Modeling and Simulation of Second-order Phase-locked Loop for Studying the Transient Behavior during Frequency Acquisition and Tracking

The Phase-Locked Loop (PLL) system is used extensively in modern electronic systems such as modems, mobile communications, satellite receivers and television systems. This work presents a method for modeling and simulation of second-order PLL in time domain to study transient behavior during frequency acquisition and tracking. Here we utilize a basic PLL system that consist a multiplier, used as phase detector (PD), a passive loop filter (LF) and a voltage controlled oscillator (VCO). The method combines a circuit level modeling for the LF and mathematical modeling for VCO and the multiplier. For circuit level modeling, the LF is represented by its equivalent companion network model. Transient analysis method for linear dynamic networks is applied for simulating the model of the LF. The complete simulation program, written in Turbo C language, combines the circuit level modeling of LF with the mathematical modeling of multiplier and the VCO. The MATLAB program is used for graphical analysis of data to observe transient behavior of PLL system. The nonlinear cycle slip phenomena occurred during acquisition process is observed. The transient response at locked condition with reference to step change in input frequency and step change in input phase verifies the mathematical descriptions of the PLL system.