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.

Phase noise in a phase-locked loop is originated from reference oscillator, phase detector, loop filter, voltage controlled oscillator and frequency divider which make the system unstable by generating high phase noise at the output spectrum. In this work, a mathematical linear phase noise model is therefore developed to investigate the effect of reference noise, phase detector noise, voltage controlled oscillator noise, frequency divider noise and specifically the loop filter noise. For this purpose, the conventional active or passive low pass filter of the phase locked loop is replaced by a proportional-integral-derivative controller during acquisition. The noise problem of each component is formulated as a transfer function derived from linear analysis of the proposed mathematical noise model. The simulation results show that the effect of noise attenuation of voltage controlled oscillator is -40dB/decade while the noise attenuation of the reference noise, phase detector noise, proportional integral derivative controller noise and frequency divider noise are approximately -20dB/decade each. The 6.21GHz proposed proportional-integral-derivative controlled phase-locked loop is also highly stable with fast switching speed of 0.238nS at damping factor of 0.625 and phase margin of 92° for minimum phase noise.

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