[time-nuts] TIC resolution impact on GPSDO's performance

[Ulrich Bangert]

Hi folks,

I am starting a new thread because this topic ist still discussed very
controversial. I hope this posting helps to get more insight. What
follows is by no means to be understood as an act of personal
aggression. Nevertheless I will phrase my point of view as clear as
possible. I suggest that you have a look at the attached pdf now.

First obey the dotted blue line. This is the Allan plot for a HP10811
OCXO as a typical example for what a lot of us have at hand. The
undotted blue line indicates the lowest ADEV that is reached anywhere
between 10 and 1000 s. 

While it is not necessary for the understanding of the further
discussion you might want to know WHY the Allan plot has this banana
like looking: Within an oscillator an number of DIFFERENT noise
processes are active and play a part in the overall noise that the
oscillator emits. Some of these processes have the property that they
tend to cancel themselves a bit when averaged over a certain time,
others do not. The minimum of the ADEV must be considered as being
located at the averaging time where further averaging leeds to no more
improvement in noise and where the other noise processes (mainly
environmental sesibilities) that do not tend to cancel start to overrule
the scene. 

While the Allan plots of different OCXOs are not identical they look all
very similar. My FTS1200 may start at 1E-12 @ 1 s and be in the range of
some parts in 1E-13 up to 1000 s. Also its ascending slope is not as
steep as the HP's one. Nevertheless it looks pretty similar. In contrast
to that the Allan plot of a simple xtal oscillator is also a banana but
may be located 4 orders of magnitude above the HP's one.

Now look to the yellow line. This is the Allan plot for a Motorola M12+
receiver if we squeeze ALL available time information out of it, i.e.
when we apply the sawtooth correction value to the 1pps. The plot starts
at 2E-9 @ 1 s and has a slope which is little bit smaller in magnitude
than -1. 

Note one thing: The sawtooth correction value of the M12+ is an integer
multiple of 1 nanosecond. To make full use of this 1 ns correction
resolution it should be clear that we need to measure the receivers's 1
pps with at least the same resolution. Bruce has already pointed out a
number of times that if we want to neglect the influence of sheer
resolution at all at this point even a few ps timing resolution need not
be considered an overshot. 

Clearly we see the crossing point with the OCXO's Allan plot located
between 1000 and 2000 s. Although I have already stressed it a lot in
the last days let us consider again what needs to be done it we are
going to marry this receiver with this OCXO in a GPSDO. What would
happen when we set the regulation loop's time constant to say 100 s?
Setting the loop time constant to a certain value means as much as:
Starting from that time the receiver more and more overrules the OCXO. 

But then: At 100 s the ADEV of the receiver is more than an order of
magnitude worse than that of the OCXO ALONE! If we allow the receiver to
overrule the OCXO at a loop time constant of 100 s the Allan plot for
the OUTPUT of the frequency standard at 100 s will be dominated by the
receiver which will give us an inferior result than if it were dominated
by the OCXO! 100 s is not a good loop time constant! 

Whats the story with a loop time constant of say 10000 s? The
argumentation is pretty much the same as for 100 s but with a role
reversal between receiver and OCXO. For the 10000 s the OCXO's ADEV is
an order of magnitude worse that that of the receiver. If we allow the
receiver to enter the scene that late the Allan plot for the OUTPUT of
the standard will be dominated by the OCXO at 10000 s which will give us
an inferior result than if it were dominated by the receiver. 10000 s is
not a good loop time constant!

For the most of you it will already now be kind of evident that the
crossing point defines the magical value that we have to set the loop
time constant to but this fact can be formulated with a bit more of
scientifical preciseness: At no observation time tau will it be possible
to have an ADEV at the OUTPUT of the standard that is lower then BOTH
Allan plots at this tau. Where should its origin come from? The very
best we can do for any tau is to find the lower of the two Allan plots
for this tau and to choose the according source as the instance that
shall dominate the standard's output at this tau. From there it is only
a small step to notice that below the crossing point the OCXO's Allan
plot is lower and above it the receiver's Allan plot is lower and that
we really have identified the crossing point as the correct loop time
constant. TVB has pointed out that marginal errors in setting the loop
time constant will not prevent the circuit to work as a frequency
standard. However this may go hand in hand with a loss in precision may
it be marginal or not so why not use the correct value?

What if we had not used the sawtooth corrected values but the raw 1pps
phase data? This situation is diagrammed by the black dotted line. Again
we have to set the loop time constant according to the crossing point
which is considerably later than with the corrected values. 

