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**GATE Syllabus for Electronics and Communication Engineering**

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Gate 2019 ece Syllabus |

**Engineering Mathematics**

**Linear Algebra-**Vector space, matrix algebra operation, calculation of eigenvalues and eigenvectors, rank, solution of linear equations – consistency or not

**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 a variety 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 variance, and standard deviation, combinatorial probability

**Probability distribution functions –**Binomial, and Poisson Equation, exponential and normal, Joint and conditional probability, Correlation and regression analysis.

**Networks Theory**

Nodal and mesh analysis, Network theorems- superposition, Thevenin and Norton’s, maximum power transfer, Wye‐Delta (Star- Delta) transformation, Steady state sinusoidal analysis, Time domain analysis of simple linear circuits, Solution of LTI System/equations using Laplace transform, Frequency domain analysis of RLC (Series and Parallel) circuits.

Two port network parameters- driving point and transfer functions, State equations for networks.

**Signal and System**

Linear, causality, stability, impulse response, convolution, poles and zeros, parallel and cascade structure, Fourier series and Fourier transform representations, sampling theorem, and applications.

Discrete-Time signals - discrete-time Fourier transform, DFT(Discrete Fourier transform), FFT, Z-transform.

LTI systems- definition and properties, frequency response, group delay, phase delay, digital filter design techniques.

**Electronic Devices Circuits(EDC)**

Energy bands in intrinsic and extrinsic silicon, Carrier transport- diffusion current, drift current, mobility and resistivity, Diffusion constant, Generation and recombination of carriers, Poisson and continuity equations.

BJT (Bipolar Junction Transistor), MOS capacitor & Application, P-N junction Transistor, Zener diode, MOSFET, LED(Light Emitting Diode), a photodiode and solar cell.

The fabrication process of the Integrated circuit - oxidation, diffusion, ion implantation, photolithography and twin-tub CMOS process.

**Analog Electronics**

Small signal equivalent circuits of diodes, BJT(Bipolar Junction Transistor), and MOSFETs, Simple diode circuits- clipping, clamping, and rectifiers.

Single-stage BJT and MOSFET amplifiers- all biasing, bias stability, mid-frequency small signal analysis and frequency response.

BJT and MOSFET amplifiers- multi-stage, differential, feedback, power and operational, Operational Amplifier circuits, Active filters.

Sinusoidal oscillators- criterion for oscillation, RC Phase Shift, using transistor and FET, Wein bridge, Clapp’s, Colpitts oscillator, single-transistor and op-amp configurations,

Function generators, wave-shaping circuits and 555 timers, Voltage reference circuits, Power supplies- ripple removal and regulation.

**Digital Electronics**

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 all flip‐flops, counters, shift‐registers and finite state machines

Data converters- sample and hold circuits, ADC (Analog To Digital Converter) and DAC (Digital To Alanog Converter), Semiconductor memories- ROM(Read Only Memory), SRAM (Static Read Access Memory), DRAM(Dynamic read Access Memory)

Microprocessor (8085- 8 Bit), - Architecture,Instruction, programming, memory and I/O (Input-output) interfacing.

**Control Systems**

Basic control system components, Feedback principle, Transfer function, Block diagram representation, Signal flow graph.

Transient and steady-state analysis of LTI systems- First and Second Order System

Frequency response- Routh-Hurwitz criterion, Polar Plot analysis, and Nyquist stability criteria, Bode plot and root-locus plots, Calculation of Gain and Phase Margin, Lag, lead and lag-lead compensation. P, PI, PD, and PID

State variable Analysis- State model solution of LTI systems, State model to transfer function, Controllability, and Observability.

**Analog Communication System**

Amplitude modulation and demodulation For Sinusoidal, Rectangular and Triangular Signal, Angle modulation(Frequency and Phase Modulation) and demodulation, AM and FM Spectrum Analysis, superheterodyne receivers.

Information theory- Entropy, mutual information and channel capacity theorem.

**Digital communications**

PCM (Pulse Code Modulation), DPCM(Delta Pulse Code Modulation), digital modulation schemes, amplitude, phase and frequency shift keying (ASK, PSK, FSK), QAM, MAP and ML decoding, matched filter receiver.

Bandwidth Calculation, SNR(Signal to Noise ratio) and BER/Probability error for digital modulation, Fundamentals of error correction, Hamming codes, Timing and frequency synchronization, inter-symbol interference.

Basics of TDMA, FDMA, and CDMA(Code-division Multiple access).

**Communications Random processes**

Autocorrelation and power spectral density, properties of white noise, filtering of random signals through Linear time-invariant systems.

**Electromagnetics**

Electrostatics, Maxwell’s equations- differential and integral forms and their interpretation, boundary conditions, all wave equation, Poynting theorem & vector.

Plane waves- Reflection and refraction, polarization, phase and group velocity, propagation through various media, calculation of skin depth.

Transmission lines- Equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart.

Antennas- Types of Antenna, radiation pattern, gain, and directivity, return loss, antenna arrays Concept.

Basics of radar, Light propagation in optical fibers.

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GATE Syllabus for ECE | Gate Syllabus for ECE 2019
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February 12, 2018
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