The Effects of Bandpass Limiters on n-Phase Tracking Systems

The combination of a bandpass limiter and an nthpower tracking loop is considered. It is shown that the performance of the combination does not depend on the form of the nonlinear function used to create the nthharmonic signal as long as some energy in that zone is produced. Furthermore, the order in which the limiter and n power nonlinearity occur is unimportant so that the results apply equally well to the n -phase Costas type of implementations of the nthpower loops. Closed form expressions for the signal suppression factors are obtained, and it is shown that the coherent and noncoherent SNR's out of the nthpower-limiter combination can be expressed in terms of two of these suppression factors. This latter point enables one to estimate the loop SNR of an nthpower-limited phase locked loop by simply calculating the suppression factors for nthand ( (2n)^{th} ) power loops. Finally, n thpower phase locked loops without limiters are compared with similar loops with limiters where it is shown that the presence of the limiter can actually enhance the output SNR at moderate to large values of input SNR.