[time-nuts] 10 MHz to 32.768 kHz converter

Attila Kinali attila at kinali.ch
Mon Mar 21 18:44:16 EDT 2016


On Mon, 21 Mar 2016 11:31:23 -0700
Alex Pummer <alex at pcscons.com> wrote:

> On 3/21/2016 6:00 AM, Attila Kinali wrote:
> > Given that the crytsal has an accuracy of better than 100ppm, then
> > even a very weak coupling at 128Hz should be enough to keep it locked.
> > Upper bound on the jitter is 1/128Hz*100ppm=781ps (very simplified
> > calculation, but it should be definitly less than 1-2ns)

> there was a very good  paper written on injection locking: R. Adler, “A 
> study of locking phenomena in oscillators,”Proc. IEEE, vol. 61, no. 10, 
> pp. 1380–1385, Oct. 1973

Actually, if you want to calculate the jitter of an injection locked
oscillator, then the publications from Kurokawa from the 70s and 80s
are more approriate than Alders paper form '45 (the '73 version is
just an unmodified reprint of the original paper).

The value i gave with <2ns is a worst case bound on the jitter,
under the assumption that the oscialltor Q is low and it will
imediatly switch back to its original frequency once the phase
shift induced by the pulse is over. In reality the phase jump
should be much less as the Q acts as an integrator and thus
averages the phase jumps out. As modern 32kHz crystals have a Q in
the 10k-100k range, you can assume that the "averaging" time of
the crystal will be in the 0.3-3s range. I didn't orignally
include this complication in the mail, because I cannot reproduce
the formulas from the top of my head and the parameters of these
formulas are not always easy to extract. Hence the above worst
case bound for the jitter, which is easy to see and good enough
for this kind of application.

			Attila Kinali

-- 
Reading can seriously damage your ignorance.
		-- unknown


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