[time-nuts] Averaging effects

Magnus Danielson magnus at rubidium.dyndns.org
Sun Dec 26 17:43:41 UTC 2010


Fellow Time-nuts,

The last couple of days I have been playing around with TimeLab, a 
DTS-2070C, a TADD-2 and a pair of 5 MHz OSA 8600 oscillators.

Since I lack slew-rate amplifiers (linear amplifiers can only be used if 
they clip or is limited or else I will burn the DTS-2070C inputs), I 
will be limited by input trigger jitter, which is about 14,5 ps. Ah 
well, not too shabby for 5 MHz sine.

I've used various arming rates to the DTS-2070C from 1 Hz to 10 kHz and 
also varied the averaging block size accordingly such that I will get 
one reading every second.

As you can see on the plot (if it makes it through) is that this will 
eat the white-noise trigger jitter limit in the expected sqrt(N) 
fashion. It is best seen when comparing the 1 sample (blue) and 100 
sample (green) curves as the are separated by a decade as they slope down.

There is a downside to this approach which should be understood, it will 
also averaging out the white noise of the DUTs.

The V-shape of the curves comes from the white-noise limit slope (low 
taus) and the drift-rate limit (high taus). I have not performed any 
drift rate compensation and the OSA 8600 has only been heated a few 
days, so the drift is still a bit high.

A peculiar effect is that to make good readings for low-tau values I 
need to trim the oscillators to be very near each other. Otherwise there 
will be a polution of the lower taus compared to my selected good plots. 
This polution and the slope is insensitive to any drift rate 
compensation, so Hadamard analysis does not help.

Averaging can in fact give significant errors if the frequency error is 
not handled, and it shall be recalled that wrapping is not handled for 
the individual samples. If you would save the burst you could do it, but 
then you can use the full time-series and do propper ADEV on them instead.

I have not been able to pin-point how this frequency offset effect 
really works with ADEV, but currently I suspect it has something to do 
with quantization and averaging... but I haven't had time to verify that.

I will do experiments with other burst forms than evenly spread out bursts.

Anyway, I am having a fun Christmas in the lab and I hope you also enjoy 
the warmth of ovens and instruments with the blinking red LEDs :)

Merry Christmas,
Magnus
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