# (Syllabus) GATE Examination (EC - ELECTRONICS AND COMMUNICATION ENGINEERING )

**Syllabus
: ****GATE
Examination (National Level Entrance Exam****)**

**EC
- ELECTRONICS AND COMMUNICATION ENGINEERING**

**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.