Licchavi Lyceum

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# GATE Electrical

## Section 1- Engineering Mathematics

### Linear Algebra

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

### Calculus

• Theorems of Integral Calculus
• Mean Value Theorems
• Evaluation Of Definite And Improper Integrals
• Maxima And Minima
• Partial Derivatives
• Multiple Integrals
• Vector Identities
• Fourier Series
• Directional Derivatives
• Surface Integral
• Line Integral
• Volume Integral
• Stokes’s Theorem
• Divergence Theorem
• Gauss’s Theorem
• Green’s Theorem

### Differential equations

• Cauchy’s Equation
• Higher-Order Linear Differential Equations With Constant Coefficients
• First-Order Equations (Linear And Nonlinear)
• Method Of Variation Of Parameters
• Partial Differential Equations
• Initial And Boundary Value Problems
• Euler’s Equation
• Method Of Separation Of Variables

### Complex variables

• Solution Integrals
• Cauchy’s Integral Theorem
• Analytic Functions
• Cauchy’s Integral Formula
• Laurent Series
• Taylor Series
• Residue Theorem

### Probability and Statistics

• Conditional Probability
• Sampling Theorems
• Mean
• Mode
• Median
• Standard Deviation
• Discrete and Continuous distributions
• Random Variables
• Poisson Distribution
• Binomial Distribution
• Normal Distribution
• Correlation Analysis
• Regression Analysis

## Section 2- Electric circuits

Network elements

• Dependent Sources, R, L, C, M Elements
• Ideal Voltage And Current Sources
• Network solution methods: KVL, KCL, Node And Mesh Analysis
• Network Theorems: Thevenin’s, Norton’s, Superposition and Maximum Power Transfer Theorem
• Resonance
• Transient Response of dc & ac networks
• Balanced Three-Phase Circuits
• Two-Port Networks
• Complex Power And Power Factor in ac circuits
• Star-Delta Transformation

## Section 3- Electromagnetic Fields

• Electric Field Intensity
• Coulomb’s Law
• Electric Flux Density
• Divergence
• Gauss’s Law
• Electric field and potential due to point, line, plane and spherical charge distributions
• Effect Of Dielectric Medium
• Biot-Savart’s Law
• Capacitance Of Simple Configurations
• Ampere’s Law
• Curl
• Self And Mutual Inductance Of Simple Configurations
• Lorentz Force
• Inductance
• Magnetomotive Force
• Magnetic Circuits
• Reluctance

## Section 4- Signals and Systems

• Average Value Calculation for any General Periodic Waveform
• Shifting and Scaling Properties
• Representation of Continuous and Discrete-Time Signals
• Linear Time-Invariant and Causal Systems
• Laplace Transform and Z Transform
• R.M.S. Value
• Sampling Theorem
• Fourier Series Representation of Continuous and Discrete-Time Periodic Signals
• Applications of Fourier Transform for Continuous and Discrete-Time Signals

## Section 5- Electrical Machines

• Single-phase transformer: Equivalent Circuit, Open Circuit And Short Circuit Tests, Phasor Diagram, Regulation And Efficiency
• Three-phase transformers: connections, vector groups, parallel operation
• Electromechanical Energy Conversion Principles
• Auto-Transformer
• DC machines: separately excited, series and shunt, motoring and generating
• mode of operation and their characteristics, speed control of dc motors
• Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control
• Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors
• Types Of Losses And Efficiency Calculations Of Electric Machines

## Section 6- Power Systems

• Models And Performance Of Transmission Lines And Cables
• Basic Concepts Of Electrical Power Generation
• Ac And Dc Transmission Concepts
• Economic Load Dispatch (With And Without Considering Transmission Losses)
• Electric Field Distribution And Insulators
• Series And Shunt Compensation
• Distribution Systems
• Per-Unit Quantities
• Gauss- Seidel And Newton-Raphson Load Flow Methods
• Power Factor Correction
• Voltage And Frequency Control
• Symmetrical Components
• Principles of Over-Current, Differential, Directional And Distance Protection
• Symmetrical and Unsymmetrical Fault Analysis
• Circuit Breakers
• System stability concepts
• Equal Area Criterion

