[time-nuts] ADEV measurement question

John Miles john at miles.io
Wed Aug 19 15:49:06 EDT 2015

I think the simplest way to explain the evils of TI averaging is that white noise doesn't alias in a conventional sense.  If a value is perfectly random, then it doesn't matter how you sample it.  Your sampling bandwidth -- and nothing else -- determines how much energy you get.  You can legitimately change that bandwidth after the fact by resampling or averaging the data.  (Another way to say this is that components of the white noise spectrum above the Nyquist frequency don't have a net effect on the observed spectrum.)  But this is only true for white noise; with any other variety of signal or noise energy, once it's sampled, it's there for good.  

So, postprocessing a sampled stream with averaging has the effect of reducing the white-noise component of the data to a greater extent than the rest.  This is why you see tend to see 'better' results from an MDEV plot than an ADEV plot.  MDEV has some built-in averaging properties, while ADEV does not.  Energy in a given part of the spectrum will influence an ADEV plot to a greater extent than with MDEV.  

ADEV isn't particularly frequency-selective.  If you've ever seen 1-pps or 50/60 Hz interference in an ADEV plot, you've noticed that its influence can corrupt the plot for the next decade or two.   So if you must use your counter's averaging feature to get good ADEV plots, it's important to carry out that averaging at a very small fraction of the tau-zero interval.  The more 1/f^n noise is present in your measurement, the more important that becomes.  Otherwise you end up with a transfer function that isn't really ADEV, even though that's what the label on the plot says it is.  

This gets more complicated with counters that dither their sampling clock, and/or apply other filter functions in their averaging process.  Some appear to be give better ADEV fidelity than others.  If nothing else, I would expect that averaging at sub-t0 intervals would introduce a dead-time effect in the portion of t0 over which the data is not contributing to the average.  It is always going to be better to avoid TI averaging whenever possible, and use great care in interpreting the data.

-- john, KE5FX
Miles Design LLC

> -----Original Message-----
> From: time-nuts [mailto:time-nuts-bounces at febo.com] On Behalf Of Matthias
> Jelen
> Sent: Wednesday, August 19, 2015 9:40 AM
> To: Discussion of precise time and frequency measurement
> Subject: [time-nuts] ADEV measurement question
> Hello,
> I´ve got a question concerning ADEV-measurements.
> I´m measuring the 15 MHz output of a KS-24361 with my SR-620
> with it´s internal (Wenzel) OCXO using Timelab. For the
> first shot I used the counters frequency mode with 1s
> gatetime. ADEV at tau=1s turned out to be arounf 2E-11,
> which fits the 20 ps single shot resolution of the SR-620
> nicely.
> To overcome this limitation without setting up a DMTD
> system, I used the counter as TIC, feeding 1 kHz (derived
> from the counter´s reference) to the start channel, the 15
> MHz to the stop channel and put the counter into average
> mode / 1k samples. This gives me one averaged result per second.
> The idea was that this shouldn´t change the measurement
> itself, because like in frequency mode with 1s gate time I
> get the averaged value over one second, but I expected
> trigger noise etc. to be averaged out to a certain amount. I
> have to watch out for phase wraps, but as the two frequencys
> are quite equal, this is not a big issue here.
> As expected, ADEV at tau=1s got much better, it is now in
> the 4E-12 area, which sound reasonable.
> What makes me wonder is the fact that result are
> significantly better now at longer taus (10..100s) also,
> despite of the fact that also in frequency mode these result
> were well aboce the noise floor (2E-12 @ 10s and so on...).
> So, is it a good idea to use this kind of averaging, or am I
> overlooking something which turns the numbers better than
> they really are? I´m pretty sure I am not the first one to
> try this...
> I´m looking forward to your comments.
> Best regards,
> Matthias
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