A Computer Model of a Phase Lock Loop

A computer model is reported of a PLL (phase-lock loop), preceded by a bandpass filter, which is valid when the bandwidth of the bandpass filter is of the same order of magnitude as the natural frequency of the PLL. New results for the PLL natural frequency equal to the bandpass filter bandwidth are presented for a second order PLL operating with carrier plus noise as the input. However, it is shown that extensions to higher order loops, and to the case of a modulated carrier are straightforward. The new results presented give the cycle skipping rate of the PLL as a function of the input carrier to noise ratio when the PLL natural frequency is equal to the bandpass filter bandwidth. Preliminary results showing the variation of the output noise power and cycle skipping rates of the PLL as a function of the loop damping ratio for the PLL natural frequency equal to the bandpass filter bandwidth are also included.