MATLAB Code Implementation of Phase-Locked Loop (PLL)

This repository contains a complete MATLAB implementation of a Phase-Locked Loop (PLL) system. The code models realistic scenarios including Gaussian noise interference, frequency offset, and phase offset conditions. The implementation demonstrates the PLL's convergence behavior with final frequency and phase tracking results visualized through convergence plots. The MATLAB code utilizes key signal processing functions including: - Phase detector implementation using multiplier or XOR gate logic - Loop filter design (proportional-integral controller) for error signal processing - Voltage-controlled oscillator (VCO) modeling with frequency adjustment capability - Noise injection using randn() function for Gaussian distribution simulation Each section contains detailed inline comments explaining the mathematical foundations and implementation approach, making it accessible for both beginners and experienced users. The code structure follows standard PLL components: reference signal generation, phase comparison, filtering, and oscillator control. The implementation demonstrates important PLL characteristics: - Lock-in range and pull-in range analysis - Noise robustness performance metrics - Convergence time optimization parameters - Frequency and phase error tracking algorithms This practical example serves as an educational resource for understanding PLL operation principles while providing a functional MATLAB implementation suitable for communication systems and signal processing applications.