The
Graduate Aptitude Test in Engineering (GATE) is an all India
examination conducted jointly by the Indian Institute of Science and
seven IIT's (IIT Bombay, IIT Guwahati, IIT Kanpur, IIT Kharagpur, IIT
Delhi, IIT Madras and IIT Roorkee) on behalf of the National
Coordination Board – GATE, Department of Higher Education, Ministry of
Human Resource Development (MHRD), Government of India. The GATE Score
of a candidate reflects the relative performance level of a candidate.
The score is used for admissions to various post-graduate programmes
(e.g. M.E., M.Tech, direct Ph.D.) in Indian higher education institutes
with financial assistance provided by MHRD and other Government
agencies.

#### Gate Syllabus for Electronics and Communication Engineering

This post is regarding the Syllabus for Electronics and Communication Engineering
(ECE) for the year 2014. The 2014 syllabus is mainly divided into
Engineering Mathematics, Electronics and Communication Engineering.
Below given is the detailed 2014 syllabus for 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.
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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