## GATE Syllabus for 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.