Optimum Filters for Second- and Third-Order Phase-Locked Loops by an Error-Function Criterion

The advantages of a third-order phase-locked loop for FM television is considered here. The bandwidth is maintained small and since the operation is generally at frequencies small compared to the bandwidth, the criterion is to keep error as small as possible in this frequency range. A study is made by comparing second- and third-order phase-locked loops designed from Wiener filtering theory, as advanced by Jaffe and Rechtin [1]; considerable improvement in error is evident using a third-order phase-locked loop for frequencies up to about one-twentieth of the bandwidth. To improve the error function still further, a new error-function criterion is established whereby the error at the lower frequencies of interest is minimized. Such a minimum is obtained for both second- and third-order phase-locked loops. Transfer function behavior, transient response, and root locus plots of all these cases are given to emphasize the advantages of this new design. Error is reduced up to six decibels with no degradation of transient response, overshoot, etc. It is shown that the bandwidth can be reduced without increasing the error if the filter designed by this new criterion is used.