Vector space, basis, linear dependence and independence, matrix algebra, eigen values and eigen vectors, rank, solution of linear equations – existence and uniqueness.
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.
Linear differential equations, Euler–Cauchy equation, Nonhomogeneous equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.
Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's theorem, Green's theorem, and Stokes’ theorem.
Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, sequences, series, convergence tests, Taylor series, Laurent series, residue theorem.
Mean, median, mode, standard deviation, combinatorial probability, probability distributions, binomial distribution, Poisson distribution, exponential distribution, normal distribution, joint and conditional probability, correlation and regression analysis.
Node and mesh analysis, superposition, Thevenin's theorem, Norton's theorem, reciprocity. Sinusoidal steady state analysis: phasors, complex power, maximum power transfer.
Time and frequency domain analysis of linear circuits: RL, RC and RLC circuits, solution of network equations using Laplace transform. Linear 2-port network parameters, wye-delta transformation.
Definition and properties, causality, stability, impulse response, convolution, poles and zeroes, frequency response, group delay, phase delay.
Fourier series, Fourier transform, Nyquist sampling theorem, sampling and reconstruction.
DTFT, DFT, z-transform, FIR filter design, IIR filter design.
Semiconductor Physics, Carrier Transport, PN Junction, MOS Devices & Optoelectronics
Formation of energy bands in solids
Energy bands in intrinsic semiconductors
Energy bands in extrinsic semiconductors
Equilibrium carrier concentration
Direct and indirect band-gap semiconductors
PN Junction Diode
Breakdown Characteristics
Bipolar Junction Transistor
MOS Capacitor & MOSFET
Light Emitting Diode
Optical Detection Device
Photovoltaic Energy Conversion
This section covers the complete fundamentals of analog electronic circuits including diode applications, transistor amplifiers, operational amplifiers, active filters, oscillators and compensation techniques frequently asked in GATE Electronics & Communication Engineering.
✔ High Weightage Topic
Focus on circuit analysis, transistor biasing, frequency response and operational amplifier applications.
Positive, negative and biased clipping circuits.
Positive and negative clamper circuits.
Half-wave and full-wave rectifier circuits.
Learn the fundamentals of digital electronics including number systems, combinational and sequential logic, semiconductor memories, data converters and computer organization.
Understand the principles of automatic control systems including system modelling, stability analysis, frequency response, controllers and state-space representation.
Explore the principles of communication engineering including random processes, analog and digital communication systems, information theory, modulation techniques, detection methods, and error control coding.
Study the fundamentals of electromagnetic fields, wave propagation, transmission lines, waveguides, optical communication and antenna systems used in modern electronic and communication engineering.