[time-nuts] Question about effect of spurious frequency modulation on Allan Deviation

Magnus Danielson magnus at rubidium.dyndns.org
Mon Aug 6 02:07:59 EDT 2018

Hi Rick,

On 08/06/2018 07:12 AM, Richard (Rick) Karlquist wrote:
> I need to measure ADEV on a source that has spurious
> sine wave frequency modulation on it.  I am looking for a
> formula that would tell me ADEV, vs FM deviation and
> carrier frequency. I'm not sure if modulation frequency
> or tau matter.  I am hoping to determine how much
> I need to clean up the signal order to get down to a particular
> ADEV measurement threshold.
> I tried a literature search but didn't turn up anything
> I could use.
> I remember when I worked on the output section of the 5071A
> we specified 100 kHz and 1 MHz spurs to be down -80 dBc.
> These didn't seem to affect the ADEV of the 10 MHz outputs,
> but I can't prove why this should be the case.  Does the
> f-sub-h measurement bandwidth come into play?
> Thanks.

What does exists is a formula for how a single sine spur would produce
ADEV. A FM deviation with low enough modulation index creates two
side-bands of opposite sign but same amplitude. The modulation index,
which is just another aspect of frequency deviation, is direct steering
the amplitude of these sidebands through Bessel polynomial, but for low
deviations this is linear. The modulation frequency will care, and it
will depend on tau. The actual sample rate of the ADEV will interact
with the sideband "spurs" and add onto each other.

The additional ADEV comes on top of any other ADEV response, so it is
clearly a factor on ADEV polution.

Without doing the math, expect the double amplitude to that of the
single sideband sine of the same amplitude itself.


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