[time-nuts] Estimating expected time error using info from manufacturers' data sheets

[BJ]

I should add that the numbers in the attachment are for illustrative
purposes only and are not necessarily representative of the particular
frequency reference mentioned.

-----Original Message-----
From: time-nuts <time-nuts-bounces at lists.febo.com> On Behalf Of BJ
Sent: Friday, 29 November 2019 11:54
To: time-nuts at lists.febo.com
Subject: [time-nuts] Estimating expected time error using info from
manufacturers' data sheets

Dear fellow timenuts,

 

I am looking for some advice and insight from others wiser and more
experienced (than me) in the following:

 

I want to be able to estimate the ability of a variety of (free running)
time & frequency references (ranging from crystal oscillators to Rb and Cs
frequency references) to remain synchronised to some hypothetical 'perfect'
reference over time. I.e. for each device I want to calculate expected time
error at some time t, given that the device was synchronised to the
'perfect' reference at t=0. And I need to do this based on what is provided
in the datasheets. I thought this should be a straightforward exercise, but
(probably due to my ignorance) I'm finding this trickier than anticipated. I
have come up with a possible approach, but wanted to get some feedback from
anyone else out there that might have already gone down this path.

 

The parameters (that appear relevant) in the data sheets are:

Frequency accuracy

Frequency stability over temperature

Aging (per day/week/month/year.)

Frequency stability (ADEV)

 

The question then becomes, how do I combine these figures sensibly to come
up with the information I seek? For starters, there is some inconsistency in
how the parameters are recorded in the data sheets. Then there is the fact
that ADEV is often only given for one or a couple of values of tau. Anyway,
I have scoured the literature and came up with a couple of equations that
seemed promising, with the Time Interval Error (TIE) appearing to be the
most applicable. In particular, I have been using RMS TIE_est(t) as
specified in IEEE Std1139-2008. 

 

Without getting too heavily into the maths, the variables in this equation
are:

1. Uncertainty in initial synchronisation (sigma_x0), which I am setting
equal to zero, as I am assuming perfect sync at t=0

2. Uncertainty in frequency (sigma_y0), which I am using to represent the
frequency stability over temperature component (although, perhaps I should
be considering the frequency accuracy here as well?)

3. Random frequency instability at time t (sigma_y(t)) after linear
frequency drift has been removed, which I am equating to ADEV for tau=t 

4. Normalised linear frequency drift per unit of time (a), which I am using
to represent the aging component if applicable

 

I have attached a worked example and would like to know if this makes sense,
or if I am on the wrong track. Note that I have included further questions
(and concerns) in red text in the worked example. I am quite uncomfortable
about all the assumptions I am forced to make and all the interpolating and
extrapolating I am forced to do, due to lack of information in the data
sheets. But at the end of the day I am just looking at a ballpark figure and
this is a bit of a learning exercise of sorts for me, to try to understand
how to interpret the manufacturers' specs and what they really mean in terms
of how long it might be before a free-running clock becomes too inaccurate
for certain purposes.

 

So, in summary:

1.	Does the TIE estimate I am using seem like a sensible choice for
what I am trying to do? If not, what would be a better approach?
2.	Am I implementing the data sheet parameters sensibly in this
equation? (as per the worked example in the attachment)

 

Thanks folks!

 

Belinda