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

[Dr Bruce Griffiths]

Brooks Shera wrote:
> 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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>   
Brooks

Stop fooling yourself try reading:

/Time Interval Averaging: Theory, Problems, and Solutions/, David Chu, 
HP Journal June 1974 pp12-15.


Bruce