# GATE Electrical Engineering Syllabus

## Subject Code: EE

### Course Structure

Sections/Units Topics
Section A Engineering Mathematics
Unit 1 Linear Algebra
Unit 2 Calculus
Unit 3 Differential Equations
Unit 4 Complex Variables
Unit 5 Probability and Statistics
Unit 6 Numerical Methods
Unit 7 Transform Theory
Section B Electric Circuits
Section C Electromagnetic Fields
Section D Signals and Systems
Section E Algorithms
Section F Electrical Machines
Section G Power Systems
Section H Control Systems
Section I Electrical and Electronic Measurements
Section J Analog and Digital Electronics
Section K Power Electronics

### Course Syllabus

Section A: Engineering Mathematics

Unit 1: Linear Algebra

• Matrix Algebra
• Systems of linear equations
• Eigenvalues
• Eigenvectors

Unit 2: Calculus

• Mean value theorems
• Theorems of integral calculus
• Evaluation of definite and improper integrals
• Partial Derivatives
• Maxima and minima
• Multiple integrals
• Fourier series
• Vector identities
• Directional derivatives
• Line integral
• Surface integral
• Volume integral
• Stokes’s theorem
• Gauss’s theorem
• Green’s theorem

Unit 3: Differential equations

• First order equations (linear and nonlinear)
• Higher order linear differential equations with constant coefficients
• Method of variation of parameters
• Cauchy’s equation
• Euler’s equation
• Initial and boundary value problems
• Partial Differential Equations
• Method of separation of variables

Unit 4: Complex variables

• Analytic functions
• Cauchy’s integral theorem
• Cauchy’s integral formula
• Taylor series
• Laurent series
• Residue theorem
• Solution integrals

Unit 5: Probability and Statistics

• Sampling theorems

• Conditional probability

• Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions

• Poisson distribution

• Normal distribution

• Binomial distribution

• Correlation analysis,

• Regression analysis

Unit 6: Numerical Methods

• Solutions of nonlinear algebraic equations
• Single and Multi-step methods for differential equations

Unit 7: Transform Theory

• Fourier Transform
• Laplace Transform
• z-Transform

Section B: Electric Circuits

• Network graph
• KCL, KVL, Node and Mesh analysis
• Transient response of dc and ac networks
• Sinusoidal steady-state analysis
• Resonance
• Passive filter, Ideal current and voltage sources
• Thevenin’s theorem
• Norton’s theorem
• Superposition theorem
• Maximum power transfer theorem
• Two-port networks
• Three phase circuits
• Power and power factor in ac circuits

Section C: Electromagnetic Fields

• Coulomb's Law

• Electric Field Intensity

• Electric Flux Density

• Gauss's Law

• Divergence, Electric field and potential due to point, line, plane and spherical charge distributions

• Effect of dielectric medium

• Capacitance of simple configurations

• Biot-Savart’s law

• Ampere’s law

• Curl

• Lorentz force

• Inductance

• Magnetomotive force

• Reluctance

• Magnetic circuits

• Self and Mutual inductance of simple configurations

Section D: Signals and Systems

• Representation of continuous and discrete-time signals
• Shifting and scaling operations
• Linear Time Invariant and Causal systems
• Fourier series representation of continuous periodic signals
• Sampling theorem
• Applications of Fourier Transform
• Laplace Transform and z-Transform

Section E: Electrical Machines

• Single phase transformer −
• Equivalent circuit
• Phasor diagram
• Open circuit and short circuit tests
• Regulation and efficiency
• Three phase transformers −
• Connections
• Parallel operation
• Auto-transformer
• Electromechanical energy conversion principles
• DC machines −
• Separately excited
• Series and shunt
• Motoring and generating mode of operation and their characteristics
• Starting and speed control of dc motors
• Three phase induction motors −
• Principle of operation
• Types
• Performance
• Torque-speed characteristics
• No-load and blocked rotor tests
• Equivalent circuit
• Starting and speed control
• Operating principle of single phase induction motors
• Synchronous machines −
• Cylindrical and salient pole machines
• Performance
• Regulation and parallel operation of generators
• Starting of synchronous motor
• Characteristics
• Types of losses and efficiency calculations of electric machines

Section F: Power Systems

• Power generation concepts
• ac and dc transmission concepts
• Models and performance of transmission lines and cables
• Series and shunt compensation
• Electric field distribution and insulators
• Distribution systems
• Per-unit quantities
• Bus admittance matrix
• GaussSeidel and Newton-Raphson load flow methods
• Voltage and Frequency control
• Power factor correction
• Symmetrical components
• Symmetrical and unsymmetrical fault analysis
• Principles of over-current
• Differential and distance protection
• Circuit breakers
• System stability concepts
• Equal area criterion

Section G: Control Systems

• Mathematical modeling and representation of systems

• Feedback principle

• Transfer function

• Block diagrams and Signal flow graphs

• Transient and Steady-state analysis of linear time invariant systems

• Routh-Hurwitz and Nyquist criteria

• Bode plots, Root loci, Stability analysis, Lag, Lead and Lead-Lag compensators

• P, PI and PID controllers

• State space model

• State transition matrix

Section H: Electrical and Electronic Measurements

• Bridges and Potentiometers

• Measurement of voltage, current, power, energy and power factor

• Instrument transformers, Digital voltmeters and multimeters, Phase, Time and Frequency measurement

• Oscilloscopes

• Error analysis

Section I: Analog and Digital Electronics

• Characteristics of diodes, BJT, MOSFET
• Simple diode circuits: clipping, clamping, rectifiers
• Amplifiers: Biasing, Equivalent circuit and Frequency response
• Oscillators and Feedback amplifiers
• Operational amplifiers: Characteristics and applications
• Simple active filters
• VCOs and Timers
• Combinational and Sequential logic circuits
• Multiplexer
• Demultiplexer
• Schmitt trigger
• Sample and hold circuits
• A/D and D/A converters
• 8085Microprocessor −
• Architecture
• Programming
• Interfacing

Section H: Power Electronics

• Characteristics of semiconductor power devices −
• Diode
• Thyristor
• Triac
• GTO
• MOSFET
• IGBT
• DC to DC conversion −
• Buck
• Boost
• Buck-Boost converters
• Single and three phase configuration of uncontrolled rectifiers
• Line commutated thyristor based converters
• Bidirectional ac to dc voltage source converters
• Issues of line current harmonics
• Power factor
• Distortion factor of ac to dc converters
• Single phase and three phase inverters
• Sinusoidal pulse width modulation