[time-nuts] GPS orthodontics: sawteeth & hanging bridges - theeffect of time averaging
Brooke Clarke
brooke at pacific.net
Fri Dec 22 22:27:42 UTC 2006
Hi Bruce:
OK so the plot at will level off at about 5E-14.
Suppose that I'm now using the SR620 to make averages of 5,000 seconds
and plotting those where the inputs are from an M12+T and a FTS4060
Cesium standard. At 5,000 seconds Ulrich's plot shows about 4E-12.
Does that mean with a perfect standard I would expect to see noise of
about 4E-12?
So I should set the averaging to about 1E6 seconds (11 days)? to get the
best possible result?
Have Fun,
Brooke Clarke
w/Java http://www.PRC68.com
w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
http://www.precisionclock.com
Dr Bruce Griffiths wrote:
>Brooke Clarke wrote:
>
>
>>Hi Ulrich:
>>
>>Your M12+T plot ends at a little over a day (100k seconds) and the
>>stability is on the order of 4E-13.
>>But Cesium and other oscillators can be better than this. So how do you
>>check them, use longer averaging time?
>>
>>Have Fun,
>>
>>Brooke Clarke
>>
>>w/Java http://www.PRC68.com
>>w/o Java http://www.pacificsites.com/~brooke/PRC68COM.shtml
>>http://www.precisionclock.com
>>
>>
>>
>>Ulrich Bangert wrote:
>>
>>
>>
>>
>>>Brooks,
>>>
>>>
>>>
>>>
>>>
>>>
>>>>Excel computed that the unaveraged correction data had a
>>>>standard deviation
>>>>of 8.4 nsec, which is consistent with the actual measured 9.5
>>>>nsec rms
>>>>jitter reported by Rich Hambly (Dec 06, PTTI paper by Clark
>>>>and Hambly, p.
>>>>15).
>>>>
>>>>
>>>>
>>>>
>>>>
>>>Even if this scientifical improvement has not found its way into Excel:
>>>A certain Mr. Allan has shown that the standard deviaton is NOT the
>>>appropiate measure for noise processes in oscillators. Therefore he had
>>>to find a new statitistics on its own. If you don't own a software to
>>>calculate ADEV and other relevant statistical measures with you may
>>>download one for free from my homepage:
>>>
>>>http://www.ulrich-bangert.de/plotter.zip
>>>
>>>
>>>
>>>
>>>
>>>
>>>>But the question remains "what time averaging is needed to reduce the
>>>>sawtooth/bridge jitter from a typical +/-15 nsec to something
>>>>negligible,
>>>>perhaps +/-1 nsec?
>>>>
>>>>
>>>>
>>>>
>>>>
>>>Have a look to
>>>
>>>http://www.ulrich-bangert.de/html/photo_gallery_44.html
>>>
>>>If you can read it it will immediatly give you the answer to your
>>>questions: in order to get to a certain precision draw a horizontal line
>>>at this precisision on the vertical axis and at the two crossing points
>>>read the necessary time for SAW corrected and uncorrected data on the
>>>horizontal axis.
>>>
>>>Nevertheless, pardon to contradict you: One simply has NO choice to
>>>average this long or to average that long. You have to set the
>>>regulation loop time constant up to exactly where the OCXO's
>>>tau-sigma-diagram meets the receiver's tau-sigma. Every loop time
>>>constant different from that is a faulty design and nothing else. The
>>>regulation loop dynamics may be improved a bit by pre-averaging the
>>>phase data before they are fed into the loop but not by computing the
>>>arithmetic mean over a time but by a gliding exponential average as is
>>>explained in detail in the PRS-10's handbook. Due to stability reasons
>>>even this time constant of this pre-filter is more or less fixed to abt.
>>>1/3 the main loop's time constant.
