Analysis and Simulation of the Impact of Gamma parameter and Phase Noise on Phase-Locked Loop with PID Controller

Abstract

In this work, detailed simulation and analysis of impact of gamma parameter and phase noise on the proportional-integral-derivative controlled phase-locked loop is carried out. The linear mathematical model for gamma parameter along with the phase noise model of the proposed system is developed. To improve the loop dynamics, a new type of loop filter is designed by considering a parallel combination of second order passive low pass filter and a proportional-integral-derivative controller in place of the traditional loop filter. The transfer function of gamma parameter as well as noise sources of each component of the phase-locked loop is derived from the proposed model in s-domain. Simulation is carried out on MATLAB to study how gamma parameter impacts on system response as well as on the phase noise contribution to the proposed system. The impact of gamma parameter on lock time, phase margin and loop bandwidth is also studied for gamma parameter less than one and greater than one. Finally, a comparison is done between second order low pass filter, proportional-integral-derivative controller and the newly designed loop filter. Simulation results shows that the proposed system with newly designed loop filter improves the system stability with fast switching speed and reduced the phase noise with gamma greater than one.

Basic Concepts of a Phase-Locked Loop Control System

“…as we know there is a relationship between phase and frequency q (t) = ∫w(t)dt, e o (t) is a error voltage input of VCO [15], as is shown in Figure 3 we have a linear equation Where w c is free running frequency.…”