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

[WarrenS]

Bruce posted

>The RC filter doesn't accurately integrate the frequency difference over 
>time interval Tau0.
For you to even state that means you still have NO idea what I'm doing, It 
is getting sort of sad.

Correct the RC filter is not an integrator, it is used for the combination 
Bandwidth and anti-aliasing filter.
It is the oversampling average that does the integration.
What would explain a lot is, if you do not know what oversampling even is?
You need to get yourself a refresher course on the advantages of 
oversampling to do integration, brick wall filtering, anti-aliasing and
why a single RC works just fine for integration when oversampling is used 
and why you don't need anything but simple averaging of sum n samples /n 
when oversampling is used.
Don't need all the unnecessary fir filter crap, just oversample.
If you have spare bandwidth like I have, then it sure saves a lot of  stuff. 
Ever hear of "KISS'.
You need to ask someone to explain that to you some day, along with "close 
enough"
Hint, the simple Tester BB only takes ONE IC and it is just a single op Amp.
And Although John's Software makes it all much more user friendly and makes 
user mistakes less likely to occur, It is not needed. Works just fine with 
no special S/W code or filter S/W.
AND it still does integration just fine. (Send me that data file if you want 
to see how it works).

ws

**************
Bruce last posted:

John Miles wrote:
>>> The integration secret  (which is no secret to anyone but
>>>
>> Bruce)  is to analog filter, Oversample, then average the
>> Frequency data at a rate much faster than the tau0 data rate.
>>
>>>
>> Which again is misleading as you specify neither the averaging method
>> nor the analog filter.
>>
> I can't speak for the analog side as I never saw a schematic of the PLL, 
> but
> it may be worthwhile to point out that the averaging code in question is 
> in
> SOURCE_DI154_proc() in ti.cpp, which is installed with
> http://www.ke5fx.com/gpib/setup.exe .  This is my code, not Warren's.  It
> does a simple boxcar average on phase-difference data, the same as my TSC
> 5120 acquisition routine does.  Previous tests indicated that simple
> averaging yields a good match to most ADEV graphs on TSC's LCD display, so 
> I
> used it for the PLL DAQ code as well.
>
> I also tried a Kaiser-synthesized FIR kernel for decimating the incoming 
> TSC
> data, but found that its conformance against the TSC's display was worse
> than what I saw with the simple average.  More work needs to be done here.
>
>
>> When will you understand that phase differences and differences of
>> average frequency (unit weight to frequency measures over the sampling
>> interval zero weight outside) are equivalent.
>>
> One subtlety is the question of whether to average (or otherwise filter) 
> the
> DAQ voltage readings immediately after they're acquired and linearly 
> scaled
> to frequency-difference values, versus after conversion of the
> frequency-difference values to phase differences.  I found that the best
> agreement with the TSC plots was obtained by doing the latter:
>
>  val = (read and scale the DAQ voltage)
>
>  // val is now a frequency difference
>  // averaging val here yields somewhat higher
>  // sigma(tau) values in the first few bins
>  // after tau0
>
>  val = last_phase + (val / DI154_RATE_HZ);
>  last_phase = val;
>
>
This appears to use a rectangular approximation to the required integral.
A trapezoidal or even Simpson's rule integration technique should be
more accurate for a given sample rate.
One could even try a higher order polynomial fit to the sample points,
however this isnt the optimum technique to use.

If one uses WKS interpolation to reconstruct the continuous frequency vs
time function and integrates the result for a finite time interval
(Tau0) then one ends up with a digital filter with infinite number of terms.
Since an infinite number of samples is required to do this using a
suitable window function is probably advisable.

The paper (below) illustrates how AVAR etc can be calculated from the
sampled frequency difference data using DFT techniques:

http://hal.archives-ouvertes.fr/docs/00/37/63/05/PDF/alaa_p1_v4a.pdf

>  // val is now a phase difference
>  // averaging val here matches the TSC better
>
> The difference is not huge but it's readily noticeable.
>
> This is subtly disturbing because the RC filter before the DAQ *does*
> integrate the frequency-difference data directly.  If it's correct to
> band-limit the frequency-to-voltage data in the last analog stage of the
> pipeline, it should be correct to do it in the first digital stage, I'd
> think.
>
>
The RC filter doesnt accurately integrate the frequency difference over
time interval Tau0.
> Further complicating matters is the question of whether the TSC 5120A's
> filtering process is really all that 'correct,' itself.  When they
> downsample their own data by a large fraction, e.g. when you select 
> tau0=100
> msec / NEQ BW = 5 Hz, there is often a slight droop near tau0 that does 
> not
> correspond to anything visible at higher rates.  To some extent we may be
> attempting to match someone else's bug.
>
This is the result of the choice of the low pass filter bandwidth made
by the designers.
The filter bandwidth increases as Tau0 decreases.
The traditional analyses of the dependence of AVAR on bandwidth of this
filter assume a brickwall filter.

> At any rate I've run out of time/inclination to pursue it, at least for 
> now.
> The SOURCE_DI154_proc() routine in TI.CPP is open for inspection and
> modification by any interested parties, lines 6753-7045 in the current
> build. :)  Warren has his hardware back now, and would presumably be able 
> to
> try any modifications.
>
> -- john, KE5FX
>