[time-nuts] GPSDO TC

Magnus Danielson magnus at rubidium.dyndns.org
Sat Jan 10 05:31:28 EST 2009


>> Yes, but the bump comes from the increase gain around the resonance and 
>> spoils the OCXO/GPS cross-over. The simplified noise-bandwidth measure 
>> does not really comply here since they usually build on a simplified 
>> model of noise type (white noise - gaussian). A simple check in Gardiner 
>> provides both the generic integrating formula, simplified results and a 
>> graph showing the smae numbers that you give.
> Whilst the phase noise of a sawtooth corrected M12+T GPS timing receiver
> approximates white phase noise (at least for tau < 1 day), this may not
> be so for the receiver used in the Thunderbolt.
> The phase noise of the OCXO certainly cannot be accurately modeled as
> white phase noise for large tau.

As the PLL filters the noise of the OCXO and passes noise from the input 
side and the noise have several different components to it from either 

You can't really extrapolate direction the results of an asynchronous 
reciever such as the M12+T to that of a synchronous receiver such as the 
Thunderbolt. The time-solution of thunderbolt is used in replacement of 
the time-interval counter fluff slapped onto a PPS based receiver such 
as the M12+T. Also, the Thunderbolt enjoys a much quiter and stable 
reference than the M12+T which allows for narrower filters in the 
sat-tracking as the phasenoise is lower. Notice how the Thunderbolt can 
be configured for different uses, they are direct hints to what the 
tracking loops may do as it reduces the physical dynamics of position as 
well as inflicted G effects on the OCXO.

With just two Thunderbolts and a reasonable TIC you can infact build a 
three-cornered hat. You have three clocks: GPS, OCXO1 and OCXO2 and the 
thunderbolts will measure GPS-OCXO1 and GPS-OCXO2 and the TIC will be 
able to measure the OCXO1-OCXO2. An interesting aspect of this is that 
when lockedup, the PPSes of the Thunderbolts will be confined into a 
rather small area. This arrangement will, as any other, give not the 
standalone OCXO noise when beeing steered, but it is not entierly lying 
for those longer taus.

>> I rather beleive what ADEV, MDEV and TDEV experience in this context.
> Yes measurements are the key but if one doesnt have a suitable
> statistically independent low noise frequency reference it isnt possible
> to optimise the loop parameters for an individual GPSDO.

True. However, I think there is still some more theoretical work to be 
done to give us better tools. These does not remove the need for 
measurements and I have never been foolish enougth to beleive so, but it 
could guide us in the right direction for selecting and steering our 

>> We could go back to the real integration formula, adapt it to various 
>> powers of f^-n noises and analyse it for the same set of PLL loop 
>> filters as analysed by Gardiner. Similarly we could cook up a simulation 
>> and do the ADEV, MDEV and TDEV measures. Traditional noise bandwidth 
>> measures can be calculated alongside.
>> I am somewhat surprised that you missed the opportunity to correct me as 
>> I was giving the incorrect value for damping factor of a critically 
>> damped system. It is the square root of 1/2 and not 2, thus 0.7071 is 
>> the appropriate damping factor for critically damped systems.
> I had noted that your quoted damping factor was incorrect but I
> suspected that you would realise that.
> Actually according to Gardener critical damping factor is 1 ( minimum
> settling with no overshoot for a phase step).
> However a damping factor of 0.7071 is widely used.

It is interesting to clear up why this difference exists. Could be 
"critical" is judged different for different applications.

>> I am somewhat surprised that when we have been discussing the bandwidth 
>> of the PLLs and considering OCXOs being running with fairly high drift 
>> rate we have been assuming second degree loops. This form of 
>> acceleration requires third degree responses for proper handling, as 
>> being well documented in literature such as Gardiner. Going for third 
>> degree response the bandwidth of the loop can be (at least more freely) 
>> disconnected from tracking requirements due to drift rate.
> I only mentioned second order type II loops as the analysis is somewhat
> simpler and there is no indication from the number of tuning parameters
> for the Thunderbolt that a higher order loop is involved.

My point was that regardless of implementation, second order type II 
loops seems to be the reference mark, which not necessarilly is a good 
one. Third order loops should be considered as it removes or reduces a 
type of problem and allows a more freer setting of parameters with less 
things to compromise between. When doing the loop in digital processing 
it is not that more expensive. There are re-tunable architectures which 
is being used in for instance GPS receivers which is not hard at all to 
use for both PI and PID controllers.


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