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

[Brooks Shera]

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.