GATE Syllabus 2018 for ECE

1	Engineering Mathematics-Linear Algebra, Calculus,Differential Equations,Vector Analysis,Complex Analysis,Numerical Methods,Probability and Statistics
2	Networks, Signals and Systems-Network solution methods,Continuous-time signals
3	Electronic Devices Energy bands in intrinsic and extrinsic silicon; Carrier transport 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 etc.

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 etc. Recommended
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 etc.
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 etc.
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 communication etc.

8-Electromagnetics

Electrostatics; Maxwell’s equations: differential and integral forms and their interpretation, boundary conditions, wave equation, Poynting vector; Plane waves and properties: reflection and refraction, polarization, phase and group velocity, propagation through various media, skin depth; Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation etc.

You can consider below given syllabus -
Section 1: Engineering Mathematics
Linear Algebra: Vector space, basis, linear dependence and independence, matrix
algebra, eigen values 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.
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 Nortons, maximum power transfer; WyeDelta 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 2port 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.

To know the complete syllabus, you can go through the below provided article -

Gate Syllabus

Hope this helps!!!!

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