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

[Steve Rooke]

Magnus,

Thanks for taking the time to unravel what seems to be a lack of
communication between parties here. They speak of two countries
divided by a common language, well this is almost trivial to the
divisions caused by misunderstandings that can occur in the areas of
science and technology. I believe we may now be able to move further;
below:-

On 7 June 2010 00:56, Magnus Danielson <magnus at rubidium.dyndns.org> wrote:
>>> 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.

Maybe I have been unable to communicate this properly but this is what
I have been trying to say. Indeed it is important to understand that
to enable the measurement of noise, the BW of the loop-filter has to
be wide enough to pass those frequencies. The other point I have been
trying to make is, if the BW of the loop filter set to include these
frequencies, then an instantaneous sample taken only at Tau will not
reflect the integrated frequency over the period up to Tau. To
overcome this problem it is important to make interim measurements of
the control voltage and calculate the average of them, therefore
determining an approximation for the integrated value for the
frequency. The accuracy of this approximation depends upon the number
of interim measurements and will reach 100% with an infinite number of
samples but for all intents and purposes, a number considerably lower
than infinity will produce results which are inside the limits of
accuracy of other parts of the testing system.

In other methods, for instance directly measuring timing the unknown
frequency, the true length of the sampled period of the waveform is
recorded and will directly reflect the integrated value of it's
frequency at that point.

> 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.

Well, this assumes that one would alter the sampling period to match
each Tau0 one was measuring. To my knowledge, the calculation of ADEV
is generally not made this way as it would mean the test being
performed over and over for each Tau0. From what I have seen so far,
tests are made with a sample rate at minimum Tau0 required and the
calculation for other Tau is then calculated by adding adjacent
samples together and recalculating for the new Tau0. In this way one
set of data is used for the calculation of all values of Tau that are
possible given the length of the data set.

In the case we are discussing here, with the loop filter set at a
certain BW, the oversampling rectangular integrating rate set at less
than 1 / BW of loop filter, and the actual minimum Tau set at less
than the oversampling rate, this system will create a series of
integrated samples at the minimum Tau rate, IE. 1s, 0.1s, (possibly)
0.01s... This provides data for the calculation of the minimum Tau
selected and the calculation for greater Tau can be obtained by adding
the values of adjacent non-overlapping (or overlapping, if desired)
samples together. As each of these samples is the result of an
oversampled, and integrated, measurement, the addition of any samples
will produce a further integrated result over the new longer Tau time.

> 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.

Yes, if the same filter is used for different Tau sample rates. The
interesting thing to note with the design proposed by warren though is
that, say, for instance the BW of the loop filter is set as detailed
above such that the oversampling rate is set at 10Hz and the original
Tau0 sample rate is 1Hz, 1s, then if it is desired to sample Tau at
2s, it is just as easy to sum and average 20 of the oversampled
measurements.

> 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.

OK, now you have managed to decipher what Bruce was saying, then this
is a mute point as the same ADEV calculation for Warren's method is
used as for every other way it is calculated. Therefore the same
equivalent filtering effect of averaging averages is equally applied
to this method. With the PLL filter set as described for Warren's
method above, it can be seen that it's properties are unlikely to
constrain the limits of calculations formed via this system.

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

The "filtering" performed by the actual calculation of ADEV is always
implicit in any method of calculating this metric. It is mearly the
function of taking a large amount of measured data and, via a system
of averaged averages, boiling all of this down to a single value that
can be easily used, compared, understood...

The other two "filtering" mechanisms are both really to be considered
as a form of two stage integration. If only one stage of integration
is attempted, the effects of the PLL filter will either produce a
correctly integrated value that excludes noise from the measurement,
or it will produce an incorrect value as the integration of the filter
is not match to the sampling rate. IE. this wider BW filter will not
converge at the Tau sampling time. Warren's choice of making the PLL
filter wide band band to allow it to track the effects of noise and to
perform an averaged measurement via rectangular integration due to
oversampling, overcomes the drawbacks of implementations of the TPLL
with a loop filter which can only be a compromise if samples are only
taken at the chosen Tau. In fact if you look at the original NIST
block diagram for the TPLL you will see that they have used a VFC
which will track changes in the EFC directly, and as the number of
cycles produced by this device is always directly proportion to the
instantaneous value of the EFC, the counter will measure an integrated
value of the EFC voltage over the Tau period. Obviously, this setup is
not as simple as Warren's implementation and it too requires some form
of loop filter just to damp the PLL, which will be a constraint on the
noise BW of that implementation.

>>> 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.

I have already described how the PLL loop filter and any of the
measurement system does not have to be changed to allow the
measurement at any Tau providing, I suppose, it was initially setup
for a 1s Tau and then a 1.5s Tau calculation was desired. Still, I
understand that Kmart are having a sale on hair-shirts for those that
are interested.

>> 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.

Well, I know what I'm talking about but I'm obviously having problems
understanding the other party.

Agreed!

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

Ah, yes! I agree with you there and this can still be easily performed
with Warren's design. Before we got to such uses as this, I think that
the original design was aimed at the sort of plot we have become used
to being posted on this list which contains a plot of, supposedly,
ADEV including all noise over a range of Tau. For the average time-nut
member, this sort of setup will be what they are looking for but, as
you have pointed out, even for such measurements that you list, this
proposed system could be adapted easy for this provided those noise
effects were measurable inside the current limits of this
implementation.

Cheers,
Steve

> Cheers,
> Magnus
>
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-- 
Steve Rooke - ZL3TUV & G8KVD
The only reason for time is so that everything doesn't happen at once.
- Einstein