GATE SYLLABUS FOR ELECTRONICS AND COMMUNICATION ENGINEERING (EC)

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, ztransform.

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.



Source: http://gate.iitd.ac.in/
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