GATE Electronics and Communications Syllabus

Subject Code: EC

Course Structure

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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