Investigations on optimal choice of Gamma parameter for Fast-locking PID controlled Phaselocked loop

In this work, we developed a mathematical model of proportional-integral-derivative controlled phase-locked loop to study the impact of gamma-optimization parameter on lock-time, phase margin and loop bandwidth of the system through behavioural simulation of the respective transfer functions in s-domain using MATLAB. Due to the addition of proportional-integral-derivative controller instead of traditional active or passive low-pass filter, it has been observed that increasing the gamma value decreases peaking and the flatness of the loop filter response. The lock-time of the proposed system tends to be faster with increasing gamma from 1.5213 to 10.3463 providing more system stability along with optimal phase margin of 38. 5degree to 77. 4degree and high loop bandwidth of 0.2641GHz to 0. 3705GHz. Simulation results shows that gamma value of 10.3463 gives the fastest lock-time of 1.7181nS with a maximum achievable loop bandwidth of 0. 3705GHz at phase margin of 77. 4degree. The proposed PID controlled system improves the switching speed up to 99.99%.