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From: =?UTF-8?Q?Wolfgang_B=c3=bcscher?= <dl4yhf@freenet.de>
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Date: Sun, 30 Oct 2016 18:22:14 +0100
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Subject: GPS pulse timing (was: Re: LF: Idiot's guide to receiving Ebnaut?)
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Hello Paul,

Thanks for the details. I guess the pulse jitter cannot go down much 
further, unless the GPS receiver can "pull" its own oscillator in 
frequency, which is definitely not the case with the Garmin (but maybe 
with the trimble).
The Garmin receiver can only shift the output pulses in multiples of its 
internal CPU clock, which iirc was 40 MHz, and thus 25 ns "stepwidtdh" 
(can easily be seen with an oscilloscope triggered by a good GPSDO).


you wrote:
> Wolf wrote:
> > measured the standard deviation in the GPS sync pulse
> > timing. Used an E-MU 0202 at 192 kSamples/second.
>
> Ran a quick trial here.
>
> With the Trimble 10uS directly into an E-MU 0202 at 192k/sec I
> get 100nS std dev of the raw intervals.  The timing system here
> uses smoothed intervals which reduces the jitter to below 30nS.
>
> Same setup at 48k/sec is useless, the raw std dev is around
> 6uS.  Watching the pulse on vtscope, the waveform changes
> significantly from one pulse to the next.  This is so at both
> sample rates but seems worse at 48k.   Looks like waveshape
> depends on just when the pulse arrives with respect to the
> soundcard's internal A/D sampling.
>
Yes, but that's not a bad waveform - it *must* be like that if the card 
uses a good delta-sigma converter.
And that's what my interpolation algorithm actually relies on. By 
interpolating those ugly waveforms, and running them through a windowed 
sinc filter (with cutoff frequency at half the original sampling rate) 
we get a *constant* waveform again, which only shifts along the 
timescale depending on the relative pulse time (within one ADC sample). 
But the peak of the reconstructed pulse at f_sample_interpolated = 4 * 
192 kHz is always identical, even if the waveforms *before* the 
interpolation look very different.
The principle would completely fail with a simple (non delta-sigma) ADC 
as built inside many microcontroller.
Consider it this way: The "frontend" of the ADC is a one-bit A/D 
converter running at a sample rate of dozens of Megahertz, and the 
output at the end of the decimator chain is perfectly predictable, even 
if the waveform looks strange and seems to vary.
The interpolator / windowed sinc lowpass in the software delivers a 
signal at a higher sampling rate than delivered by the soundcard, but 
the information about the precise GPS pulse time "is still in there". It 
only depends on the number of sigma-delta stages and the ADC's 
"oversampling" factor. Example: 24 stages (for up to 24 bit resolution) 
plus 8-fold oversampling : 24 * 8 * 192 kHz = 36.864 MHz for the 
"one-bit" input stage, which is a crystal frequency seen in many 
soundcards. This should be good enough for a time resolution of 27 
nanoseconds (if there was no noise and other imperfections) -> std dev 
around 14 ns. Add the jitter from the GPS itself, say another 25 ns for 
the GPS18LVC, and -i guess- even less for 'better' receivers.
With the Trimble GPS, you already arrive there, which is remarkable !

All the best,
   Wolf .