Message ID: 1045
Entry time: Tue Mar 18 16:10:09 2014
In reply to: 1042
Reply to this: 1340

Author:

Dmass

Type:

Noise Hunting

Category:

Beat Spectrum

Subject:

JILA Si cavity frequency noise

I calculated the JILA Si cavity noise based on the Allan deviation, and have posted it here for posterity.

I have also included a plot of the frequency noise for comparison with our noisebudget.

Some finer points on Allan Variance <---> Power Spectral Density Conversion:

We can trust the derived formula in the band of fourier frequencies: [fmin,fmax] = [1/Tmax, 1/Tmin] = [10 mHz, 10Hz]

We do not know what low passing was done on the data to make the Allan Deviation number lower, so we do not really know anything about the frequency noise past 10 Hz

The wikipedia explanation for this is actually decent - as you can see from the table converting Allan Variances to PSDs, the measurement bandwidth (f_H in the table) used in the experiment (which could be the width of a bandpass about the beat frequency, for example), couples into the absolute allan variance level if your phase noise decreases any slower than 1/sqrt(f) in ASD (1/f in PSD). Since we see white phase noise at high frequency ALL THE TIME in our readouts, we should use caution. The assumption that we are implicitly making by using the calculated PSD at 10Hz is: "we believe that the bandpass they put around their beat to filter out white+flicker phase noise had a bandwidth greater than 10Hz" - this seems like a reasonable assumption