GATE SYLLABUS (ELECTRONICS AND COMMUNICATION ENGINEERING )

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
usingLaplace 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 ofLaplace
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.