GATE 2015 Syllabus for Electronics and Communication Engineering

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GATE 2015 syllabus for ECE

Syllabus for Electronics and Communication Engineering (ECE)

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.

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. 

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.