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.
Cheers,
Magnus
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