[time-nuts] Phase modulation question

John Miles john at miles.io
Sat Aug 31 19:00:30 EDT 2013


Normally any higher-order sidebands are ignored when dealing with PM.  You
can think of it as NBFM with a very low modulation index -- all of the
"intelligence" is in the first sideband.

Put another way, the modulation index for FM is the peak frequency deviation
divided by the highest frequency present in the modulating signal.  In phase
modulation the carrier frequency is normally considered constant.  So the
numerator of the fraction you would use to index a table of Bessel functions
is 0, yielding a result of 1.

It gets more complicated when the PM at a given offset frequency shifts the
carrier by a radian or more.  This is where the small-angle assumption for
standard L(f) phase noise measurements becomes invalid.  If you are going to
measure the phase noise of a Cs standard at offsets of small fractions of a
Hz, this will eventually be an issue given the steep PN slope close to the
carrier.  Is that what you're doing?

For finer-grained Bessel resolution it make sense to evaluate the function
yourself.  I think there's a BESSEL() keyword in Excel, and Matlab or Octave
could certainly do it.

-- john, KE5FX
Miles Design LLC


> -----Original Message-----
> From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On
> Behalf Of cdelect at juno.com
> Sent: Saturday, August 31, 2013 11:52 AM
> To: time-nuts at febo.com
> Subject: [time-nuts] Phase modulation question
> 
> Hi,
> 
> I'm making some phase mod index measurements as it relates to Rubidium
> and Cesium standards.
> 
> Two questions.
> 
> 1. Is a Bessel table for sine wave modulated FM used for PM also?
> 
> 2. Where can I find a Bessel table that has fine resolution, the ones I'm
> seeing only have large increments of Mod index. (like .25  .5 1.0 1.5
> 2.0) I need to measure in between these values.
> 
> Thanks,
> 
> Corby
> 
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