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GATE Online Preparation - 2019

We fill the gap between Aspiration & Reality of GATE

GATE 2019 Syllabus for Electronics and Communication Engineering

Engineering Mathematics


Linear Algebra
  • Matrix algebra

  • Systems of linear equations

  • Eigen values and Eigen vectors

Ordinary Differential Equation ( ODE )
  • First order ( linear and non – linear ) equations

  • higher order linear equations with constant coefficients

  • Euler – Cauchy equations

  • Laplace transform and its application in solving linear ODEs

  • Initial and boundary value problems.

Partial Differential Equation ( PDE ) : Fourier series
  • separation of variables

  • solutions of onedimensional diffusion equation

  • first and second order one – dimensional wave equation and two-dimensional Laplace equation.

Calculus
  • Functions of single variable

  • Limit, continuity and differentiability

  • Mean value theorems

  • local maxima and minima

  • Taylor and Maclaurin series

  • Evaluation of definite and indefinite integrals

  • application of definite integral to obtain area and volume

  • Partial derivatives

  • Total derivative

  • Gradient

  • Divergence and Curl, Vector identities

  • Directional derivatives

  • Line, Surface and Volume integrals

  • Stokes

  • Gauss and Green's theorems.

Probability and Statistics
  • Definitions of probability and sampling theorems

  • Conditional probability

  • Discrete Random variables

  • Poisson and Binomial distributions

  • Continuous random variables

  • normal and exponential distributions

  • Descriptive statistics – Mean, median, mode and standard deviation

  • Hypothesis testing.

Numerical Methods
  • Accuracy and precision

  • error analysis

  • Numerical solutions of linear and non – linear algebraic equations

  • Least square approximation

  • Newton's and Lagrange polynomials

  • numerical differentiation

  • Integration by trapezoidal and Simpson's rule

  • single and multi – step methods for first order differential equations.

Networks, Signals and Systems


Network 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

  • Time domain analysis of simple linear circuits

  • Solution of network equations using Laplace transform

  • Frequency domain analysis of RLC circuits

  • Linear 2 ‐ port network parameters: driving point and transfer functions; State equations for networks.

Continuous – time signals
  • Fourier series and Fourier transform representations

  • sampling theorem and applications

  • Discrete – time signals

  • discrete – time Fourier transform ( DTFT ), DFT, FFT

  • Z – t ransform

  • interpolation of discrete – time signals

  • LTI systems definition and properties

  • Causality

  • Stability

  • impulse response

  • convolution

  • poles and zeros

  • parallel and cascade structure

  • frequency response

  • group delay

  • phase delay

  • digital filter design techniques.

Electronic Devices


  • Energy bands in intrinsic and extrinsic silicon

  • 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

  • photo diode and solar cell

  • Integrated circuit fabrication process

  • Oxidation

  • Diffusion

  • ion implantation

  • photolithography and twin – tub CMOS process.

Analog Circuits


  • Small signal equivalent circuits of diodes

  • BJTs and MOSFETs

  • Simple diode circuits

  • Clipping

  • clamping and rectifiers

  • Single – stage BJT and MOSFET amplifiers

  • Biasing

  • bias stability

  • mid – frequency small signal analysis and frequency response

  • BJT and MOSFET amplifiers

  • multi – stage

  • differentialfeedback power and operational

  • Simple op – amp circuits

  • Active filters

  • Sinusoidal oscillators

  • criterion for oscillation

  • single – transistor and op-amp configurations

  • Function generators

  • wave-shaping circuits and 555 timers

  • Voltage reference circuits

  • Power supplies

  • ripple removal and regulation.

Digital Circuits


  • Number systems

  • 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 and PLAs

  • Sequential circuits

  • latches and flip ‐ flops

  • Counters

  • shift ‐ registers and finite state machines

  • Data converters : sample and hold circuits,ADCs and DACs;

  • Semiconductor memories ROM, SRAM, DRAM

  • 8 – bit microprocessor ( 8085 ) : architecture, programming, memory and I/O interfacing.

Control Systems


  • 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.

Communications


  • 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,circuits for analog communications

  • Information theory

  • entropy, mutual information and channel capacity theorem

  • Digital communications

  • PCM, DPCM, digital modulation schemes

  • Amplitude

  • phase and frequency shift keying ( ASK, PSK, FSK ), QAM, MAP and ML decoding

  • matched filter receiver calculation of bandwidth

  • SNR and BER for digital modulation

  • Fundamentals of error correction, Hamming codes

  • Timing and frequency synchronization

  • inter – symbol interference and its mitigation

  • Basics of TDMA, FDMA and CDMA.

Electromagnetics


  • Electrostatics

  • Maxwell's equations

  • differential and integral forms and their interpretation

  • boundary conditions

  • wave equation

  • Poynting vector

  • Plane waves and properties

  • reflection and refraction

  • polarization

  • propagation through various media

  • skin depth

  • Transmission lines equations

  • Characteristic impedance, impedence matching, impedance transformation

  • S – parameters

  • Smith chart

  • Waveguides

  • modes, boundary conditions

  • cut-off frequencies

  • dispersion relations

  • Antennas

  • antenna types

  • Radiation pattern

  • gain and directivity

  • return loss

  • antenna arrays

  • Basics of radar

  • Light propagation in optical fibers

TOPICS NOT INCLUDED IN GATE SYLLABUS


1. Electrical Materials
2. Electrical and Electronics measurement.
  • A. Basic of sensors, Transducers.

  • B. Basic of data acquisition systems.

3. Computer fundamentals.
4. Basic of electronics engineering.
5. Communication Systems.
6. Signal Processing
  • A. Discrete cosine transform

  • B. FIR, IIR, filter

  • C. Bilinear transformation.

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