Hi If you are in the region that a low noise reference will apply to a low deviation precision standard, you are deep into “small angle” territory. The higher order stuff simply does not apply. Rotate the spectrum by 1/f (FM -> PM) and calculate the level at 1 Hz …..end of story. If when you are done you have phase noise that is above -60 dbc in a 1Hz bandwidth above 1 Hz, go back and look at the small angle assumption. 60 db is still well inside the safe region so you still are likely to come back with “no problem”.
Bob > On Aug 1, 2016, at 3:01 PM, jimlux <[email protected]> wrote: > > On 8/1/16 8:18 AM, Attila Kinali wrote: >> On Mon, 01 Aug 2016 14:36:28 +0000 >> "Poul-Henning Kamp" <[email protected]> wrote: >> >>>> I need some formulas that relate EFC noise to the (added) phase noise of >>>> an OCXO. It shouldn't be too difficult to come up with something. But >>>> before I make some stupid mistakes, i wanted to ask whether someone >>>> has already done this or has any references to papers? My google-foo >>>> was not strong enough to find something. >>> >>> Isn't that just FM modulation ? >> >> Yes, it is. The problem is not the theory. The problem is to calculate >> the correct values. I know i can figure it out, but if there are ready >> to use formulas that are known to be correct, I rather use those. > > Rather than deriving Bessel functions from first principles? > > It's an interesting problem.. What you're really looking for is the spectrum > of the output with the FM modulation process acting on the spectrum of the > modulation. As noted by others, you need to know the bandwidth (and then > assume that it's "flat" within that bandwidth). > > FM modulation isn't linear: that is, if I feed a 10 Hz and a 15 Hz signal > into a FM modulator, the spectrum I get out is not just the superposition of > the spectrum with just 10 Hz and just 15 Hz. > > The spectrum of a single tone modulation is easy: it's the Bessel function of > the appropriate order with the appropriate scale factors. > > Somewhere I've got a derivation of this: I was more concerned with phase > modulation (heartbeat motion and respiration motion both modulate the > reflected radar signal, so the spectrum you see is a combination of the two): > it isn't pretty in an analytical sense. I wound up just doing numerical > simulation: you don't have to worry about whether you are violating the small > angle approximation, etc. > > A couple of papers from the 60s that seem to be on point... > > > http://www.sciencedirect.com/science/article/pii/S0019995866800062 > > http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=5245193 > > The Medhurst paper seems to be the one you want. > "When the frequency modulation may be simulated by a band of > random noise (as in multiplex telephony carrying large numbers of > channels), the spectra of the distortion products can, in principle, > be described by simple algebraic functions of the characteristics > (i.e. the minimum and maximum frequencies and the r.m.s. frequency > deviaion) of the modulating noise band." > > > I note that "simple algebraic functions" take up the better part of a page. > Simulation looks more and more attractive. > > > > > > >> >> Attila Kinali >> > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts > and follow the instructions there. _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts and follow the instructions there.
