[time-nuts] TPLL secret reveled

[Ulrich Bangert]

Warren,

I know you like my software and therefore please allow me to put my 50 cts.
into the discussion:

> The reason that the simple TPLL works so good 
> but is hard for some "experts" to accept, seems 
> to come down to the fact that this method uses 
> Frequency and not Phase to make the raw data 
> log used to then calculate ADEV data.

This belief is the biggest misconceptions of yours. No one has ever denied
that correct ADEV values can be computed from frequency data and (as far as
I believe) Allan came out with a formula for phase data and for frequency
data at the same time. The problem is a bit more subtle but by far not out
of the reach as a good technician as you.

I would like to keep the topic of deadtime out of the discussion. Therefore
please consider a situation where two old fashion frequency counters (the
ones that were only counting) are synchronized in such a way that they
produce frequency data at a Tau0 of 1 second without any deadtime, the first
counter for second n then the second counter for second n+1 then the first
counter for second n+2 and so on. If you feed the produced data into Allans
frequency formula then you will get a perfect ADEV calculation out ouf it.
The only drawback is that it will have a high noise floor because with the
counters counting complete periods of the wave their effective resolution
may be considered 1 period length of the wave. 

Now let us consider what the old fashioned counter REALLY does: Over a gate
time of 1 second (identical to Tau0) it COUNTS the number of WHOLE periods.
Basically the old fashioned counter does make an integrating phase
measurement over the time integral Tau0. The result is not displayed in
units of the phase domain but it units of the frequency domain but the key
point is that the frequency measurement gathered this way contains the same
information contents as if a phase measurement had taken place. Therefore it
becomes clear immediately why one must use a slightly different formula for
the frequency values but why otherwise everything we know from phase data is
contained in in the frequency data as well. 

Next consider the case that the frequency of the DUT lineary changes with a
negative slope during the first half of a second to a minimum at the center
of the second and then changes with the same but positive slope so that at
the end of the second the frequency is the same as at the beginning of the
second. Clearly a phase measurement will reveal this behaviour and the old
fashioned counter will as well. This is why we say that the phase
measurement as well as the frequency measurement gathered this way are
characteristic for the WHOLE of the second of Tau0.

The next improvement to the old fashioned pure counter was the invention of
subclock interpolation schemes. A counter using this works so: After the
beginning of the gate time it waits of the next zero crossing and then
measures the time up to the last zero crossing within the gate time with a
fixed resolution of say 1 ns (like the well known Racal Dana
1992/1996/1998). The frequency value is then the result of a computation. If
you consider this working principle you notice that this is even more a
phase meter like thing than the original counter only thing. For that reason
frequency measurements with a counter like that are suited as well for ADEV
calculation.

The next improvement in counter technology is applying tricks as not to
measure a single time interval during the gate time but instead making
thousands of time-delayed measurements and then applying statistics to it.
The Agilent 53131/2 and the new Pendulum counters belong to this class. They
deliver even more frequency resolution but is has been shown and discussed
in another thread here why frequency measurements with these class of
counters are NOT WELL suited for ADEV calculation. That is why we let them
out.

Once we have understood these facts let us return to the tight pll method.
Let us consider what would happen with the above case with the frequency
changing down and up lineary within one second. Well, since the pll tightly
tracks the dut in frequency the loop voltage will be the exact copy in the
voltage domain of what is happening in the frequency domain. The key point
is that the integrating process that is involved in the nature of the
counter only measurement and also in the improved counter measurement does
NOT take place INSIDE the pll loop. 

Had you looked to the loop voltage at a Tau0 of 1 s you would not have
noticed ANYTHING from the frequency changes because the loop voltage
measurements deliver an instantaneous frequency information and not one that
is characteristic for your Tau0. Because the loop voltage contains
INSTANTANEOUS frequency information it is different from counter originated
data and needs special treatment: It needs integration afterwards which in
the original NIST method is applied by the voltage to frequency counter and
the following impulse counter. The case of the frequency changing down and
up lineary within one second documents in the impulse counter values if
looked at at a Tau0 of 1 s but it does not document in the loop voltage if
looked at at 1 s. That is the reason why measuring the loop voltage with an
a/d converter delivers samples of instantaneous frequency data that do not
compare 1:1 to values measured with conventional counters. 

Had you included the voltage to frequency converter and counted the impulses
coming from it with a PC and some software then Bruce would have applauded
to you because these ingredients would have performed the necessary
integration over the loop voltage. Since you left out the integration in
hardware Bruce has been pointing to the fact that you need integration in
the software if you want to claim that you have build an implementation of
NIST's tight pll method. If you leave out the integration in software IT IS
NOT NIST'S TIGHT PLL METHOD with its well known properties. Instead it is
WARREN'S TIGHT PLL METHOD with its not so well known properties. WARREN'S
TIGHT PLL METHOD must not be bad a priori but since it is different from the
NIST method you cannot rely on annything that has been said about the NIST
method. You will have to show in what cases it works well and in what cases
it works not so well completely on your own. 

