## ISRO Syllabus for Electrical Engineering

Engineering Mathematics

Linear Algebra- Matrix Algebra, Eigenvalues, Eigenvectors, Systems of linear equations

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.

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.

Complex variables-  Analytic functions, Cauchy’s integral theorem, Cauchy’s integral 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- Numerical Solutions of Linear Equations, Numerical Solution of Algebraic, Numerical Integration, Numerical Solution of Differential Equation.

Transformation : Fourier Transform, Laplace Transform, zTransform.

#### Electric Circuits

KCL, KVL, Node Analysis and Mesh analysis, Transient response(dc and ac networks), Sinusoidal steadystate analysis, Resonance, Passive filters(LC).

Ideal current and voltage sources, Thevenin’s theorem, Norton’s theorem, Superposition theorem, Maximum power transfer theorem.

Twoport networks, Three phase circuits, Power and power factor in ac circuits Network graph.

#### Signals and Systems

Continuous-time signal and discretetime signals, Shifting and scaling and time reversal operations.

Linear Time-Invariant and Causal systems, Stability, Time reversal Theorem
Fourier series for continuous periodic signals, Sampling theorem.

Applications of Fourier Transform, Laplace Transform, and z-Transform.

#### Electromagnetic Fields

Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law. And their Application

Divergence Law, Curl Theorem, Electric field and potential due to point & line.
Charge distributions concept of Plane and Spherical, Dielectric medium Effects.
The capacitance of simple configurations.

BiotSavart’s law, Ampere’s law, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

#### Electrical Machines

1-Phase transformer - Equivalent circuit, phasor diagrams, open circuit and short circuit testing, regulation and efficiency.

Three phase transformers-  connections, parallel operation. Autotransformer, Electromechanical energy conversion principles.

3-Phase induction motors - Operation principle, characteristics of torque-speed, no-load and blocked rotor test, starting and speed control, Operating principle of 1-Phase induction motors.

DC machines - separately excited, series and shunt, Operation modes of motoring and generating, starting and speed control of dc motors.

Synchronous machines- Cylindrical & salient pole machine, performance, regulation and parallel operation of generators, synchronous motor starting, characteristics, All types of losses & efficiency calculation of electric machines.

#### Control Systems

Feedback principle (Positive and Negative feedback), transfer function, Block diagrams and Signal flow graphs Theory. Meson’s Gain Formula.

Transient and Steadystate analysis of linear time-invariant systems, Routh-Hurwitz Criterion, Polar and Nyquist Plot criteria, Bode plots, gain & Phase margin, Root loci, Stability analysis.

Lag, Lead and LeadLag compensators; Proportion, proportion and Intergration(PI) and Proportion Integration and Differentiator (PID) controllers.

State space model, State transition matrix, transfer function of State model, Controlability and Obserbability.

Mathematical modelling and representation of systems.

#### Electrical & Electronics measurements

Measurement of voltage, current, power, energy and power factor Meaurement, Bridges and Potentiometers mesurement.

Instrument transformers, , Phase, Time and Frequency measurement, Oscilloscopes, and Error analysis, Multimeters, and Digital voltmeters.

#### Power Systems

Concepts of Power generation, 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, Gauss-Seidel and Newton-Raphson load flow concept.

Voltage & Frequency control, Power factor correction, and modification, all Symmetrical components, Symmetrical and unsymmetrical fault concept, overcurrent Principle, distance and differential protection, breakers of circuits, Criterion of an Equal area.

#### Analog Electronics

Bipolar junction transistor, MOSFET.

Diodes and Its Characteristics and Application.

Diode circuits: clipping, clamping, rectifiers.

Amplifiers: Biasing, Equivalent circuit and Frequency response.

Oscillators and Feedback amplifiers.

Operational amplifiers: Ideal and Practical Characteristics of OP-AMP & applications, Active filters, VCOs and Timers.

#### Power Electronics

Semiconductor devices: Diode, Thyristor (SCR), Triac Diode, GTO, MOSFET, and IGBT.
DC to DC conversion: Buck, Boost, and Buck-Boost converters.

Single and three phase configuration of uncontrolled rectifiers.

Line-commutated thyristor(SCR) based converters, Bidirectional ac to dc voltage converters, Issues of line current harmonics.

Power factor, Distortion factor of ac to dc converters, 1-Phase and 3-phase inverters.

Communication- Sinusoidal pulse width modulation.

#### Digital Electronics

Combinational and Sequential logic circuits, Multiplexer, Demultiplexer, Schmitt trigger, Sample and hold circuits, Analog to Digital Converter(A/D) and Digital to Analog Converter (D/A)

8085 Microprocessor: Architecture, Programming, and Interfacing.

S.N.