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Entry  Tue Sep 14 04:14:25 2010, Dmass, Misc, Doubling, Doubling results summary 
    Reply  Wed Sep 15 17:04:36 2010, Dmass, Misc, Doubling, DON'T REMOVE OPTICS YET 
       Reply  Wed Sep 15 22:59:37 2010, Frank, Misc, Doubling, DON'T REMOVE OPTICS YET 
    Reply  Tue Sep 21 01:52:05 2010, Dmass, Misc, Doubling, Doubling results summary AllanVarSep2.pdf
       Reply  Thu Oct 6 23:44:09 2011, Dmass, Misc, Doubling, Finishing SHG paper AvarWhitePhase.pdfAvarWhiteFreqNoise.pdfAvarPhase1onfhalf.pdf
          Reply  Mon Oct 10 11:55:59 2011, Dmass, Misc, Doubling, Finishing SHG paper Avar2PhaseSchnatz.pdf
    Reply  Wed Sep 22 17:16:09 2010, Dmass, Misc, Doubling, Some notes on previous bounds 
       Reply  Mon Jan 24 17:17:59 2011, Dmass, Misc, Doubling, Some notes on previous bounds 
Message ID: 1547     Entry time: Thu Oct 6 23:44:09 2011     In reply to: 1074     Reply to this: 1548
Author: Dmass 
Type: Misc 
Category: Doubling 
Subject: Finishing SHG paper 

As part of finishing up my doubling phase noise paper, I had to revisit this question:

"How much information do we need from a reported Allan variance/deviation in order t compare it to a phase noise power spectral density"

This is important to me because some of the low noise measurement people only report (and some only measure) Allan deviation of their (clock) signal.

One of the results I wanted to compare with was in the paper: Optical Frequency Synthesis and Comparison with Uncertainty at the 10^-19 level (Science), (figure 2B, curve (ii))...

 

As described in elog:1074, you can directly convert from a phase/frequency noise PSD to an Allan deviation...if you look at the equation for conversion (section titled: Time response and frequency filter properties), you can see that in the case of white phase noise (frequency noise which goes up as f in amplitude), the Allan deviation level at all times depends on measurement bandwidth (increases linearly with bandwidth).

To figure out what the heck is going on, I made some pretend noise spectra in MATLAB, and forced a 1/f^4 roll-off at different frequencies, and looked at different noise shapes...

(1) White Phase Noise with different frequency roll-offs

(2) White Frequency Noise with different roll-offs

(3) 1/f^0.5 Phase Noise with different roll-offs

From the wiki page:

PSD Shape ADEV Shape
White Freq 1 / sqrt(Tau)
White Phase 1 / Tau
1/f Phase [rad^2/Hz] sqrt(ln(Tau)) / Tau

The first two are obviously consistent. I'm not sure about the third by inspection, but it easily could be consistent

Attachment 1: AvarWhitePhase.pdf  337 kB  | Hide | Hide all
AvarWhitePhase.pdf
Attachment 2: AvarWhiteFreqNoise.pdf  290 kB  | Hide | Hide all
AvarWhiteFreqNoise.pdf
Attachment 3: AvarPhase1onfhalf.pdf  317 kB  | Hide | Hide all
AvarPhase1onfhalf.pdf
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