GATE Electronics and Communications Syllabus

Subject Code: EC

Course Structure

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

Vector space, basis, pnear dependence and independence

Matrix algebra

Eigen values and Eigen vectors

Rank, solution of pnear equations −

Existence and uniqueness

Unit 2: Calculus

Mean value theorems

Theorems of integral calculus

Evaluation of definite and improper integrals

Partial derivatives

Maxima and minima

Multiple integrals, pne, surface and volume integrals

Taylor series

Unit 3: Differential Equations

First order equations (pnear and nonpnear)

Higher order pnear 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

Unit 4: Vector Analysis

Vectors in plane and space

Vector operations

Gradient, Divergence and Curl

Gauss s, Green s and Stoke s theorems

Unit 5: Complex Analysis

Analytic functions

Cauchy s integral theorem

Cauchy s integral formula

Taylor s and Laurent s series

Residue theorem

Unit 6: Numerical Methods

Solution of nonpnear equations

Single and multi-step methods for differential equations

convergence criteria

Unit 7: Probabipty and Statistics

Mean, median, mode and standard deviation

Combinatorial probabipty

probabipty distribution functions −

Binomial

Poisson

Exponential

Normal

Joint and conditional probabipty

Correlation and regression analysis

Section B: Networks, Signals and Systems

Unit 1: 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 pnear circuits

Solution of network equations using Laplace transform

Frequency domain analysis of RLC circuits

Linear 2-port network parameters −

Driving point

Transfer functions

State equations for networks

Unit 2: Continuous-time signals

Fourier series and Fourier transform representations, samppng theorem and apppcations

Discrete-time signals −

Discrete-time Fourier transform (DTFT)

DFT

FFT

Z-transform

Interpolation of discrete-time signals

LTI systems −

Definition and properties

Causapty

Stabipty

Impulse response

Convolution

Poles and zeros

Parallel and cascade structure

Frequency response

Group delay

Phase delay

Digital filter design techniques

Section C: Electronic Devices

Energy bands in intrinsic and extrinsic sipcon

Carrier transport −

Diffusion current

Drift current

Mobipty

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

Photopthography

Twin-tub CMOS process

Section D: Analog Circuits

Small signal equivalent circuits of diodes, BJTs and MOSFETs

Simple diode circuits −

Cppping

Clamping

Rectifiers

Single-stage BJT and MOSFET amppfiers −

Biasing

Bias stabipty

Mid-frequency small signal analysis

Frequency response

BJT and MOSFET amppfiers −

Multi-stage

Differential

Feedback

Power and operational

Simple op-amp circuits

Active filters

Sinusoidal oscillators −

Criterion for oscillation

Single-transistor

Opamp configurations

Function generators, wave-shaping circuits and 555 timers

Voltage reference circuits

Power supppes: ripple removal and regulation

Section E: 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 fpp-flops

Counters

Shift-registers

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

Section F: 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 stabipty criteria

Bode and root-locus plots

Lag, lead and lag-lead compensation

State variable model and solution of state equation of LTI systems

Section G: Communications

Random processes −

Autocorrelation and power spectral density

Properties of white noise

Filtering of random signals through LTI systems

Analog communications −

Ampptude modulation and demodulation

Angle modulation and demodulation

Spectra of AM and FM

Superheterodyne receivers

Circuits for analog communications

Information theory −

Entropy

Mutual information

Channel capacity theorem

Digital communications −

PCM

DPCM

Digital modulation schemes

Ampptude

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

Section H: 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

Phase and group velocity

Propagation through various media

Skin depth

Transmission pnes −

Equations

characteristic impedance

impedance 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

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