A QUANTITATIVE RESEARCH OF NONLINEAR BEHAVIOUR OF A SECOND-ORDER PHASE-LOCKED LOOP BY PERTURBATION METHOD

It is found that the linear frequency modulation is used on a voltage-controlled oseillator and a phase-locked loop to lock its starting-frequency phase for generating a coherent chirp signal. For a high-gain second-order loop, the loop parameters and the modulating frequency rate must be chosen to satisfy the condition, O 1, and then it is possible to realize the FM on the VCO, while the loop is not necessarily broken during FM pulse.In this paper, the PLL' s equation is transformed into a nearly linear differential equation and its asymptotic solution is given by perburbation metho. Thus, the quantitative relationships about the effects of the PLL on the LFM waveform are obtained. Finally, results of simulation by means of computer show good agreement with the theoretical analysis.