GATE 2023 Electronics and Communications Engineering

Vector space, basis, linear dependence and independence, matrix algebra, Eigen values and eigen vectors, rank, solution of linear equations- existence and uniqueness.

Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series.

First order equations (linear and nonlinear), higher order linear differential equations, Cauchy’s and Euler’s equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.

Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss’s, Green’s and Stokes’ theorems.

Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor and Laurent series, residue theorem.

Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability.

Node and mesh analysis, superposition, Thevenin’s theorem, Norton’s theorem, reciprocity. Sinusoidal steady state analysis: phasors, complex power, maximum power transfer. Time and frequency domain analysis of linear circuits: RL, RC and RLC circuits, solution of network equations using Laplace transform.

Fourier series and Fourier transform, sampling theorem and applications.

DTFT, DFT, z-transform, discrete-time processing of continuous-time signals. LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeroes, frequency response, group delay, phase delay

diffusion current, drift current, mobility and resistivity, generation and recombination of carriers, Poisson and continuity equations.

clipping, clamping and rectifiers.

: biasing, ac coupling, small signal analysis, frequency response. Current mirrors and differential amplifiers.

Amplifiers, summers, differentiators, integrators, active filters, Schmitt triggers and oscillators.

binary, integer and floating-point- numbers. Combinatorial circuits: Boolean algebra, minimization of functions using Boolean identities and Karnaugh map, logic gates and their static CMOS implementations, arithmetic circuits, code converters, multiplexers, decoders.

latches and flip-flops, counters, shift-registers, finite state machines, propagation delay, setup and hold time, critical path delay.

sample and hold circuits, ADCs and DACs.

ROM, SRAM, DRAM.

Machine instructions and addressing modes, ALU, data-path and control unit, instruction pipelining.

auto correlation and power spectral density, properties of white noise, filtering of random signals through LTI systems.

amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, super heterodyne receivers.

entropy, mutual information and channel capacity theorem.

PCM, DPCM, digital modulation schemes (ASK, PSK, FSK, QAM), bandwidth, inter-symbol interference, MAP, ML detection, matched filter receiver, SNR and BER. Fundamentals of error correction, Hamming codes, CRC.

differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector.

reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth.

equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart. Rectangular and circular waveguides, light propagation in optical fibers, dipole and monopole antennas, linear antenna arrays.