### GATE 2015 Electronics & Communication Engineering Syllabus:

The following given below is the GATE 2015 Electronics & Communication Engineering Syllabus

### (a)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 equation with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equation, 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 and mode and standard deviation, Random Variables, Discrete and continous 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.

### (b)Electronics and Communication Engineering:

**Networks:**

Networks 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 of simple RLC circuits, Solution of network equation using Laplace transform: frequency domain analysis of RLC circuits. 2 port network parameters: driving point and transfer functions. State equation for network

**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 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 suppliers.

**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, ADC AND DACs. Semiconductors memories. Microprocessor (8085): architecture, programming, memory and I/O interfacing

**Signals and systems:**

Definitions and properties of Laplace transform, continous time and discrete time Fourier series, continous 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 communications 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 system: 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, bandwith 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 theorem, Maxwell’s equation: 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 and 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 fibres. Basics of propagation in dielectric waveguide and optical fibres. Basics of Antennas: Dipole antennas; radiation pattern; antenna gain.