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# GATE syllabus - A Comprehensive List of GATE syllabus for ECE

### GATE syllabus for ECE

The GATE Exam is one of the most prestigious exams in the country. A perfect opportunity to not only pursue higher studies from some of India's topmost colleges but also to secure a job with one of the PSUs. GATE exam syllabus is quite comprehensive. The GATE syllabus for ECE is spread across 9 sections, with two sections dedicated to Engineering Mathematics and General Ability, and the other 7 dedicated to EC core subjects. The number of questions is 65 in the GATE exam. According to GATE syllabus for ECE with weightage, 10 questions are asked from the section of general aptitude and the remaining 55 pertains to Engineering Mathematics, Networks, Electronic Devices, Analog Circuits, Digital Circuits, Signals and Systems, Control Systems, Communications, Electromagnetic. With the help of GATE syllabus for ECE 2021 and GATE exam pattern, candidates get the immense clarity on the important topics to score well in the exam. The GATE syllabus for ECE branch consists of all the important topics and sub-topics that aspirants need to study to crack the entrance exam, which is listed below:

#### Engineering Mathematics

Linear Algebra
• Matrix algebra
• Systems of linear equations
• Eigen values and Eigen vectors
Ordinary Differential Equation ( ODE )
• First order ( linear and non – linear ) equations
• higher order linear equations with constant coefficients
• Euler – Cauchy equations
• Laplace transform and its application in solving linear ODEs
• Initial and boundary value problems.
Partial Differential Equation ( PDE ) : Fourier series
• separation of variables
• solutions of onedimensional diffusion equation
• first and second order one – dimensional wave equation and two-dimensional Laplace equation.
Calculus
• Functions of single variable
• Limit, continuity and differentiability
• Mean value theorems
• local maxima and minima
• Taylor and Maclaurin series
• Evaluation of definite and indefinite integrals
• application of definite integral to obtain area and volume
• Partial derivatives
• Total derivative
• Divergence and Curl, Vector identities
• Directional derivatives
• Line, Surface and Volume integrals
• Stokes
• Gauss and Green's theorems.
Probability and Statistics
• Definitions of probability and sampling theorems
• Conditional probability
• Discrete Random variables
• Poisson and Binomial distributions
• Continuous random variables
• normal and exponential distributions
• Descriptive statistics – Mean, median, mode and standard deviation
• Hypothesis testing.
Numerical Methods
• Accuracy and precision
• error analysis
• Numerical solutions of linear and non – linear algebraic equations
• Least square approximation
• Newton's and Lagrange polynomials
• numerical differentiation
• Integration by trapezoidal and Simpson's rule
• single and multi – step methods for first order differential equations.

#### Networks, Signals and Systems

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 and transfer functions; State equations for networks.
Continuous – time signals
• Fourier series and Fourier transform representations
• sampling theorem and applications
• Discrete – time signals
• discrete – time Fourier transform ( DTFT ), DFT, FFT
• Z – t ransform
• 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.

#### Electronic Devices

• Energy bands in intrinsic and extrinsic silicon
• Carrier transport
• diffusion current
• drift current
• mobility and 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 and twin – tub CMOS process.

#### Analog Circuits

• Small signal equivalent circuits of diodes
• BJTs and MOSFETs
• Simple diode circuits
• Clipping
• clamping and rectifiers
• Single – stage BJT and MOSFET amplifiers
• Biasing
• bias stability
• mid – frequency small signal analysis and frequency response
• BJT and MOSFET amplifiers
• multi – stage
• differentialfeedback power and operational
• Simple op – amp circuits
• Active filters
• Sinusoidal oscillators
• criterion for oscillation
• single – transistor and op-amp configurations
• Function generators
• wave-shaping circuits and 555 timers
• Voltage reference circuits
• Power supplies
• ripple removal and regulation.

#### 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 and 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.

#### 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.

#### 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 and 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.

#### 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
• propagation through various media
• skin depth
• Transmission lines equations
• Characteristic impedance, impedence matching, impedance transformation
• S – parameters
• Smith chart
• Waveguides
• modes, boundary conditions
• cut-off frequencies
• dispersion relations
• Antennas
• antenna types
• gain and directivity
• return loss
• antenna arrays
• Light propagation in optical fibers

#### TOPICS NOT INCLUDED IN GATE SYLLABUS

1. Electrical Materials
2. Electrical and Electronics measurement.
• A. Basic of sensors, Transducers.
• B. Basic of data acquisition systems.
3. Computer fundamentals.
4. Basic of electronics engineering.
5. Communication Systems.
6. Signal Processing
• A. Discrete cosine transform
• B. FIR, IIR, filter
• C. Bilinear transformation.