GATE 2019 Online Preparation platform

# 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

• 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

• 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

• 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

• gain and directivity

• return loss

• antenna arrays

• 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.

### GATE Toppers from VANI Institute

AKASH
ALL INDIA 1st RANK(CIVIL)
GATE-2018

Pinaki Mondal
ALL INDIA 3rd RANK(EEE)
GATE-2018

Namitha Kalra
ALL INDIA 1st RANK(CSE)
GATE-2018

ALL INDIA 4th RANK(ECE)
GATE-2018

Lohith Kayal
ALL INDIA 6th RANK(CH)
GATE-2018

AKASH
ALL INDIA 1st RANK(CIVIL)
GATE-2018

M.Biswajit
ALL INDIA 5th RANK(ME)
GATE-2018

Mainul Haque
ALL INDIA 2nd RANK(IN)
GATE-2018

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