An Analytical Model for a Proportional–Integral–Derivative Controlled Phase-Locked Loop for Communication Systems

We propose here an analytical model for proportional–integral–derivative controlled phase-locked loop for communication systems. The transfer function of the system has been derived and simulated to analyze the various aspects, e.g. settling time, phase margin, damping factor, overshoot, bandwidth and stability of the system. From the analysis of simulation results it is observed that the settling time of the system decreases exponentially with increasing phase margin and it increases exponentially with increasing damping factor. It is also observed that the settling time and percentage of overshoot of the system is inversely proportional to each other. The settling time is also decreased exponentially with the increase in bandwidth. The Bode plot and Root Locus analysis show that the proposed system is highly stable. The system provides a fastest settling time of up to 238.57 ps. The system can also improve the settling time by 99.9% over the conventional system with a maximum frequency of 6.21802 GHz, which is the novelty of the proposed work.