[time-nuts] GPSDO TC

Bruce Griffiths bruce.griffiths at xtra.co.nz
Sat Jan 10 07:37:32 EST 2009

Hej Magnus

Magnus Danielson wrote:
> Bruce,
>>> 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 
> source.
> 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.
I wasn't attempting to do so.
However the phase noise of the GPS receiver will still dominate for
short tau whilst that of the OCXO is dominant for longer tau.
> 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.
The 3 cornered hat technique only works well (even in the extended form
where finite correlations between sources are included) when the noise
of each of the 3 sources are comparable.
That is this technique will only work well in the vicinity of the point
where the GPS receiver and OCXO ADEVs crossover or equivalently near the
drift corrected minimum of the ADEV as measured by the Thunderbolt when
the OCXO is undisciplined. For shorter tau the GPS phase noise dominates.
>>> 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 
> parameters.
It would be helpful if the ADEV (and MDEV) plots for several
Thunderbolts were plotted using the Thunderbolt's internal phase error
measures obtained when the OCXO is undisciplined.
This can easily be setup using the Trimble Thunderbolt Monitor program.
>>> 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.
The usual meaning of critical damping in a second order differential
equation is for no overshoot to a step input.
Thus critical probably isn't the appropriate term when optimising for
other factors.
Optimum damping for a particular criterion is perhaps better description.
>>> 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.
> Cheers,
> Magnus
In particular the ability of a third order loop to track linear frequency drift can be very useful.

The last time I let my Thunderbolt OCXO free run there was a very strong
quasi parabolic component to the phase drift as measured by the
Thunderbolt itself.
However, this was soon after I first powered it up, its drift may have
settled down somewhat by now.


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