I understand that an important part of your argumentation is the fact that
you do not look at the loop voltage at a rate of Tau0 (which would be a
catastrophe for my example) but at a much higher rate that you call
oversampling with some right. Therefore the down and up in frequency of my
example indeed is contained in your samples of the loop voltage. What you
have to proove is that the signal processing that you apply to your samples
basically IS EQUIVALENT to the integration of the NIST method. My last
posting concerning this case already indicated that real world experiments
are a limited tool for that purpose. You would need a strong mathematical
treatment to show this equivalence for ALL practical cases. Otherwise it
will stay Warren's tight pll method and we need to wait for the next years
to come to see its impact on the world of scientifics. 

It is by far not as simple as that:

> The reason that the simple TPLL works so good 
> but is hard for some "experts" to accept, seems 
> to come down to the fact that this method uses 
> Frequency and not Phase to make the raw data 
> log used to then calculate ADEV data.

and you should check yourself whether you really want to stay at claimes
like that. Had you listened a bit more on what Bruce has been saying in the
last weeks we would perhaps already have a nice hardware (Yours!) AND a
correct mathematical treatment of the samples (delivered by Bruce). This
missed opportunity is a real pity.  

Best regards
Ulrich Bangert

> -----Ursprüngliche Nachricht-----
> Von: time-nuts-bounces at febo.com 
> [mailto:time-nuts-bounces at febo.com] Im Auftrag von WarrenS
> Gesendet: Donnerstag, 10. Juni 2010 06:06
> An: Discussion of precise time and frequency measurement
> Betreff: [time-nuts] TPLL secret reveled
> 
> 
> 
> There has been speculation on why the low cost, simple, TPLL 
> tester compares 
> so favorably with the TSC 5120A over a wide range of taus, 
> even when  using 
> different Oscillators. The theories range from pure luck to 
> some special 
> secret magic hardware.
> 
> If I was that lucky, I'd be doing Lottery and not ADEV.
> And If I could build some secret simple Hardware, and was 
> able to adjust it 
> to give some desired effect on future random noise, I'd be in 
> politics or 
> the stock market, not making ADEV Breadboards.
> There is another more likely explanation that is within my limited 
> capabilities, that many refuse to consider.
> That is this method just works correctly without doing 
> anything very special 
> at all.
> 
> The reason that the simple TPLL works so good but is hard for 
> some "experts" 
> to accept, seems to come down to the fact that this method 
> uses Frequency 
> and not Phase to make the raw data log used to then calculate 
> ADEV data.
> 
> Most if not all other methods depend on Phase differences (i.e time 
> differences) to calculate the Frequency difference.
> The simple analog TPLL method holds the Phase difference to 
> zero (with-in 1 
> femtosecond) and calculates the average Frequency differences 
> by  measuring 
> the voltage on the EFC of the reference Oscillator. That way 
> no variable 
> phase is involved.
> This filtered Frequency data log can then be used to 
> calculate ADEV without 
> first needing to convert from or to phase.
> The fact that average Frequency differences do not start out as wide 
> bandwidth Phase, means that all the fancy write-ups that tell 
> how best to do 
> that, do not apply.
> 
> Some have argued that Phase and freq are the same thing, so 
> the fact that 
> this uses freq would make no difference.
> Others have argued that one can not average Freq, so you have 
> to convert to 
> phase first.
> Both have a basis of truth for some methods, but neither is 
> correct here, as 
> proven by the end results.
>  (unless one wants to also assume that I'm either the 
> luckiest or smartest 
> person in the universal for getting it right the first time.)
> 
> While it is true that the TPLL Freq data can be turned into accurate 
> controlled Bandwidth Phase data, Wide band phase data can not 
> be so easily 
> turned into controlled limited Bandwidth, zero dead time, 
> integrated Freq 
> data, which is the thing that is needed to get good ADEV 
> results. The reason is, to get high resolution, such as 1 
> femtosecond (1e-15) phase 
> data, it takes a  wide bandwidth, which means high noise and 
> many other 
> problems. To get 1e-15 freq data from the EFC (limited by the 
> ref osc), this 
> can be done with the B/W equal to tau0.
> 
> The short Over simplified summery is:
> At 1sec Tau0, the up to 1e15 to one difference in bandwidth 
> between Phase 
> and Frequency measurements makes a big difference that some 
> seem to be 
> missing. (think Phase trigger jitter)
> The simple TPLL has No secrets, just some basic differences 
> that seem to of 
> been forgotten or not considered.  The way that frequency is 
> measured is 
> what is different between the TPLL frequency method and the 
> other more 
> popular phase methods.
> 
> The fact is, that the simple TPLL in spite of it limitations, 
> has been shown 
> to work just fine in the real world.
>  If one can not understand or accept that measuring frequency without 
> needing to first measure phase is the real secret reason why 
> the TPLL works 
> so good, without needing any special H/W or S/W 
> 'adjustments', then feel 
> free to propose a better reason besides Luck.
> 
> ws
>