ECE Gate Cheat Sheet by [deleted]

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.

GENERAL APTITU­DE(GA):
Verbal Ability: English grammar, sentence comple­tion, verbal analogies, word groups, instru­ctions, critical reasoning and verbal deduction.

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.