🎓 GATE 2025 Syllabus – Electronics & Communication Engineering (EC)

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🧮 Section 1: Engineering Mathematics

Linear Algebra: Vector space, basis, linear dependence/independence, matrix algebra, eigenvalues & eigenvectors, rank, linear equations.
Calculus: Mean value theorems, definite/improper integrals, partial derivatives, maxima/minima, multiple/line/surface/volume integrals, Taylor series.
Differential Equations: First/higher-order, Cauchy’s & Euler’s equations, variation of parameters, partial DEs, initial/boundary value problems.
Vector Analysis: Plane/space vectors, gradient, divergence, curl, Gauss, Green, Stokes’ theorems.
Complex Analysis: Analytic functions, Cauchy theorems/formula, convergence, Taylor/Laurent/residue theorems.
Probability & Statistics: Mean, median, mode, distributions (binomial, Poisson, exponential, normal), combinatorial, joint/conditional probability.

🔌 Section 2: Networks, Signals & Systems

Circuit Analysis: Node/mesh analysis, Thevenin/Norton, reciprocity, phasors, complex power, max power transfer, Laplace domain.
2-Port Networks, wye-delta transformation.
Signals: Continuous/discrete-time, Fourier/DTFT/DFT/z-transform, LTI properties, sampling, causality, impulse response, poles, frequency/group/phase delay.

🧪 Section 3: Electronic Devices

Energy Bands, Semiconductors: Intrinsic/extrinsic, carrier concentration, band-gaps.
Carrier Transport: Drift/diffusion, mobility/resistivity, recombination, Poisson and continuity equations.
Devices: P-N junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, photodiode, solar cell.

🎚️ Section 4: Analog Circuits

Diode Circuits: Clipping, clamping, rectification.
Amplifiers: BJT/MOSFET biasing, AC coupling, small-signal, frequency response.
Op-amps: Differentiators, integrators, summers, filters, Schmitt triggers, oscillators, current mirrors, differential amplifiers.

💾 Section 5: Digital Circuits

Number Systems: Binary, integer, floating-point.
Combinatorial Circuits: Boolean algebra/identities, K-map, logic gates (CMOS), arithmetic, converters, multiplexers, decoders.
Sequential Circuits: Latches/flip-flops, counters, shift-registers, FSMs, timing/delays.
Data Converters: S/H, ADCs, DACs.
Memories: ROM, SRAM, DRAM.
Computer Organization: Machine instructions, ALU, pipelining, datapath/control.

🔁 Section 6: Control Systems

Components, feedback, transfer function, block diagrams, signal flow.
Transient/steady-state analysis, frequency response, Routh-Hurwitz, Nyquist, Bode, root-locus, compensation (lag, lead, lag-lead), state space models.

📡 Section 7: Communications

Random Processes: Correlation, PSD, noise properties, LTI filtering.
Analog: AM/FM modulation/demodulation, spectra, superheterodyne.
Information Theory: Entropy, mutual info, channel capacity theorem.
Digital: PCM, DPCM, ASK/PSK/FSK/QAM, ISI, MAP/ML, SNR, BER, error correction (Hamming, CRC).

⚡ Section 8: Electromagnetics

Maxwell’s Equations: Diff/integral forms, boundary conditions, wave equation, Poynting vector.
Plane Waves: Reflection, refraction, polarization, velocity, skin depth.
Transmission Lines: Equations, impedance, matching, S-parameters, Smith chart.
Waveguides, Optical Fibers, Antennas: Rectangular/circular, light propagation, dipole/monopole, arrays.

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