Gate 2012 Electronics and Communication Engineering
Syllabus
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 regr ession 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.
HELLOSIR.CO.IN
Page 1
GATE 2012 SYLLABUS, PAPERS, BOOKS, NOTES@
HELLOSIR.CO.IN
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, progr amming, 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 fr equency 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 hardwar e, 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.
Syllabus
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 regr ession 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.
HELLOSIR.CO.IN
Page 1
GATE 2012 SYLLABUS, PAPERS, BOOKS, NOTES@
HELLOSIR.CO.IN
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, progr amming, 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 fr equency 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 hardwar e, 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.
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