# Gate Electrical Engineering Syllabus

Table of Contents

Table of Contents

Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.

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.

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.

formula, Taylor series, Laurent series, Residue theorem, Solution integrals.

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.

Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step

methods for differential equations.

Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.

Network graph, KCL, KVL, Node and Mesh analysis, Transient response of dc and ac

networks, Sinusoidal steady‐state analysis, Resonance, Passive filters, 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.

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, Faraday’s law, Lorentz force, Inductance, Magnetomotive force,

Reluctance, Magnetic circuits,Self and Mutual inductance of simple configurations.

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.

tests, regulation and efficiency; Three phase transformers: connections, parallel operation;

Auto‐transformer, Electro-mechanical 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.

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.

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.

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.

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 and Interfacing.

Characteristics of semiconductor power devices: Diode, Thyristor, Triac, GTO, MOSFET,

IGBT; DC to DC conversion: Buck, Boost and 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.