ELECTRONICS AND COMMUNICATION
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 & COMMUNICATION
ENGINEERING
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, 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, LASERs.
Device technology: integrated circuits
fabrication process, oxidation, diffusion,
ion implantation, photolithography, n-tub,
p-tub and twin-tub CMOS process.
Analog Circuits: Equivalent circuits (large
and small-signal) of diodes, BJTs, JFETs,
and MOSFETs. Simple diode circuits,
clipping, clamping, rectifier. Biasing and
bias stability of transistor and FET
amplifiers. Amplifiers: single-and
multi-stage, differential, operational,
feedback and power. Analysis of amplifiers;
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. Power supplies.
Digital circuits: Boolean algebra,
minimization of Boolean functions; logic
gates digital IC families (DTL, TTL, ECL,
MOS, CMOS). Combinational circuits:
arithmetic circuits, code converters,
multiplexers and decoders. 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, z-transform. Sampling
theorems. Linear Time-Invariant (LTI)
Systems: definitions and properties;
casuality, stability, impulse response,
convolution, poles and zeros frequency
response, group delay, phase delay. Signal
transmission through LTI systems. Random
signals and noise: probability, random
variables, probability density function,
autocorrelation, power spectral density.
Controls 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: 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. Digital communication
systems: pulse code modulation (PCM),
differential pulse code modulation (DPCM),
delta modulation (DM); digital modulation
schemes-amplitude, phase and frequency shift
keying schemes (ASK, PSK, FSK), matched
filter receivers, bandwith consideration and
probability of error calculations for these
schemes.
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; pulse excitation. Waveguides:
modes in rectangular waveguides; boundary
conditions; cut-off frequencies; dispersion
relations. Antennas: Dipole antennas;
antenna arrays; radiation pattern;
reciprocity theorem, antenna gain.
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