>>>
>>>Regards
>>>Ulrich Bangert,DF6JB
>>>
>>>
>>>
>>>
>>>
>>>
>>>
>>>>-----Ursprüngliche Nachricht-----
>>>>Von: time-nuts-bounces at febo.com
>>>>[mailto:time-nuts-bounces at febo.com] Im Auftrag von Brooks Shera
>>>>Gesendet: Donnerstag, 21. Dezember 2006 18:50
>>>>An: Discussion of precise time and frequency measurement
>>>>Betreff: [time-nuts] GPS orthodontics: sawteeth & hanging
>>>>bridges - theeffect of time averaging
>>>>
>>>>
>>>>Recently there has been some mention of the influence of 1pps
>>>>sawtooth and
>>>>hanging bridges jitter on the performance of a GPSDO.
>>>>
>>>>It would seem to me that the jitter must average to zero in
>>>>the long run,
>>>>for if it did not the 1pps signal would drift away from its
>>>>relation to UTC.
>>>>
>>>>But the question remains "what time averaging is needed to reduce the
>>>>sawtooth/bridge jitter from a typical +/-15 nsec to something
>>>>negligible,
>>>>perhaps +/-1 nsec?"
>>>>
>>>>To explore this I used TAC32 to record the 1 pps sawtooth
>>>>correction message
>>>>
>>>>
>>>>
>>>>from a Motorola M12+ receiver for about 1 hour, during which
>>>
>>>
>>>
>>>>time many
>>>>bridges occurred (1). Excel's statistical toolbox was then
>>>>used to examine
>>>>the data.
>>>>
>>>>Excel computed that the unaveraged correction data had a
>>>>standard deviation
>>>>of 8.4 nsec, which is consistent with the actual measured 9.5
>>>>nsec rms
>>>>jitter reported by Rich Hambly (Dec 06, PTTI paper by Clark
>>>>and Hambly, p.
>>>>15).
>>>>
>>>>Averaging the sawtooth/bridge correction data for several
>>>>averaging times
>>>>produced the following results (2):
>>>>
>>>>Avg Time Standard Deviation Residual Jitter
>>>>none 8.4 nsec +/- 15 nsec
>>>>30 sec 1.53 +/- 4.3
>>>>100 sec 0.79 +/- 2.2
>>>>300 sec 0.33 +/- 0.7
>>>>
>>>>It is evident that jitter is greatly reduced with a bit of
>>>>time-averaging.
>>>>In addition, the hanging bridges quickly disappeared into the
>>>>residual
>>>>jitter of the smoothed data.
>>>>
>>>>It appears to me that a typical GPSDO, which has an
>>>>integration time in the
>>>>range of 100's to many 1000's of sec is not likely to be
>>>>impaired by the
>>>>sawtooth/bridge noise of a GPS rcvr. A GPS-based clock is a
>>>>different story
>>>>since a precise 1pps timing signal without time averaging would be
>>>>desirable.
>>>>
>>>>In summary, it appears that 1pps sawtooth/bridge noise can be
>>>>ignored for a
>>>>GPSDO. In some designs it may even be helpful by introducing further
>>>>deterministic randomness to the phase measurement process.
>>>>
>>>>Regards, Brooks
>>>>
>>>>(1) the M12+ correction-message resolution is 1 nsec and this
>>>>seems adequate
>>>>for a jitter statistics investigation. But as a check, I
>>>>compared the
>>>>correction message data with the actual 1 pps jitter measured
>>>>with a 5370B
>>>>TIC, a PRS10 and a M12+ . This approach has higher
>>>>resolution but does not
>>>>change the conclusions.
>>>>
>>>>(2) I choose 30 sec as the shortest averaging time because
>>>>30 sec is the
>>>>summation time of the phase-measuring circuit of my GPSDO
>>>>design and hence
>>>>the shortest integration time available. Of course, the PLL filter
>>>>configuration switches can extend the integration to many
>>>>hours if desired.
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
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>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
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>>
>>
>Brooke
>
>The GPS system has a frequency noise floor with an Allan deviation of
>about 5E-14 for averaging periods of a day or more.
>If you need more accuracy than this one has to use techniques like
>Common view, All in view and related time transfer techniques to compare
>one's frequency standards with more accurate standards located elsewhere.
>
>Bruce
>
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