[time-nuts] Re: Practical relation between Phase Noise and ADEV

[Magnus Danielson]

Erik,

On 2022-07-22 17:50, Erik Kaashoek via time-nuts wrote:
> Both ADEV and Phase Noise can be measured around 1 to 10Hz so for my 
> own understanding I made an empirical graph that relates a certain 
> phase noise with its impact on the ADEV to allow checking for 
> consistency in measurements.
> All data mentioned is only correct for a signal at 10MHz
> The table was made by generating a 10MHz test signal with just the 
> right level of phase noise at the wanted frequency and measuring the 
> ADEV of the test signal. Of course it should be possible to calculate 
> this relation but these calculations are not my strongest point.
> And I did not verify how the summing of noise impacts the total ADEV
> Phase noise with frequency f has maximum contribution to ADEV at 
> frequency f*2.
> Phase noise of -60dBc at 1Hz contributes maximum 1E-10 to ADEV at 0.5Hz
> Every 20dB of decrease in noise level decreases ADEV contribution with 
> a factor 10
> Every factor 10 increase in frequency increases the ADEV contribution 
> with a factor 10.
> A simple graph showing the relation can be found here: 
> http://athome.kaashoek.com/time-nuts/PNvsADEV.PNG

You should consult Enrico's chart:

https://zenodo.org/record/6476977#.YtsgN8FBw6E

This is also included into IEEE Std 1139-2022 in a similar form.

It is key to understand that ADEV does not determine phase-noise slopes.

Yes, there is a relationship, but the troublesome issue is that ADEV in 
practice is unable to make white phase modulation and flicker phase 
modulation phase noise slopes into different slopes in ADEV, they both 
show up as 1/tau slopes despite having different phase-noise slopes. 
This means that you with the ADEV slopes does not know if the 1/tau 
slope is white or flicker phase modulation. This annoyed David Allan and 
his colleagues and it took another 15 years to resolve it and that was 
only achieved with the introduction of MDEV.

Another aspect is that any systematic signal like a sine or even a 
narrow-band noise-spike will add additional wide-band energy ontop of 
the ADEV obscuring the view of the random noise slope behaviours.

So, You can put things in relation sure, but be careful not to 
overinterpret your plots and think they replace phase-noise. It's very 
hard to achieve that, even if ADEV was developed to serve the purpose. 
It's another tool and serve another purpose. I therefore want to see 
both, as they provide different information to me.

Cheers,
Magnus - now in summerhouse