GATE Syllabus for Electrical Engineering - EE

ENGINEERING MATHEMATICS

Linear Algebra:

• Matrix Algebra
• Systems of linear equations
• Eigen values and eigen vectors.

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, Surface and Volume integrals
• Stokes, Gauss and Green’s theorems.

Differential equations:

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

Complex variables:

• Analytic functions,
• Cauchy’s integral theorem and integral formula,
• Taylor’s and Laurent’ series,
• Residue theorem, solution integrals.

Probability and Statistics:

• Sampling theorems,
• Conditional probability,
• Mean, median, mode and standard deviation,
• Random variables,
• Discrete and continuous distributions,
• Poisson, Normal and Binomial distribution,
• Correlation and regression analysis.

Numerical Methods:

• Solutions of non-linear algebraic equations,
• single and multi-step methods for differential equations.

Transform Theory:

• Fourier transform,
• Laplace transform,
• Z-transform.

ELECTRICAL ENGINEERING

Electric Circuits and Fields:

• Network graph,
• KCL, KVL, node and mesh analysis,
• transient response of dc and ac networks;
• sinusoidal steady-state analysis, resonance,
• basic filter concepts;
  
• ideal current and voltage sources,
• Thevenin’s, Norton’s and Superposition and Maximum Power Transfer theorems,
• two-port networks,
• three phase circuits;
• Gauss Theorem,
• electric field and potential due to point, line, plane and spherical charge distributions;
• Ampere’s and Biot-Savart’s laws;
• inductance; dielectrics; capacitance.

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;
• Fourier, Laplace and Z transforms.

Electrical Machines:

• Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation;
• auto-transformer;
• energy conversion principles;
• DC machines - types, windings, generator characteristics, armature reaction and commutation, starting and speed control of motors;
• three phase induction motors - principles, types, performance characteristics, starting and speed control;
• single phase induction motors;
• synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications;
• servo and stepper motors.

Power Systems:

• Basic power generation concepts;
• transmission line models and performance;
• cable performance, insulation;
• corona and radio interference;
• distribution systems; per-unit quantities;
• bus impedance and admittance matrices;
• load flow;
• voltage control;
• power factor correction;
• economic operation;
• symmetrical components;
• fault analysis;
• principles of over-current, differential and distance protection;
• solid state relays and digital protection;
• circuit breakers;
• system stability concepts,
• swing curves and equal area criterion;
• HVDC transmission and FACTS concepts.

Control Systems:

• Principles of feedback;
• transfer function;
• block diagrams;
• steady-state errors;
• Routh and Niquist techniques;
• Bode plots;
• root loci;
• lag, lead and lead-lag compensation;
• state space model;
• state transition matrix,
• controllability and observability.

Electrical and Electronic Measurements:

• Bridges and potentiometers;
• PMMC, moving iron, dynamometer and induction type instruments;
• measurement of voltage, current, power, energy and power factor;
• instrument transformers;
• digital voltmeters and multimeters;
• phase, time and frequency measurement;
• Q-meters;
• oscilloscopes;
• potentiometric recorders;
• error analysis.

Analog and Digital Electronics:

• Characteristics of diodes, BJT, FET;
• 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; Schmitt trigger;
• multi-vibrators;
• sample and hold circuits;
• A/D and D/A converters;
• 8-bit microprocessor basics, architecture, programming and interfacing.

Power Electronics and Drives:

• Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation;
• triggering circuits;
• phase control rectifiers;
• bridge converters - fully controlled and half controlled;
• principles of choppers and inverters;
• basis concepts of adjustable speed dc and ac drives.