This alone should not bother us but let us consider its impact: Since
below the crossing point the standard OUTPUT's Allan plot is dominated
by the OCXO we are going to create a local maximum in the standard
OUTPUT's Allan plot which we should not be especially proud of. But the
more important point is: At least up to a day or more the Allan plot of
the SAW corrected data is significant BELOW that of the uncorrected data
and this can be expressed in two ways:

1) For a given observation time tau the standard's output will exhibit
more stability whith the corrected data

or

2) In order to get to an certain stability of the standard's output you
will need longer measurement times with the uncorrected data compared to
the corrected phase data.

This discussion does NOT take into account the awkward effects of
bridge-building that make everything even worse.

What does that all mean in reality? Suppose the distance of a satellite
in an orbit around planet Mars is going to be measured up to a
resolution and precision of a few meters (!) by means of a 'time of
flight' measurement on an electromagnetic wave that is transmitted to
the satellite and answered by an transponder. What may sound like
'rocket science' for some of you this is what radio amateurs (!) of the
AMSAT hopefully will do within a timeplan of a few years! Of course the
delay introduced by the transponder alone is determined before the start
of the satellite!

With the speed of light being app. 0.3 m/ns this will involve to measure
a time interval of some thousand s (runtime forth and back for a medium
distance Earth to Mars) with some ns precision and resolution what asks
for a abt. 1E-12 relative resolution and precision. If we do not want
that our measurements are disturbed by the statistical fluctuations of
the timebase used, these fluctuations shall be less than 1E-12 at a few
thousand seconds. With a GPSDO using SAW corrected data this is achieved
at abt. 4000-5000 s. A GPSDO using uncorrected data will have
statistical fluctuations 5 times the planned measurement resolution and
precision at this tau and will not make a suitable timebase for that
purpose. 

And yes, I know that the TIE RMS and the MTIE are the better suited
statistical measures for this kind of problem but I did not want to
complicate the discussion by introducing new terms. (For those
interested: Not only does my Plotter utility compute TIE RMS and MTIE
from phase data, in the case of MTIE it does it orders of magnitude
faster than Stable32 due to a modern binary matrix de-composition
algorithm). In case you did not know: Plotter can be downloaded for free
from

http://www.ulrich-bangert.de/plotter.zip

Even for the uncorrected data we had assumed that we had measured them
with a TIC resolution small enough to neglect the effects of
quantization. What happens if the TIC in use has a quantization interval
that is in the order of the effect being measured or even bigger? If we
were measuring an infinite stable and jitter-free signal with a TIC
having a quantization interval of 41.6 ns (as in the case in the Shera
design) we will introduce statistical fluctuation sheer due to the
quantization and nothing else that are diagrammed by the red dotted
line. 

The vertical distance to the yellow line (stability using SAW corrected
phase data) is almost an order of magnitude! And please don't mistake
the red dotted line with the overall result of measuring the raw phase
data with 41.6 ns quantization interval! It shows the effect of
quantization ALONE! Computing the real noise to be expected when
measureing the receiver's pps would involve to compute the RMS sum of
BOTH the receiver's noise and the quantization noise resulting in a line
that is located even adverse compared to the red line!

Brooks Shera's argument that he may average over raw phase data measured
with his 41.6 ns quantization to remove noise is correct! Indeed, the
red line may serve him as an (a bit too optimistic) estimation on how
long to average for a given noise level. His misconception has its roots
in the false conclusion that when averaging does remove noise it is
pretty much EQUIVALENT to using sawtooth corrected data. THAT is NOT
true! 

Compare the red and the yellow line: Whenever the red line has reached a
certain noise level, the yellow line has reached the same noise level in
1/10 the time. Or argument the other way around: Surely a Shera standard
can reach a stability level of 1E-12 (We leave questions of DAC
resolution and/or tempcos of parts and solder joints(!) out of the
discussion. They can only make things worse) But consider at what
observation times tau this is possible: 40000-50000 s. Not to be used
for the Mars ranging where we need this stability at 4000 s! Where the
Shera design needs to get by heavy averaging a design using SAW
corrected values gets in 1/10 the time due to using less noisier input
data! Got the clue?

This is ONLY due to the 41.6 ns quantization interval and that is the
reason why Bruce and I insist on the proposition that the noise
introduced by the 41.6 ns quantization interval is the dominant one in
the Shera design and that this noise is a factor 10-20 worse than that
of the best receivers available today.

I leave it to your own judgement whether claims like

> In most cases you can... Forget the quantization error.

or

> In summary, it appears that 1pps sawtooth/bridge noise can be ignored
for a 
> GPSDO.

are consistent with the laws of physics and mathematics.

Hey Brooks, you are an fantastic engineer but claims like this are not
worth to leave your mouth!
     

Best regards and a Merry Christmas for everyone in the group
Ulrich Bangert, DF6JB
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