# Assume that the input to a perfect second-order PLL is an un modulated sinusoid plus band limited…

Assume that the input to a perfect second-order PLL is an un modulated sinusoid plus band limited AWGN. In other words, the PLL input is represented by

Also assume that the SNR at the loop input is large so that the phase jitter (error) is sufficiently small to justify use of the linear PLL model. Using the linear model derive an expression for the variance of the loop phase error due to noise in terms of the standard PLL parameters defined in Chapter 3. Show that the probability density function of the phase error is Gaussian and that the variance of the phase error is inversely proportional to the SNR at the loop input.

### Save your time - order a paper!

Get your paper written from scratch within the tight deadline. Our service is a reliable solution to all your troubles. Place an order on any task and we will take care of it. You won’t have to worry about the quality and deadlines

Order Paper NowSection 7.5