# [time-nuts] Effect of EFC noise on phase noise

Bob Camp kb8tq at n1k.org
Mon Aug 1 16:41:45 EDT 2016

```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 <jimlux at earthlink.net> wrote:
>
> On 8/1/16 8:18 AM, Attila Kinali wrote:
>> On Mon, 01 Aug 2016 14:36:28 +0000
>> "Poul-Henning Kamp" <phk at phk.freebsd.dk> 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 -- time-nuts at febo.com
> To unsubscribe, go to https://www.febo.com/cgi-bin/mailman/listinfo/time-nuts
> and follow the instructions there.

```