## Section 7- Control Systems

• Feedback Principle
• Mathematical Modelling And Representation Of Systems
• Transfer Function
• Transient And Steady-State Analysis Of Linear Time-Invariant Systems
• Block Diagrams And Signal Flow Graphs
• Stability Analysis Using Routh-Hurwitz And Nyquist Criteria
• Root Loci
• Bode Plots
• Solution Of State Equations Of LTI Systems
• P, PI And PID Controllers
• State-Space Model

## Section 8- Electrical and Electronic Measurements

• Measurement Of Voltage, Current, Power, Energy And Power Factor
• Bridges And Potentiometers
• Instrument Transformers
• Oscilloscopes, Error Analysis
• Phase, Time and Frequency measurement
• Digital Voltmeters And Multimeters
• Time And Frequency Measurement

## Section 9: Analog and Digital Electronics

• Simple diode circuits: Clamping, Clipping, Rectifiers
• Amplifiers: Biasing, Equivalent Circuit and Frequency Response
• Oscillators And Feedback Amplifiers
• Operational amplifiers: characteristics and applications; single stage active filters
• Active Filters: Sallen Key, Butterwoth, VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers, Schmitt triggers, sample and hold circuits, A/D and D/A converters.

## Section 10- Power Electronics

• Static V-I characteristics and firing/gating circuits for Thyristor, MOSFET, IGBT; DC to DC conversion
• Buck, Boost And Buck-Boost Converters
• Single and Three-Phase Configuration Of Uncontrolled Rectifiers
• Bidirectional ac to dc Voltage Source Converters
• Voltage And Current Commutated Thyristor Based Converters
• Magnitude And Phase Of Line Current Harmonics For Uncontrolled and Thyristor-Based Converters
• Single-Phase And Three-Phase Voltage And Current Source Inverters
• Power Factor And Distortion Factor Of ac to dc Converters
• Sinusoidal Pulse Width Modulation

# Section 1: Engineering Mathematics

## Linear Algebra

Matrix algebra, systems of linear equations, eigenvalues, and eigenvectors.

## 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, divergence theorem, and 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, and the method of separation of variables.

## Complex Variables

Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, residue theorem, and 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, and regression analysis.

# Section 2: Electric Circuits

• Ideal Voltage Source
• and ideal current source, dependent sources, R, L, C, M elements; Network solution methods: KCL, KVL, Node and Mesh analysis; Network Theorems: Thevenin’s, Norton’s, Superposition and Maximum Power Transfer theorem; Transient response of dc and ac networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in ac circuits.

# Section 3: 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, Faraday’s law, Lorentz force, Inductance, Magnetomotive force, Reluctance, Magnetic circuits, Self and Mutual inductance of simple configurations.

# Section 4: Signals and Systems

Representation of continuous and discrete time signals, shifting and scaling properties, linear time invariant and causal systems, Fourier series representation of continuous and discrete time periodic signals, sampling theorem, Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform. R.M.S. value, average value calculation for any general periodic waveform.

# Section 5: Electrical Machines

## Single Phase Transformer

Equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency.

## Three-phase Transformers

Connections, vector groups, parallel operation.

## Auto-transformer

Principles and applications.

## DC Machines

Separately excited, series and shunt, motoring and generating mode of operation and their characteristics, speed control of DC motors.

## Three-phase Induction Machines

Principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control.

## Single-phase Induction Motors

Operating principle.

## Synchronous Machines

Cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors.

## Losses and Efficiency

Types of losses and efficiency calculations of electric machines.

# Section 6: Power Systems

Basic concepts of electrical power generation, ac and dc transmission concepts, Models and performance of transmission lines and cables, Economic Load Dispatch (with and without considering transmission losses), Series and shunt compensation, Electric field distribution and insulators, Distribution systems, Per-unit quantities, Bus admittance matrix, Gauss- Seidel 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, directional and distance protection; Circuit breakers, System stability concepts, Equal area criterion.