Linear phase-locked loop theory for cyclostationary input disturbances

A general expression is obtained for the linearized mean-square phase error incurred during clock synchronization in a phase-locked loop. The phase of an unmodulated sinusoid corrupted by an additive disturbance is described in terms of cyclostationary processes. Sidebands are noted to cause most errors in carrier modulated systems, creating errors in the carrier phase, or timing errors in baseband pulse amplitude modulation systems through pattern-dependent jitter. Comparisons of the derived linearized mean-square phase errors with those predicted by conventional linear phase-locked loop theory are presented. It is demonstrated that phase errors can be overestimated by substituting a stationary process with an equal power spectral density for the disturbance.