# [time-nuts] frequency stabilty question

Jim Lux jimlux at earthlink.net
Mon Aug 15 13:31:21 UTC 2011

```On 8/14/11 8:10 PM, 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.
>
> Does this mean the observations made were at the very begining and the very end of the 1 second time.
> If so what value about all the values in between?   What happens if the oscillator deviated far worse than this during the interrim.
>

A measurement at tau=1 second doesn't say anything about what happened
at shorter intervals.

>
> 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??
>

Nope..
It's if you measured the frequency (instantaneously) at one second
intervals, and calculated the standard deviation, that would be the ADEV
for tau=1 second.

measure at 10 second intervals and you get ADEV(Tau=10sec), etc.

That's why you typically see an ADEV as a series of performances at
different taus.

You can also fill in the gaps in the curve, to a certain extent, because
physical oscillators have constraints on what the ADEV can do (i.e.
you're not likely to see 1E-9 at tau=1 second, 1E-5 at tau=2 seconds,
1E-10 at tau=3 seconds)

In fact, if you do the ADEV measurement and it's NOT a nice curve and
has spikes and weirdnesses, that starts to tell you have either a
measurement system problem or a problem with your frequency standard.

(sort of like spurs in a phase noise plot from 120Hz line interference,
or reference clock leakage)

As an example of measurement system problems, it's pretty common to see
a "hump" in ADEV around 500-1500 seconds (around 15-20 minutes) because
of temperature effects on the test equipment or unit under test as the
airconditioning/heating cycles on and off.

> Maybe a very basic tutorial on this topic would help but I cant find one
>
>
> Signed very confused,
> Thank You
>
> PauLC
> W1VLF
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```