dynamic range is limited. Only few quantization levels are needed. step size  can be reduced and thus quantization noise .

148) Ans(B)

149) Ans(C)

Video transmission – AM

Audio transmission – FM

150) Ans(C)

Higher frequency => narrow beam => accurate focussing a satellite in the crowded satellite space

 

 

GATE2011ECE(1)

GATE 2011

1) The modes in a rectangular waveguide are denoted by TE_mn ,TM_mn where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

(A) The TM10 mode of the wave does not exist

(B) The TE10 mode of the wave does not exist

(C) The TM10 and the TE10 modes both exist and have the same cut-off

frequencies

(D) The TM10 and TM01 modes both exist and have the same cut-off frequencies

Solution

For TM₁₀ mode , the electric and magnetic field components will vanish. So it will not exist

Answer is (A)

(B) – incorrect because TE₁₀ exists

(C) – incorrect because TM₁₀  does not exist

(D) - incorrect because TM₀₁ cannot exist.For TM wave in rectangular waveguide m and n cannot be zero.Cutoff frequencies are same for same modes of TE and TM.

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2)  The Column-I lists the attributes and the Column-II lists the modulation systems. Match the attribute to the modulation system that best meets it 

          Column-I                                                            Column-II

P Power efficient transmission of signals          1 Conventional AM

Q Most bandwidth efficient transmission of       2 FM

voice signals

R Simplest receiver structure                          3 VSB

S Bandwidth efficient transmission of

signals with Significant dc component              4 SSB-SC

(A) P-4;Q-2;R-1;S-3            (B) P-2;Q-4;R-1;S-3

(C) P-3;Q-2;R-1;S-4            (D) P-2;Q-4;R-3;S-1

 

Solution

Power efficient transmission of signals – FM 

Most bandwidth efficient transmission of voice signals – SSB with Suppressed Carrier because there is only one sideband(bandwidth efficiency ) and no carrier(power efficiency) .

Simplest receiver structure – AM

Bandwidth efficient transmission of signals with Significant dc component – Vestigial Side Band(VSB) is used when low frequencies(DC) contain significant information(as in case of TV signals).

Answer is (B) 

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3)   For the transfer function G(jw) = 5 + jw , the corresponding Nyquist plot for positive frequency has the form

 

Solution

Magnitude of G(jw) = √(5² + w²)

Angle of G(jw) = tan^-1(w/5)

when w = 0,

Magnitude of G(jw) = √(5² ) = 5

Angle of G(jw) = 0

when w = ∞,

Magnitude of G(jw) = ∞

Angle of G(jw) = +90

So answer is (A) where magnitude starts from 5 (angle = 0 ie X axis) and move towards ∞ as w approaches ∞ (direction is vertical because angle approaches 90 ie positive Y axis).

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4)  The trigonometric Fourier series of an even function does not have the

(A) dc term           (B) cosine terms

(C) sine terms       (D) odd harmonic terms

Solution

even symmetry - no sine terms will be there, cosine and DC components will be present.

Answer is (C) 

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5)  When the output Y in the circuit below is ‘1’, it implies that data has 

 

(A) changed from 0 to 1                 (B) changed from 1 to 0

(C) changed in either direction        (D) not changed

 

 Solution

The method we follow is to go back from output to input side

AND gate

For output to be 1 both inputs should be 1.

Let us assume Q₁ be output of first D flip flop and be Q₂ output of second flipflop

So Q₁ = Q₂ = 1

Similarly assume terms D₁,D₂,Q’₁,Q₂’ for inputs and complement outputs of the two flipflops respectively

Second D Flip flop

Q₂ = 1

Implies D₂ input of previous clock cycle is 1

First D Flip flop

D₂ input of previous clock cycle is 1 implies Q’₁ of previous cycle is 1 (since they are interconnected)

Q’₁ =1 means  Q₁ = 0 , that happen only when D₁=0(at cycle before above mentioned previous) .

At current clock cycle Q₁=1 , so previously D₁=1

So we can see that D₁ changed from 0 to 1

Answer is (A)

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6)   A Zener diode, when used in voltage stabilization circuits, is biased in
 

(A) reverse bias region below the breakdown voltage
 

(B) reverse breakdown region
 

(C) forward bias region
 

(D) forward bias constant current mode

 Solution

At breakdown region voltage across zener will be constant, and this property is used in voltage stabilization circuits

Answer is (B)

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