Jitter Man
Community Member
Offline
Am I? Or am I so sane that u just blew your mind?
Posts: 50
|
[quote author=McCorquodale link=1036525104/15#16 date=1057873899]Speaking of conversions, I have a simple observation. In the paper, "Predicting the Phase Noise and Jitter of PLL-Based Frequency Synthesizers," page 30, section 10.1, I am confused by the relationship between the PSD and the autocorrelation function. Specifically, they do not appear to be related correctly, unless I am overlooking something.
The PSD and the autocorrelation function should be Fourier transform pairs. Thus, by integrating the autocorrelation function in tau (i.e. t1 - t2), one should obtain the DSB PSD. Thus, integrating equation (64) in tau would yield "c." However, the SSB PSD given in equation (63) is "2c." Considering that this is an SSB PSD, I would assume it should be c/2, thus giving a DSB PSD of "c" as is obtained by integration.
Or, similarly, the equations would be as follows:
(63) Sn(f) = c
(64) Rn(t1 - t2) = 2c delta(t1 - t2)
Where (63) is an SSB PSD. I find this to be of significace because it changes the phase noise to period jitter conversion expressions using (73) and (77) by a factor of 2. I also have a copy of an earlier version of this article where these particular expressions are different by a factor of 2.
Any help is appreciated.
Thanks,
Michael [/quote]
The single- and double-sided PSDs are related as follows (found in a footnote on page 13), SDS(0) = SSS(0) SDS(f) = SSS(f)/2 for f != 0 As such, the double-sided equivalent to (63) is Sn(f) = c, which is the transform of (64). Thus, the equations given in the paper appear to be correct (or at least consistent).
|