The jitter generated by two different approaches to synchronization of an external timing source is analyzed. The two approaches are: the use of conventional stuffing and the use of a simpler frame sampling synchronizer. It is shown that these two approaches have the same jitter power density spectrum. The result is obtained using a new time domain method developed in the paper. Exact expressions for the jitter on the synchronized external timing source are obtained. Furthermore the effect of quantization in the conventional stuffing synchronizer on the jitter expressions obtained is also explored. Jitter generated by the frame sampling synchronizer is also analyzed using the time domain method which again produces an exact expression. In the case where certain parameters of the two approaches are related the location of spectral lines in their respective jitter spectra is shown to be identical. It is also shown that both approaches to synchronization introduce the so-called waiting-time jitter.