# [time-nuts] various question on stability, jitter, PN, ...

Magnus Danielson magnus at rubidium.dyndns.org
Wed Sep 17 15:24:54 EDT 2014

```Stéphane,

Welcome!

On 09/16/2014 09:25 PM, Stéphane Rey wrote:
> Hi guys,
>
>
>
> I told you ! Some questions were to arise...   ;-)
>
>
>
> At work I'm working on 1.5, 3 and 12 GHz pulsed systems with pulses length
> between 0.1 and 5 us. We are especially interested in phase stability pulse
> to pulse (repetition rate) and possibly with minor priority on the length of
> the phase pulses, pulse to pulse.
>
>
>
> 1. When plotting the phase noise response of a CW signal, one can determine
> the RMS jitter in ps or fs. I'm wondering what is corresponding to this
> value. As it's RMS I would expect this is the square root of the maximum of
> the Gaussian distribution of the frequency jitter. Is it right ? If so this
> correspond roughly to 1 sigma deviation, right ?

Well, RMS calculation can be a poor or good estimator for 1 sigma
deviation depending on the noise and systematics. If the dominant noise
is white and systematics is low, it will be relatively good.

We tend to use Allan deviation in replace of standard deviation for
frequency stability when we have non-white noise.

> 2. Is there any link between this frequency jitter and the phase jitter ? I
> assume no, but...

There is... phase jitter is frequency jitter integrated

> 3. What does bring the Allan deviation plot ? This gives stability vs
> integration time I know, but how to make an interpretation of this ? Is it a
> way to plot the frequency jitter in a more detailed way than just giving the
> rms jitter ?
>
>   In practical use, for a pulsed system does it mean that only the very short
> term jitter is of interest ?

Integration time is misleading to some degree, rather it is called the
observation time.

Allan deviation (ADEV) gives a RMS like measure of noise, normalized to
white frequency noise. Notice that ADEV gives you frequency stability,
as normalized by the carrier frequency. It aims to give the random noise
RMS value as measured over some observation-time. The observation-time
is really just the distance between the phase-measurements. By measuring
the phase at each burst can you then make the ADEV plot for any integer
multiple of the burst period.

ADEV is meant to handle noise-types which would otherwise prohibit
proper convergence.

> 4. Is the Allan deviation plot a representation of the jitter vs integration
> time, meaning there is a direct relation between the RMS jitter computed at
> various offsets from the carrier in the PN plot ?

Observation time is the term being used. Allan deviation is the RMSish
value of frequency stability as you observe it for tau seconds.

> 5. Is there a practical way to plot phase noise for pulsed signals ?

Well, you can. If you measure the stability of the frequency from one
pulse to the next, then it's just like normal ADEV measurements. Your
actual measurement can be frequency or phase measurement.

> That's all for now.
>
> If anyone has clues or can point me into good articles related this would be
> kind.

There is loads of them. I have tried to make the Allan Deviation
wikipedia article reasonably readable and useful.

Cheers,
Magnus
```