GATE 2013- Syllabus for Electronics and Communication Engineering(EC)
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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.
- Linear Algebra:
-
General Aptitude (GA)
- Verbal Ability
- English Grammar
- sentence completion,
- verbal Analogies
- word groups
- Instruction,
- critical reasoning and verbal deducion
- Verbal Ability
-
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.
- Networks:
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