**GATE Electronics and Communications Syllabus:**

Section 1: Engineering Mathematics

Linear Algebra:
Vector space, basis, linear dependence and independence, matrix algebra,
eigenvalues and eigen
vectors, rank, solution of linear equations – existence and uniqueness.

Calculus: Mean value theorems, theorems of integral calculus, evaluation
of definite and improper integrals, partial derivatives, maxima and minima, multiple
integrals, line, surface and volume integrals, Taylor series.

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Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.
Vector Analysis: Vectors in plane and space, vector operations, gradient,
divergence and curl, Gauss's, Green's and Stoke's theorems.

Complex Analysis:
Analytic functions, Cauchy's integral theorem, Cauchy's integral formula;
Taylor's and Laurent's
series, residue theorem.

Numerical Methods: Solution of nonlinear equations, single and multi-step methods
for differential equations, convergence criteria.

Probability and Statistics: Mean, median, mode and standard deviation; combinatorial
probability, probability
distribution functions - binomial, Poisson, exponential and normal; Joint and
conditional probability; Correlation and regression analysis.

Section 2: Networks, Signals and Systems

Network 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; Time domain analysis of simple linear circuits; Solution of network
equations using Laplace transform; Frequency domain analysis of RLC circuits;
Linear 2‐port network parameters: driving point and
transfer functions; State equations for networks.

Continuous-time signals: Fourier series and
Fourier transform representations, sampling theorem and

applications; Discrete-time signals: discrete-time Fourier
transform (DTFT), DFT, FFT, Z-transform, interpolation of discrete-time
signals; LTI systems: definition and properties, causality, stability, impulse
response, convolution, poles and zeros, parallel and cascade structure,
frequency response, group delay, phase delay, digital filter design techniques.

Section 3: Electronic Devices

Energy bands in intrinsic and extrinsic silicon; Carrier
transport: diffusion current, drift current, mobility and resistivity;
Generation and recombination of carriers; Poisson and continuity equations; P-N
junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photo diode and solar
cell; Integrated circuit fabrication process: oxidation, diffusion, ion
implantation, photolithography and twin-tub CMOS process.

Section 4: Analog Circuits

Small
signal equivalent circuits of diodes, BJTs and MOSFETs; Simple diode circuits:
clipping, clamping

and
rectifiers; Single-stage BJT and MOSFET amplifiers: biasing, bias stability,
mid-frequency small

signal analysis and frequency response; BJT and MOSFET
amplifiers: multi-stage, differential, feedback, power and operational; Simple
op-amp circuits; Active filters; Sinusoidal oscillators: criterion for
oscillation, single-transistor and op- amp configurations; Function generators,
wave-shaping circuits and 555 timers; Voltage reference circuits; Power
supplies: ripple removal and regulation.

Section 5: Digital Circuits

Number systems; Combinatorial circuits: Boolean algebra,
minimization of functions using Boolean identities and Karnaugh map, logic
gates and their static CMOS implementations, arithmetic circuits, code
converters, multiplexers, decoders and PLAs; Sequential circuits: latches and flip‐flops,
counters, shift‐registers and finite state
machines; Data converters: sample and hold circuits, ADCs and DACs;
Semiconductor memories: ROM, SRAM, DRAM; 8-bit microprocessor (8085):
architecture, programming, memory and I/O interfacing.

Section 6: Control Systems

Basic control system components; Feedback principle; Transfer
function; Block diagram representation;

Signal flow graph; Transient and steady-state analysis of LTI
systems; Frequency response; Routh-

Hurwitz
and Nyquist stability criteria; Bode and root-locus plots; Lag, lead and
lag-lead compensation;

State variable model and solution of state equation of LTI
systems.

Section 7: Communications

Random processes: autocorrelation and power spectral
density, properties of white noise, filtering of random signals through LTI
systems; Analog communications: amplitude modulation and demodulation, angle
modulation and demodulation, spectra of AM and FM, superheterodyne receivers,
circuits for analog communications; Information theory: entropy, mutual
information and channel capacity theorem; Digital communications: PCM, DPCM,
digital modulation schemes, amplitude, phase and frequency shift keying (ASK,
PSK, FSK), QAM, MAP and ML decoding, matched filter receiver, calculation of
bandwidth, SNR and BER for digital modulation; Fundamentals of error
correction, Hamming codes; Timing and frequency synchronization, inter-symbol
interference and its mitigation; Basics of TDMA, FDMA and CDMA.

Section 8:
Electromagnetics

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