Gate 2012 Electrical Engineering - EE Syllabus
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 boundar y value problems, Partial Differ ential
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 regr ession analysis.
Numerical Methods:
Solutions of non-linear algebr aic 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, par allel 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, curr ent, 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.
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 boundar y value problems, Partial Differ ential
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 regr ession analysis.
Numerical Methods:
Solutions of non-linear algebr aic 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, par allel 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, curr ent, 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.
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