GATE 2025 Syllabus for Electronics & Communication Engineering (ECE): PDF Download

Linear Algebra

Vector space | Basis | Linear Dependence and Independence | Matrix Algebra | Eigen Values and Eigen Vectors | Rank, Solution of Linear Equations - Existence and Uniqueness

Calculus

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

Differential Equations

First Order Equations (linear and non-linear) | Higher Order Linear Differential Equations | Cauchy’s and Euler’s Equations | Methods of Solution using variation of parameters | Complementary Function and Particular Integral | Partial Differential Equations | Variable Separable Method | Initial and Boundary Value Problems

Vector Analysis

Vector in plane and space | Vector operations | Gradient | Divergence and Curl, Gauss’s, Green’s and Stoke’s Theorems

Complex Analysis

Analytic functions | Cauchy’s Integral Theorem | Cauchy’s Integral Theorem | Sequences | Series | Convergence Tests | Taylor’s and Laurent series | Residue Theorem 

Probability and Statistics

Mean, Median, Mode, Standard Deviation, Combinatorial Probability | Probability Distributions | Binomial Distributions | Poisson Distribution | Exponential Distribution | Normal Distribution | Joint and Conditional Probability

Circuit Analysis

Node and Mesh Analysis | Superposition | Thevinin’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

Continuous Time Signals

Fourier Series and Fourier Transform | Sampling Theorem and Application

Discrete-Time Signals

DTFT | DFT | Z-Transform | Discrete-Time Processing of Continuous-Time Signals | LTI systems: Definitions and Properties | Casualty, Stability, Impulse Response, Convolution, Poles and Zeroes | Frequency Response | Group Delay | Phase Delay

Electronic devices

Energy bands in Intrinsic and Extrinsic semiconductors | Equilibrium Carrier Concentration | Direct and Indirect Band-Gap Semiconductors 

Carrier Transport

Diffusion Current | Drift Current | Mobility and Resistivity | Generation and Recombination of Carriers | Poisson and Continuity Equations | P-N Junction | Zener Diode | BJT | MOS Capacitor | MOSFET | LED | Photo Diode and Solar Cell

Diode Circuits

Clipping | Clamping | Rectifiers

BJT and MOSFET Amplifiers

Biasing | AC Coupling | Small Signal Analysis | Frequency Response | Current Mirrors and Differential Amplifiers

Op-Amp Circuits

Amplifiers | Summers | Differentiators | Integrators | Active Filters | Schmitt Triggers and Oscillators

Number Representations

Binary | Integer and Floating-Point Paper - Numbers | Combinatorial Circuits: Boolean Algebra, Minimization of Functions using Boolean Identities and Karnaugh Map | Logic Gates and their Static CMOS Implementations | Arithmetic Circuits | Code Convertors | Multiplexers and Decoders

Sequential Circuits

Latches and Flip Flops | Counters | Shift-Registers | Finite State Machines | Propagation Delay | Setup and Hold Time | Critical Path Delay

Data Convertors

Sample and Hold Circuits | ADCs and DACs

Semiconductor Memories

ROM | SRAM | DRAM

Computer Organization

Machine Instructions and Addressing Modes | ALU | Data-Path and Control Unit | Instruction Pipelining

Control Systems

Basic Control System Components | Feedback Principal | Transfer Function | Block Diagram Representation | Signal Flow Graph | Transient and Steady-State Analysis of LTI systems | Frequency Response | Routh -Hurwitz and Nyquist Stability Criteria | Bode and Root Locus Plots | Lag, Lead, and Lag-Lead Compensation | State Variable Model and Solution of State Equation of LTI systems

Random Processes

Auto Correlation and Power Spectral Density | Properties of White Noise | Filtering of Random Signals through LTI systems

Analog Communications

Amplitude Modulation and Demodulation | Angle Modulation and Demodulation | Spectra of AM and FM | Super Heterodyne Receivers

Information Theory

Entropy | Mutual Information and Channel Capacity Theorem

Digital Communications

PCM, DPCM, Digital Modulation Schemes (ASK, PSK, FSK, QAM) | Bandwidth | Inter-Symbol Interference | MAP, ML Detection | Matched Filter Receiver | SNR and BER | Fundamentals of Error Correction | Hamming Codes | CRC

Maxwell’s Equations

Differential and Integral Forms and Their Interpretation | Boundary Conditions | Wave Equations | Poynting Vector

Plane Waves and Properties

Reflection and Refraction | Polarization | Phase and Group Velocity | Propagation Through Various Media | Skin Depth

Transmission Lines

Equations | Characteristic Impedance | Impedance Matching | Impedance Transformation | S-Parameters | Smith Chart | Rectangular and Circular Waveguides | Light Propagation in Optical Fibers | Dipole and Monopole Antennas | Linear Antenna Arrays

Advanced Engineering Mathematics

Dr H.K Dass

Higher Engineering Mathematics

Dr BS Grewal

Quantitative Aptitude and Logical Reasoning

R.S Agarwal

Network Theory

Alexander Sadiku

Engineering Circuit Analysis

Hayt and Kammerly

Integrated Electronics

Jacob Millman and Christos C.Halkias

Semiconductor Devices

David Neaman

Linear ICs

Gaekwad

Pulse and Digital Electronics

Milliman and Taub

Fundamentals of Digital Electronics

Anand Kumar

Digital Logic and Computer Design

M. Morris Mano

Modern Control System

Katsuhiko Ogato

Modern Digital and Analog Communications Systems

BP Lathi

Antenna Theory

Balanis

GATE ECE 

R.K Kanodia