[time-nuts] GPS orthodontics: sawteeth & hanging bridges - theeffect of time averaging

Ulrich Bangert df6jb at ulrich-bangert.de
Fri Dec 22 06:22:03 EST 2006


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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