[time-nuts] Notes on tight-PLL performance versus TSC 5120A

Magnus Danielson magnus at rubidium.dyndns.org
Sun Jun 6 08:56:58 EDT 2010

Dear Steve,

On 06/06/2010 01:08 PM, Steve Rooke wrote:
>>>> I thus humbly suggest (nay, plead) that the discussion be re-focused on
>>>> the
>>>> two points above in a "just the facts, ma'am" manner.  One can certainly
>>>> characterize mathematically the differences between integration and LP
>>>> filtering, and predict the differential effect of various LPF
>>>> implementations given various statistical noise distributions.  If one is
>>>> willing to agree that certain models of noise distributions characterize
>>>> reasonably accurately the performance of the oscillators that interest
>>>> us,
>>>> one can calculate the expected magnitudes of the departures from true
>>>> ADEV
>>>> exhibited by the LPF method.  Each person can then conclude for him- or
>>>> herself whether this is "good enough" for his or her purposes.  Indeed,
>>>> careful analysis of this sort should assist in minimizing the departures
>>>> by
>>>> suggesting optimal LPF implementations.
>>> Ask yourself what is the difference between a simple R/C LPF and
>>> integration, what is integration in fact. What is the difference
>>> between an electronic LPF and an integrator designed in electronics. I
>>> think we are getting hung up between the mathematical term integration
>>> and the electrical term. Although I should say that of course ADEV is
>>> a mathematical derivation taking frequency data and finding the
>>> averages of various positional averages. Whether the frequency data is
>>> provided as the inverse of the measured period of the unknown
>>> oscillator or the voltage reading of a fancy VCO (ref osc), makes no
>>> difference, providing that each data point is accurately represented.
>>> In terms of "optimal LPF implementations" as I see mentioned here,
>>> this is the trap that previous people trying to use the tight-PLL
>>> method have fallen into. An "optimal" LPF will give a very accurate
>>> average value of the frequency for each tau0 point but only at the
>>> fundamental. It will get the effects of noise wrong unless its
>>> bandwidth is sufficient to encompass that but then the LPF will not be
>>> "optimal" and the resulting frequency data will be incorrect.
>> The above statement misses the point entirely and illustrates a fundamental
>> misconception of what the measurement of ADEV and other frequency stability
>> metrics actually require.
>> AVAR (tau) can be viewed as measuring the output noise (ordinary variance)
>> of a phase noise filter with a particular shape and bandwidth for the chosen
>> value of Tau.
>> Each Tau value requires a different filter.
> Wrong again!
> It does not have to be CONSTRAINED by the loop filter, in fact it
> should not be at all. You are still talking about making a filter
> which settles at exactly Tau and the only filter that does that is one
> that has a cutoff at the fundamental, and which will severely distort
> the results. Even the professional manufacturers don't do it that way,
> even when they make assumptions.

You are not talking about the same filter.

The PLL bandwidth of a tight-PLL setup will become the ADEV f_H upper 
bandwidth. This is the assumed system bandwidth for noise components and 
was more commonly referred to in the early work when tight-PLL setup was 
among the used setups.

The analogue PI-regulator will not effectively work as an integrator 
below some frequency where the integrator gain flattens out, so that 
will form the even less know lower frequency limit f_L. The useful 
tau-range is limited by these values, which is not to say that the 
tight-PLL is not a useful method for that range, but in its analogue 
core setup, these limits is there. A digital equivalent would overcome 
the lower frequency limit. The lower limit is often ignored, and for 
direct TIC-based measurements it can be ignored. Whenever there is a 
feedback loop and steering, care in bandwidth needs to be re-evaluated, 
so TIC measurments as such doesn't remove the issue if a DMTD setup or 
similar is used.

These are the rough model proceeding the measurement of frequency 
average data (for which time-data is the easiest form to observe).
The ADEV measurement being an average of a 2-sample variance with no 
dead-band then form a filter in the frequency plane. This filter is 
equivalent to the 2-sample variance, it is simply just the Fourier 
transformed variant and thus equivalent. This filter changes with the 
selected tau between the frequency average samples, as can be expected.

The equivalent filter that Bruce is talking about, is the filtering 
effect of the ADEV measurement as such, a direct consequence of the 
definition, where as the PLL properties form system limits that needs to 
be kept away from. The remaining issue is the way that frequency 
averages is formed and how accurate "integration" can be achieved.

Notice that there is now three different filtering mechanisms in place, 
just to keep us confused.

>> The equivalent filter of any method purporting to measure ADEV needs to
>> match that required by the definition of ADEV for all frequencies in the
>> filter pass band for which the source phase noise is significant.
>> This requirement is made more difficult to meet by the fact that the
>> equivalent filter bandwidth and maxima locations change for each end every
>> value chosen for Tau.
> Wrong again!

No, he is not wrong, but he is not quite right either. All ADEVs will 
depend on the upper frequency limit, but only two noises depends 
strongly on it. Likewise, the ADEV filtering mechanism has a null at 0 
Hz so low-frequency information is canceled out, so a lower frequency 
limit is not all the world either... considering that we have already 
accepted the fact that we can't get the complete ADEV. Now that we see 
this, we need to figure out how this affects our measurements and within 
what limits we can trust it to be near enought for various noise-forms.

> The needle is still stuck in the idea that the PLL-loop filter needs
> to have a settling time to match Tau. The BW of the loop filter can be
> made much wider to see the effects of noise and oversampling is used
> to integrate the frequency over the Tau time. This way, nothing is
> filtered out, thrown away, hidden, missed, glossed over, get it yet...

As I pointed out earlier, I think you are talking about different 
filters. The PLL loop bandwidth should not be changed with ADEV, and you 
should not be close either, because that way you would rather be 
attempting the MADEV measurement.

Changing the PLL loop bandwidth is however a method to separate WPM and 
FPM as Vessot points out in his 1966 article.


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