GATE Electronics and Communications Syllabus


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Subject Code: EC

Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Vector Analysis
Unit 5 Complex Analysis
Unit 6 Numerical Methods
Unit 7 Probability and Statistics
Section B Networks, Signals and Systems
Unit 1 Network Solution Methods
Unit 2 Continuous-time Signals
Section C Electronic Devices
Section D Analog Circuits
Section E Digital Circuits
Section F Control Systems
Section G Communications
Section H Electromagnetics

Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

  • Vector space, basis, linear dependence and independence
  • Matrix algebra
  • Eigen values and Eigen vectors
  • Rank, solution of linear 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, line, surface and volume integrals
  • Taylor series

Unit 3: Differential Equations

  • 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

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 nonlinear equations
  • Single and multi-step methods for differential equations
  • convergence criteria

Unit 7: Probability and Statistics

  • Mean, median, mode and standard deviation
  • Combinatorial probability
  • probability distribution functions −
    • Binomial
    • Poisson
    • Exponential
    • Normal
  • Joint and conditional probability
  • 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 linear 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, sampling theorem and applications

  • Discrete-time signals −

    • Discrete-time Fourier transform (DTFT)

    • DFT

    • FFT

    • Z-transform

    • 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

Section C: Electronic Devices

  • Energy bands in intrinsic and extrinsic silicon

  • Carrier transport −

    • Diffusion current

    • Drift current

    • Mobility

    • 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

    • Twin-tub CMOS process

Section D: Analog Circuits

  • Small signal equivalent circuits of diodes, BJTs and MOSFETs
  • Simple diode circuits −
    • Clipping
    • Clamping
    • Rectifiers
  • Single-stage BJT and MOSFET amplifiers −
    • Biasing
    • Bias stability
    • Mid-frequency small signal analysis
    • Frequency response
  • BJT and MOSFET amplifiers −
    • 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 supplies: 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 flip-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 stability 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 −

    • Amplitude 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

    • 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

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 lines −
    • 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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