WarrenS warrensjmail-one at yahoo.com
Sat Jun 19 17:54:01 UTC 2010

```Magnus posted:
>The square root improvement assumes white noise
>A logical gate or any other amplifier will also have flicker noise,
>To analyze it, Allan variance and friends needs to be applied.

No disagreements
What some may be missing is that this side tracked discussion and has little
at all do directly with the Simple TPLL method or it's limitations when
What the above has to do with is the effect of high speed averaging on
different frequencies
If the noise is high freq then averaging works great as stated (or even
better)
BUT say the frequency of the  noise_signal is at a low frequency such as 10
Hz and under  (a typical flicker or 1/F noise)
Does anyone need to have a detailed explanation or fancy math paper on why
averaging a Noise_signal for under 100ms (no mater samples are used) would
NOT get rid of the longer that 100ms (10 Hz) noise?
If they do not know why, then I can not or well not help with that.

Back to the TPLL
Adev is used to show the effect of all the noise signals aftering they have
been averaged (integrated) over tau0.
Integrating all signal noises, be it white, pink, black and blue, and yes
even flicker noise over Tau0 like the TPLL does,  then gives the correct raw
data to be able do ADEV for any and all noise types. This is something that
the Phase type methods do not do as easy or as well.

Maybe it would help to think of it as the Averaging (and intigrating) is
getting rid of all the unwanted High freq noise above Tau0 that are not
suppose to be include in or contribute to ADEV, so that the system can
measure all the noises at and below Tau0 freq which are suppose to be
So the fact that averaging does not get rid of flicker noise, IS NOT A BAD
THING for finding the correct Adev, IT IS A GOOD THING.
And the fact that averaging by intigration at tau0 to get rid of the
noise_Frequencies above Tau0 is not as bad thing as some have clamed in the
past but a GOOD thing

ws

*********************

Magnus Danielson magnus at rubidium.dyndns.org
Sat Jun 19 11:06:41 UTC 2010

On 06/19/2010 12:49 AM, WarrenS wrote:
> Say you have a nice logic gate with 1 ns delay
> If you make it all nice and clean, and repeatable such as constant PS,
> rise time etc.
> Then one can get repeatable results say 100 times better from cycle to
> cycle in the short term.
> so down to 10ps repeatable.
> Now make things even more clean with no variations and assuming random
> noise.
> Now if one is doing this at 10 MHz and only cares about the average over
> 0.1 sec (10 Hz)
> One can average 1,000,000 readings of the 10 ps jitter
> If they are truly random, that can give you a 1e-3 improvement (square
> root of number of samples averaged)
> so now down to 10 fs of average jitter at 10 Hz for a 10 MHZ gate
> starting with a 1ns initial delay.

The square root improvement assumes white noise, and will work when
white noise dominates. A logical gate or any other amplifier will also
have flicker noise, which doesn't average out like that. The meaningful
length of averaging thus depends on the cut-off frequency between white
and flicker noise. To analyse it, Allan variance and friends needs to be
applied. Thus, only for short-term stability may straight averaging work
for estimation.

Cheers,
Magnus

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