SYLLABI FOR THE WRITTEN TEST

Transcription

1 G u w ahat i, A ssa m, I ND IA PI N PHONE: FAX: D epa rt m en t o f E l ec tr on i c s & E l ec tri ca l Eng i nee ri n g IIT GUWAHATI SYLLABI FOR THE WRITTEN TEST Communication Engineering 1. Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations existence and uniqueness. 2. Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis 3. Signals and Systems: Continuous-time signals: Fourier series and Fourier transform representations, sampling theorem and applications; Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time signals; LTI systems:definition and properties, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, frequency response, group delay, phase delay, digital filter design techniques. 4. Communications: Random processes: autocorrelation and power spectral density, properties of white noise, filtering of random signals through LTI systems; Analog communications: amplitude modulation and demodulation, angle modulation and demodulation, spectra of AM and FM, superheterodyne receivers, circuits for analog communications; 5. Information theory: entropy, mutual information and channel capacity theorem; 6. Digital communications: PCM, DPCM, digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of bandwidth, SNR and BER for digital modulation; Fundamentals of error correction, Hamming codes; Timing and frequency synchronization, inter-symbol interference and its mitigation; Basics of TDMA, FDMA and CDMA.

2 Control Engineering 1. Control Systems - Modeling of physical systems; time and frequency response of first and second order systems; control system characteristics; stability analysis: Routh-Hurwitz test, relative stability, root locus, Bode and Nyquist plots; controller types: lag, lead, lag-lead, PID and variants of PID; controller design based on root-locus and frequency response plots; modern design techniques:canonical state-variable models, equivalence between frequency andtime-domain representations, diagonalisation 2. Linear Algebra - vector spaces, linear independence, bases and dimension, linear maps and matrices, eigenvalues, invariant subspaces, inner products, norms, orthonormal bases etc. 3. Linear Systems Theory -state variable modeling of linear dynamical systems; transfer function matrices; Stability theory: Lyapunov theorems; controllability and observability.

3 Power Engineering Section A: Technical Comprehension Section B: 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. Section C: Electrical Engineering Electric Circuits: 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.

4 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. Electrical Machines: Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency; Three phase transformers: connections, parallel operation; Auto transformer, Electromechanical 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 Systems: 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, Gauss Seidel and Newton-Raphson load flow methods, Voltage and Frequency control, Power factor correction, Symmetrical components, Symmetrical and unsymmetrical fault analysis, Principles of overcurrent, differential and distance protection; Circuit breakers, System stability concepts, Equal area criterion. Power Electronics: 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. Combinational and Sequential logic circuits

5 RF and Photonics 1. Quantitative aptitude and logical reasoning 2. Engineering Mathematics Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations existence and uniqueness. Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series. Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems. Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems. Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem. Numerical Methods: Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria. Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis. 3. Devices Energy bands in intrinsic and extrinsic silicon; Carrier transport: diffusion current, drift current, mobility and resistivity; Generation and recombination of carriers; Poisson and continuity equations; P-N junction, MOSFET; LED, Photo detectors; Lasers; Solar cell; Light propagation in optical fibres 4. Electromagnetics Electrostatics; Maxwell s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth; Transmission lines; Waveguides: modes, boundary conditions, cut-off frequencies, dispersion relations; Basics of antennas, Total internal reflection; VSWR; Snell s law

6 Signal Processing English - English grammar, sentence completion, verbal analogies, word groups etc. Mathematics - Matrix Algebra; Eigen values and Eigen vectors; Conditional Probability; Random variables; discrete and continuous distributions; Poisson, Normal and Binomial distributions; Measures of central tendency and deviation; correlation and regression analysis. Signal Processing - Classification of Signals and Systems; Tests of Linearity, Causality, Stability, Time/Shift Invariance; Convolution Theorem; Fourier Series and Transform for discrete and continuous time signals; Laplace transform; Z-Transform; Digital filters: Construction of lowpass, bandpass and highpass filters by pole-zero positioning; All pass filters; Notch and Comb filters; Linear phase FIR filters and their time/frequency representations.

7 VLSI The GATE Syllabus for the following topics 1. Engineering Mathematics 2. Network Theory 3. Signals and Systems + Control Systems 4. Semiconductor Devices 5. Digital Electronics 6. Analog Electronics