GATE Syllabus for ECE
2021
Section 1: Engineering
Mathematics
Calculus:
- Evaluation of definite and improper integrals
- Line, surface and volume integrals
- Taylor series.
- Maxima and minima
- Multiple integrals
- Mean value theorems
- Partial derivatives
- Theorems of integral calculus
Complex Analysis:
- Analytic functions
- Cauchy's integral formula
- Cauchy's integral theorem
- Residue theorem.
- Taylor's and Laurent's series
Differential Equations:
- Cauchy's and Euler's equations
- Complementary function and particular integral, partial
differential equations
- First-order equations (linear and nonlinear)
- Higher-order linear differential equations
- Initial and boundary value problems.
- Methods of solution using a variation of parameters
- Variable separable method
Linear Algebra:
- Basis, linear dependence and independence
- Matrix algebra
- Eigenvalues and Eigen vectors
- Vector space
- Rank, solution of linear equations – existence and
uniqueness.
Numerical Methods:
- Convergence criteria.
- Single and multi-step methods for differential
equations
- Solution of nonlinear equations
Probability and Statistics:
- Combinatorial probability
- Correlation and regression analysis.
- Joint and conditional probability
- Mean, median, mode and standard deviation
- Poisson, exponential and normal
- Probability distribution functions - binomial
Vector Analysis:
- Gauss's, Green's and Stoke’s theorems.
- Vectors in plane and space
- Vector operations, gradient, divergence and curl
Section 2: Networks,
Signals and Systems
Continuous-time signals:
- Discrete-time signals: discrete-time
- Fourier series and Fourier transform representations
- Interpolation of discrete-time signals
- Fourier transform (DTFT), DFT, FFT, Z-transform
- 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.
- Sampling theorem and applications
Network solution methods:
- Frequency domain analysis of RLC circuits
- Linear 2‐port
network parameters: driving point and transfer functions
- Network theorems: superposition
- Nodal and mesh analysis
- Solution of network equations using Laplace transform
- State equations for networks.
- Steady-state sinusoidal analysis using phasors
- Thevenin and Norton’s, maximum power transfer
- Time-domain analysis of simple linear circuits
- Wye‐Delta
transformation
Section 3: Electronic
Devices
- Energy bands in intrinsic and extrinsic silicon
- Carrier transport: diffusion current, drift current,
mobility and resistivity
- Generation and recombination of carriers
- Integrated circuit fabrication process: oxidation,
diffusion, ion implantation, photolithography and twin-tub CMOS process.
- MOSFET, LED, photodiode and solar cell
- Poisson and continuity equations
- P-N junction, Zener diode, BJT, MOS capacitor
Section 4: Analog
Circuits
- Active filters
- BJTs and MOSFETs
- Single-stage BJT and MOSFET amplifiers: biasing, bias
stability, mid frequency small signal analysis and frequency response
- BJT and MOSFET amplifiers: multi-stage, differential,
feedback, power and operational
- Function generators, wave-shaping circuits and 555
timers
- Power supplies: ripple removal and regulation.
- Simple op-amp circuits
- Sinusoidal oscillators: criterion for oscillation,
single-transistor and op- amp configurations
- Small signal equivalent circuits of diodes
- Simple diode circuits: clipping, clamping and
rectifiers
- Voltage reference circuits
Section 5: Digital
Circuits
- Data converters: sample and hold circuits, ADCs and
DACs
- 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
- Semiconductor memories: ROM, SRAM, DRAM; 8-bit
microprocessor (8085): architecture, programming, memory and I/O
interfacing.
- Sequential circuits: latches and flip‐flops, counters, shift‐registers
and finite state machines
Section 6: Control
Systems
- Basic control system components
- Bode and root-locus plots
- Frequency response
- Block diagram representation
- Lag, lead and lag-lead compensation
- Signal flow graph
- Feedback principle
- State variable model and solution of state equation of
LTI systems.
- Transfer function
- Routh-Hurwitz and Nyquist stability criteria
- Transient and steady-state analysis of LTI systems
Section 7:
Communications
Digital communications:
- Hamming codes
- Amplitude, phase and frequency shift keying (ASK, PSK,
FSK),
- Basics of TDMA, FDMA and CDMA.
- Fundamentals of error correction
- Matched filter receiver
- PCM, DPCM
- SNR and BER for digital modulation
- Digital modulation schemes
- QAM, MAP and ML decoding
- Calculation of bandwidth
- Timing and frequency synchronization, inter-symbol
interference and its mitigation
Random processes:
- Analog communications: amplitude modulation and
demodulation
- Angle modulation and demodulation
- Autocorrelation and power spectral density
- Circuits for analog communications
- Filtering of random signals through LTI systems
- Properties of white noise
- Spectra of AM and FM
- Information theory: entropy, mutual information and
channel capacity theorem.
- Superheterodyne receivers
Section 8:
Electromagnetics
Electrostatics
- Boundary conditions
- Maxwell’s equations: differential and integral forms
and their interpretation
- Plane waves and properties: reflection and refraction,
polarization, phase and group velocity, propagation through various media,
skin depth;
- Poynting vector
- Wave equation
Transmission lines:
- Characteristic impedance
- Equations
- Impedance matching
- Impedance transformation
- Smith chart
- S-parameters
Waveguides:
- Antennas and its’ types
- Basics of radar
- Boundary conditions
- Cut-off frequencies
- Dispersion relations
- Gain and directivity
- Light propagation in optical fibers.
- Modes
- Radiation pattern
- Return loss, antenna arrays
GATE Syllabus for ECE
Books
- Electronics and Communication Engineering
- Higher Engineering Mathematics by Dr B.S. Grewal
- Network Theory by Alexander Sadiku
- Integrated Electronics:- Jacob Millman & Christos
C. Halkias
- Signals & Systems By Alan V. Oppenheim
- Automatic Control Systems by Benjamin C. Kuo
- Analog and Digital Communication System by Simon Haykin
- Elements of Electromagnetics by Matthew N.O. Sadiku
- Semiconductor devices by David Neamen
|
SUBJECTS |
Weight age in 2020 |
2019 |
2018 |
|
Analog circuits |
10 |
12 |
10 |
|
communication |
11 |
12 |
10 |
|
Control system |
12 |
11 |
10 |
|
Digital circuits |
9 |
8 |
12 |
|
electromagnetics |
9 |
14 |
13 |
|
Electronic devices |
12 |
14 |
14 |
|
Engineering mathematics |
15 |
15 |
15 |
|
Networks and signals systems |
6 + 6 |
6 + 8 |
9 + 7 |
