Steve Rooke wrote:
On 4 June 2010 08:32, Charles P. Steinmetz
<charles_steinm...@lavabit.com> wrote:
If I may be allowed to summarize, it appears that Warren and Bruce agree
that integration is necessary to produce true ADEV results. Warren asserts
that the low-pass filtering his method uses is "close enough" to integration
to provide a useful approximation to ADEV, while Bruce disagrees. So, the
remaining points of contention seem to be:
1. How close can a LPF implementation come to integration in ADEV
calculations, and
Well, Warren uses two stages of integration. There has already been
talk of the simple R/C filter in the feedback loop. Unless my
education in electronics was completely wrong, the series R/C circuit
forms a simple LPF and is an integrator (assuming that the resistor is
in series with the input and the capacitor is in parallel with the
output). See http://en.wikipedia.org/wiki/Integrator_circuit,
http://en.wikipedia.org/wiki/RC_filter. Sorry these are not academic
papers but if you spot something wrong please feel free to edit them
appropriately. This first stage of integration is set at a much wider
frequency than tau0 and forms the PLL-loop filter allowing it to track
the FAST changes of a noisy unknown oscillator. That last bit is very
important and something some previous attempts at this method failed
to resolve.
A cascaded low pass filter and and a finite time interval integrator are
required.
A single RC LP filter can't approximate this.
Its either a low pass filter or a crude approximation to an integrator
not both.
Now there is a noisy control voltage on the reference oscillator and
it is absolutely no good trying to make a single measurement at tau0
because the settling time of the filter has not been constrained to it
so it will not give an integrated mean value. This where the second
stage of integration comes in which is the oversampling which takes a
number of readings during tau0 (please correct me if I have the
terminology wrong here) which are then averaged to give a mean,
integrated, value of the control voltage for tau0.
Speculative nonsense sampling by itself integrates nothing unless one
uses an integrator to do the sampling.
Even when the finite bandwidth of the sampler is taken into account the
equivalent "averaging time" will be too short and not under user control.
However the samples (if the sampling rate is sufficiently large) contain
sufficient information for the required finite time integrator output
values (or frequency averages) to be calculated.
A simple rectangular integration approximation may not be sufficient in
all cases.
The sampling process actually tends to whiten the sampled phase noise
spectrum.
The amount of false white phase noise contributed by the sampling
decreases as the sampling rate increases.
A simple RC low pass filter may not be a a particularly good choice in
this regard.
So why two stages, look closely above, until the idea of oversampling
was tried, the PLL-loop filter had to have a settling time, IE. cutoff
frequency, equal to tau0 so that the measurement at tau0 reflected the
mean, average, integrated, value for that tau0 period. But if a filter
with that sort of cutoff is used then the reference oscillator is not
able to track noise on the unknown oscillator at all and it would give
results for things like flicker noise, random walk, etc, which were
lower than the actual values. Now have a look at the top end of John's
graphs where there is a divergence.
The divergence at the top end of the graphs should be treated with
extreme caution one needs to know the size of the associated error bars
to be able to make statistically meaningful conclusions. In general the
error bars tend to be large in this region.
2. How close to true ADEV is "good enough"?
well, considering we have integrated frequency measurements at tau0
intervals, there is little wonder that it correlates closely to ADEV
because that's exactly what it is.
This cannot be so for each and every signal source if the weighting
function ("equivalent filter") doesn't closely match that used in the
definition of AVAR.
Without the integration/averaging the "equivalent filter" closely match
the required filter at all frequencies.
I humbly submit that trading insults has become too dreary for words, and
that neither Warren nor Bruce will ever convince the other on the latter
point.
Well, I've been on this list long enough to know that Bruce will
always resort to that sort of behaviour when he is boxed into a corner
or cannot get his point of view accepted. Anyone who speaks up against
him is usually put in their place. This saga has come about because
someone dared to challenge him so we have been subjected to his
tantrums.
The saga originated because of the wildly inaccurate claims and very
woolly explanation as to what signal processing was used.
A few equations and a circuit diagram or 2 would have made it perfectly
clear months ago what methods were used.
Vague statements on the lines of: "any person competent in the field
should be able to figure it out for themselves" are not useful if the
originator has made some fundamentally incorrect assumptions.
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.
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.
Best regards,
Steve
Best regards,
Charles
Bruce
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