GATE Syllabus for Electronics and Communication Engineering
Probability and statistics: Discrete and continuous distributions, normal and binomial distribution, poisson, correlation and regression analysis, mean, sampling theorems, median, conditional probability, mode and standard deviation, random variables.
Transform Theory: Laplace transform, Fourier transform, Z-transform.
Differential Equations: Method of variation of parameters, initial and boundary value problems, Cauchyís and Eulerís equations, partial differential equations and variable separable method, first order equation (linear and non-linear), higher order linear differential equations with constant coefficients.
Linear algebra: Systems of linear equations, matrix algebra, eigen values and eigen vectors.
Complex variables: Laurentís Taylorís series, solution integrals, analytic functions, residue theorem, Cauchyís integral theorem and integral formula.
Calculus: Multiple integrals vector identities, Fourier series, directional derivatives, volume and surface integrals, line, Gauss and Greenís theorems, Stokes, theorems of integral calculus, mean value theorems, partial derivatives, evaluation of definite and improper integrals.
Numerical Methods: Single and multi-step methods for differential equations, solutions of non-linear algebraic equations.
Electronics and Communication Engineering
Communications: Digital communication systems, differential pulse code modulation (DPCM), pulse code modulation (PCM), digital modulation schemes, matched filter receivers, phase and frequency shift keying schemes ( PSK, ASK and FSK), bandwidth consideration and probability of error calculations for these schemes, GSM, FDMA and CDMA, noise and random signals, random variables, probability, probability density function, power spectral density, autocorrelation, analog communication systems, amplitude and angle modulation and demodulation systems, spectral analysis of these operations, fundamentals of information theory and channel capacity, signal-to-noise ratio (SNR) calculations for amplitude modulation (AM) and frequency modulation (FM) for low noise condition, elements of hardware, super heterodyne receivers, realizations of analog communication systems.
Signal and Systems: Systems: Definition and properties impulse response, causality, convolution, stability, zeros and poles, frequency response, cascade and parallel structure, group delay, signal transmission through LTI systems, phase delay, Laplace transform: definitions and properties, discrete-time and continuous-time Fourier series, FFT and DFT, discrete-time and continuous-time Fourier transform, linear time-invariant (LTI), sampling theorem.
Analog Circuits: Frequency response of amplifiers, filters, simple op-amp circuits, sinusoidal oscillators, single-transistor and op-amp configurations, criterion for oscillation, 555 timers, function generators and wave-shaping circuits, MOSFETs, CMOS, and BJTs, small equivalent circuits of diodes, simple diode circuits, clamping, clipping, rectifiers, amplifier: single-and-multi-stage, biasing and bias stability of transistor and FET amplifiers, power and feedback, differential and operational.
Networks: Network graphs: matrices associated with graphs, incidence, fundamental cut set and fundamental circuit matrices, wye-delta transformation, solution methods: nodal and mesh analysis, Norton and Theveninís maximum power transfer, network theorems: superposition, steady and sinusoidal analysis using phasors, time domain analysis of simple RLC circuits, linear constant coefficient differential equations, solution of network equations using Laplace transform, state equations for networks, frequency domain analysis of RLC circuits, 2-port network parameters, transfer functions and driving point.
Electromagnetics: Transmission lines: characteristic impedance, Smith chart, impedance transformation, impedance matching, pulse excitation, S parameters, waveguides, boundary conditions, modes in rectangular waveguides, cut-off frequencies, basics of propagation in dielectric waveguide and optical fibers, dispersion relations, basics of antennas: radiation pattern, dipole antennas, antenna gain, elements of vector calculus: Gauss and Stokes theorems, divergence and curl, plane waves: reflection and refraction, propagation through various media, phase and media group velocity, skin depth, Maxwellís equations: poyning vector, differential and integral forms, wave equation.
Control systems: Tools and techniques for LTI control system analysis: Bode and Nyquist plots, Routh-Hurwitz criterion, root loci, control system compensators: elements of proportional-integral-derivate (PID) control, elements lag and lead compensation, solution of state equation of LTI control systems and state variable representation, block diagrammatic description, basic control system components, reduction of block diagrams, single flow graphs and their use in determining transfer functions of systems, open and closed loops (feedback) stability and systems analysis of these systems, transient and steady state analysis of LTI control systems and frequency response,
Digital Circuits: Sequential circuits: counters and shift-registers, flip-flops and latches, hold circuits and sample, semiconductor memories, DACs and ADCs, microprocessor (8085): memory, I/O interfacing, architecture and programming, minimization of Boolean functions, Boolean algebra, logic gates, digital IC families ( TTL, MOS, DTL, ECL, CMOS), combinatorial circuits: multiplexers, arithmetic circuits, PLAs and PROMs, code converters, decoders.
Electronics Devises: Generation and recombination of carriers, zener diode, JFET, BJT, MOS capacitor, p-n junction diode, tunnel diode, LED, MOSFET, p-I-n and avalanche photo diode, device technology: oxidation, integrated circuits fabrication process, diffusion, photolithography, twin-tub CMOS process, n-tub and p-tub, ion implantation, extrinsic and intrinsic silicon, energy bands in silicon, carrier transport in silicon, mobility, diffusion current, resistivity and drift current.