In this paper, we develop an analytical method to deal with the timing performance in an optical clock extraction circuit based on stimulated Brillouin scattering (SBS). Three kinds of SBS active filters are considered and their frequency-transfer functions are obtained under the assumption that pump depletion caused by SBS is negligible. When pump depletion is taken into account, an SBS active filter acts as a nonlinear filter. To investigate the timing performance at this situation, we introduce the concept of"dynamic frequency-transfer function"to describe its frequency-response property for a fixed-signal light and pump light. Using the obtained"frequency-transfer function,"we give analytical expressions for both root-mean-square (rms) phase jitter and rms amplitude jitter of the extracted optical clock,in which we have taken the impacts of SBS gain, pump light linewidth, optical pulse chirp, and pump detuning into account. Finally, a detailed numerical investigation on the timing performance for the three active filters is presented.
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