A Semi-Empirical Approach to the PLL Threshold

This correspondence considers the response of the PLL near threshold to an input consisting of a modulated carrier and white, Gaussian noise. For high input signal-to-noise power ratios ??, the output noise power is Gaussian with a parabolic spectrum. As ?? is decreased, the PLL tends to lose lock which gives rise to impulses or ??spikes?? in the output with a resulting white power spectrum. The additional output noise due to these ??spikes?? causes a threshold in the output signal-to-noise ratio. Unfortunately the loss of lock rate in the PLL depends on the modulation as well as the noise power. A semiempirical approximate expression for the loss of lock rate as a function of the noise and sinusoidal frequency modulation is presented and is used to determine the optimum design procedure for PLL´s to demodulate FM signals of varying modulation indexes, ??.