[time-nuts] Predicting clock stability from thevariouscharacterization methods

[Magnus Danielson]

From: Brooke Clarke <brooke at pacific.net>
Subject: Re: [time-nuts] Predicting clock stability from thevariouscharacterization methods
Date: Thu, 30 Nov 2006 13:31:53 -0800
Message-ID: <456F4DC9.9080402 at pacific.net>

> Hi Tom:
> 
> Is there a way to use the Allan plot to predict the variation in a reading?
> For example if you use the plot comparing the 1 PPS from a GPS receiver 
> to a good Cesium frequency standard, then:
> (1) what size of variation would you expect if the Cesium standard was 
> divided down to 1 kHz and that was compared to the GPS 1 PPS, or
> (2) what size of variation would you expect if the Cesium standard was 
> divided down to 1 Pulse/1,000 seconds?

First on the phase variations as they are divided:

1) The phase deviation frequency is unchanged, unless wrapped around the
   clock (Nyqvist wrapping).
2) The phase deviation amplitude is divided by the carrier divide ratio, i.e.
   dividing a 10 MHz down to 1 MHz will make the phase deviation go from say
   -130 dBc/Hz to -150 dBc/Hz (on the same offset from the carrier, say 100 Hz)
   assuming the divider chain does not add phase noise.

Allan deviation experience about the same of properties, with the natural
conversion of the above to tau language rather than frequency speak.

Then, on your GPS/Caesium issue, no. The reason being that when you measure
between two clocks, you don't know how much noise come from one or the other.
You need more sources of sufficiently low phase noise to match case to make a
three-cornered hat resolution of the individual sources phase noise. Once you
have done that there is no magic on predicting the divided down variants.

You can however make educated guesses, but that is another issue.

Cheers,
Magnus