Gate
2018 Syllabus for Electronics and Communication Engineering (EC)
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.
Electronics
and Communication Engineering
Networks:
Network graphs: matrices associated with graphs; incidence, fundamental cut set
and fundamental circuit matrices. Solution methods: nodal and mesh analysis.
Network theorems: superposition, Thevenin and Norton's maximum power transfer,
Wye-Delta transformation. Steady state sinusoidal analysis using phasors.
Linear constant coefficient differential equations; time domain analysis of
simple RLC circuits, Solution of network equations using Laplace transform:
frequency domain analysis of RLC circuits. 2-port network parameters: driving
point and transfer functions. State equations for networks.
Electronic
Devices: Energy bands in silicon, intrinsic and extrinsic
silicon. Carrier transport in silicon: diffusion current, drift current,
mobility, and resistivity. Generation and recombination of carriers. p-n
junction diode, Zener diode, tunnel diode, BJT, JFET, MOS capacitor, MOSFET,
LED, p-I-n and avalanche photo diode, Basics of LASERs. Device technology:
integrated circuits fabrication process, oxidation, diffusion, ion
implantation, photolithography, n-tub, p-tub and twin-tub CMOS process.
Analog
Circuits: Small Signal Equivalent circuits of diodes, BJTs,
MOSFETs and analog CMOS. Simple diode circuits, clipping, clamping, rectifier.
Biasing and bias stability of transistor and FET amplifiers. Amplifiers:
single-and multi-stage, differential and operational, feedback, and power.
Frequency response of amplifiers. Simple op-amp circuits. Filters. Sinusoidal
oscillators; criterion for oscillation; single-transistor and op-amp
configurations. Function generators and wave-shaping circuits, 555 Timers.
Power supplies.
Digital
circuits: Boolean algebra, minimization of Boolean functions;
logic gates; digital IC families (DTL, TTL, ECL, MOS, CMOS). Combinatorial
circuits: arithmetic circuits, code converters, multiplexers, decoders, PROMs
and PLAs. Sequential circuits: latches and flip-flops, counters and
shift-registers. Sample and hold circuits, ADCs, DACs. Semiconductor memories.
Microprocessor(8085): architecture, programming, memory and I/O interfacing.
Signals
and Systems: Definitions and properties of Laplace
transform, continuous-time and discrete-time Fourier series, continuous-time
and discrete-time Fourier Transform, DFT and FFT, z-transform. Sampling
theorem. Linear Time-Invariant (LTI) Systems: definitions and properties;
causality, stability, impulse response, convolution, poles and zeros, parallel
and cascade structure, frequency response, group delay, phase delay. Signal
transmission through LTI systems.
Control
Systems: Basic control system components; block diagrammatic
description, reduction of block diagrams. Open loop and closed loop (feedback)
systems and stability analysis of these systems. Signal flow graphs and their
use in determining transfer functions of systems; transient and steady state
analysis of LTI control systems and frequency response. Tools and techniques
for LTI control system analysis: root loci, Routh-Hurwitz criterion, Bode and
Nyquist plots. Control system compensators: elements of lead and lag compensation,
elements of Proportional-Integral-Derivative (PID) control. State variable
representation and solution of state equation of LTI control systems.
Communications:
Random
signals and noise: probability, random variables, probability density function,
autocorrelation, power spectral density. Analog communication systems:
amplitude and angle modulation and demodulation systems, spectral analysis of
these operations, superheterodyne receivers; elements of hardware, realizations
of analog communication systems; signal-to-noise ratio (SNR) calculations for
amplitude modulation (AM) and frequency modulation (FM) for low noise
conditions. Fundamentals of information theory and channel capacity theorem.
Digital communication systems: pulse code modulation (PCM), differential pulse
code modulation (DPCM), digital modulation schemes: amplitude, phase and
frequency shift keying schemes (ASK, PSK, FSK), matched filter receivers,
bandwidth consideration and probability of error calculations for these
schemes. Basics of TDMA, FDMA and CDMA and GSM.
Electromagnetics:
Elements of vector calculus: divergence and curl; Gauss' and Stokes' theorems,
Maxwell's equations: differential and integral forms. Wave equation, Poynting
vector. Plane waves: propagation through various media; reflection and
refraction; phase and group velocity; skin depth. Transmission lines:
characteristic impedance; impedance transformation; Smith chart; impedance
matching; S parameters, pulse excitation. Waveguides: modes in rectangular
waveguides; boundary conditions; cut-off frequencies; dispersion relations.
Basics of propagation in dielectric waveguide and optical fibers. Basics of
Antennas: Dipole antennas; radiation pattern; antenna gain.
No comments:
Post a Comment