[time-nuts] Phase modulation question

[Bob Camp]

Hi

The "small angle" assumption also tends to break down when testing phase noise under significant amounts of vibration. 

Bob

On Aug 31, 2013, at 7:00 PM, John Miles <john at miles.io> wrote:

> 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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