# GATE Electronics and Communications Syllabus

## 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
• 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

• 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

• 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
• 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

• 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

• 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