[time-nuts] GPS orthodontics: sawteeth & hanging bridges - theeffect of time averaging
Brooke Clarke
brooke at pacific.net
Fri Dec 22 15:02:21 EST 2006
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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