[time-nuts] frequency stabilty question

[Paul A. Cianciolo]

Magnus,

Now that I have a basic understanding, the way you explained seems just rite.
My lack of even a basic understanding is what led to the confusion.
Sorry if I caused you any  trouble.
I am going to go back and read the article again.

Thank you Magnus


Paul A. Cianciolo
W1VLF
http://www.rescueelectronics.com/
Our business computer network is  powered exclusively by solar and wind power.
Converting Photons to Electrons for over 20 years




-----Original Message-----
From: time-nuts-bounces at febo.com [mailto:time-nuts-bounces at febo.com] On Behalf Of Magnus Danielson
Sent: Monday, August 15, 2011 4:06 AM
To: time-nuts at febo.com
Subject: Re: [time-nuts] frequency stabilty question

Hi Paul,

On 15/08/11 05:10, Paul Cianciolo wrote:
> Folks,
>
> I amtrying to understand some of the terms used here quite often.
> I quoted this from Wikipedia
>
> An Allan deviation of 1.3×10−9 at observation time 1 s (i.e. τ = 1 s) should be interpreted as there being an instability in frequency between two observations a second apart with a relative root mean square(RMS) value of 1.3×10−9.

OK, I take the blame for that one, as I wrote it.

> Does this mean the observations made were at the very begining and the very end of the 1 second time.

Yes, as the observation interval is one second in this case, but you can make it arbitrary to fit your needs, your application, such as 314,159 s or whatever.

> If so what value about all the values in between?   What happens if the oscillator deviated far worse than this during the interrim.

Well, you should not interpret it as a particular interval, but rather a typical interval. ADEV is there to handle noises. If you use a shorter interval, the collection of noises will be different so your ADEV will be different. If you only have one ADEV value, you need to get the right interval. If your interval is inbetween known values, you can kind of guess as for pure noises the slopes is smooth.

But, the important aspect is that you need to measure for the interval of your interest, a single measure (such as RMS) will not satisfy your needs. It can be better or worse than the single point you have.

However, if you measure with a basic interval (tau0) you can algoritmically achieve integer multiple intervals. Modern algorithms interlace in an overlapping fashion these measures, so parts of an interval is used by several intervals being used as samples in the estimate. Hence, no particular interval can be expected.

> Or does the measurement consist of making  measurements every cycle during that 1 second and then entering all those values into a formula that accounts for them all??

Assuming that we are after ADEV(1s) then you can make say 100 measures 1 s inbetween. This takes 100 s. We process these for tau0=1 and tau-multiplier 1... which is the classic simple ADEV formula.

Another approach is to take samples more often, say every 100 ms and then take 100 such measures. This takes 10 s. We process these for
tau0=0,1 and tau-multiplier 10. The benefit is a significant shorter measurement interval, which isn't too great effort... but using 100 ms measurement interval you can get 10 times the samples for the same measurement time, so you can gain in improved predictor precission.

Thus, I toss in the confusing factor of improving quality of measure by increasing amount of samples.

However, I want to show you that you can achieve the measures by different approaches, essentially showing that you will not have to make unique measurement series for 1s, 2s, 4s, 10s etc. but that you can get these out of the same measurement series and in fact I highly encourage you to do so and regularly plot them.

> Maybe a very basic tutorial on this topic would help but I cant find 
> one

You only proove that there is more work to be done on the wikipedia article. It also lacks some illustrative plots.

Cheers,
Magnus

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