Syllabus for GATE ECE Exam

1. Engineering Mathematics
- Linear Algebra: Vector space, matrices, determinants, systems of linear equations, eigenvalues and eigenvectors.
- Calculus: Limit, continuity, and differentiability, partial derivatives, maxima and minima, sequences and series, convergence and divergence, Fourier series.
- Differential Equations: First-order equations, linear second-order differential equations with constant coefficients, partial differential equations, Fourier series, Laplace transforms.
- Probability and Statistics: Mean, median, mode, standard deviation, probability distributions, random variables, discrete and continuous distributions, hypothesis testing.

2. Networks, Signals, and Systems
- Network graphs: matrices associated with graphs; incidence, fundamental cut set and fundamental circuit matrices.
- Solution methods: nodal and mesh analysis.
- Signal representation: Fourier series, Fourier transform, Laplace transform.
- System properties: causality, stability, impulse response, convolution, poles and zeros, transfer function.
- Continuous-time signals: Fourier series and Fourier transform representations, sampling theorem, Z-transform.
- Discrete-time signals: discrete-time Fourier transform (DTFT), DFT, FFT, Z-transform.

3. Electronic Devices
- Energy bands in intrinsic and extrinsic silicon.
- Carrier transport: diffusion current, drift current, mobility, and resistivity.
- Junctions: PN junction, Zener diode, BJT, MOS capacitor, MOSFET, LED, and photodiode.
- Basics of integrated circuits: fabrication, packaging, and testing.

4. Analog Circuits
- Equivalent circuits: single-stage amplifiers, differential amplifiers.
- Feedback amplifiers: gain and phase margins, stability, oscillators.
- Operational amplifiers: characteristics and applications.
- Simple active filters, VCOs, and timers.
- Voltage reference circuits.
- Power supplies: ripple removal and regulation.

5. Digital Circuits
- Boolean algebra.
- Combinational and sequential circuits.
- Number representations and computer arithmetic (fixed and floating point).
- Memory organization: ROM, SRAM, DRAM.
- Microprocessor architecture: instruction set, memory, and I/O interfaces.

6. Control Systems
- Basic control system components.
- Feedback principle.
- Transfer function.
- Block diagrams.
- Signal flow graphs.
- Time response: steady-state and transient analysis.
- Routh-Hurwitz stability criteria.
- Bode and Nyquist plots.
- Root loci.
- Lag, lead, and lag-lead compensation.
- State variable model and solution of state equation of LTI systems.

7. Communications
- 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.
- Digital communication systems: pulse code modulation (PCM), differential pulse code modulation (DPCM), digital modulation schemes, amplitude, and frequency shift keying, phase and quadrature amplitude modulation.

8. Electromagnetics
- Electrostatics and magnetostatics.
- Maxwell's equations: wave equation, Poynting vector.
- Plane waves and properties: reflection and refraction, polarization, phase and group velocity.
- Transmission lines: equations, characteristic impedance, impedance