Linear Algebra

Matrix algebra, systems of linear equations, eigenvalues, and eigenvectors.

Calculus

Functions of a single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.

Differential equations

First-order equations (linear and nonlinear); higher-order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave, and Laplace’s equations.

Complex variables

Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series.

Probability and Statistics

Definitions of probability, sampling theorems, conditional probability; mean, median, mode, and standard deviation; random variables, binomial, Poisson, and normal
distributions.

QUANTITATIVE APTITUDE

Data interpretation: data graphs (bar graphs, pie charts, and other graphs representing the data), 2- and 3-dimensional plots, maps, and tables Numerical computation and estimation: ratios, percentages, powers, exponents, and logarithms, permutations, and combinations, and series Mensuration and geometry Elementary statistics and probability.

ANALYTICAL APTITUDE

Logic: deduction and induction, Analogy, Numerical relations, and reasoning

SPATIAL APTITUDE

Transformation of shapes: translation, rotation, scaling, mirroring, assembling, and grouping Paper folding, cutting, and patterns in 2 and 3 dimensions

VERBAL APTITUDE

Basic English grammar: tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech Basic vocabulary: words, idioms, and phrases in context Reading and comprehension Narrative sequencing

Circuit Analysis

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.
Linear 2-port network parameters, wye-delta transformation.

Continuous-time Signals

Fourier series and Fourier transform, sampling theorem and applications.

Discrete-time Signals

DTFT, DFT, z-transform, discrete-time processing of continuous-time signals.

LTI systems

Definition and properties, causality, stability, impulse response, convolution, poles and zeros, frequency response, group delay, phase delay.

Energy bands in intrinsic and extrinsic semiconductors, equilibrium carrier concentration, direct and indirect band-gap semiconductors.

Carrier Transport

diffusion current, drift current, mobility and resistivity, generation, and recombination of carriers, Poisson, and continuity equations. P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photodiode, and solar cell.

Diode Circuits

clipping, clamping, and rectifiers.

BJT and MOSFET Amplifiers

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

Op-amp Circuits

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

Number Representations

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, and decoders.

Sequential Circuits

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

Data Converters

Sample and hold circuits, ADCs, and DACs.

Semiconductor Memories

ROM, SRAM, DRAM.

Computer Organization

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

Basic control system components

Feedback principle; Transfer function; Block diagram representation; Signal flow graph; Transient and steady-state analysis of LTI systems; Frequency response; Routh-Hurwitz and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and lag lead compensation; State variable model and solution of state equation of LTI systems.

Random Processes

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

Analog Communications

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

Information Theory

entropy, mutual information, and channel capacity theorem.

Digital Communications

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.

Maxwell’s Equations

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

Plane Waves and Properties

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

Transmission Lines

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