[time-nuts] A Time-Nut's Worst Nightmare

[Magnus Danielson]

On 11/05/13 09:10, Lachlan Gunn wrote:
>  From https://github.com/akafugu/vetinari_clock :
>
> 	The firmware has a 'random' sequence of pulses which over 32 seconds
> 	moves the second hand 32 times. This sequence is long enough to give
> 	the appearance of randomness without unnecessarily consuming
> 	processor cycles. I chose 32 seconds as it means the pattern is
> constantly
> 	offset from the 60 second rotation of the minutes. The 'random'
> pattern
> 	is 128 steps (and is therefore checked 4 times a second). This means
> the
> 	clock moves between 0-4 times within each actual second. By moving
> 	more or less in each of the 32 seconds the clock looks random,
> however
> 	the sequence always moves the clock exactly 32 seconds in the 128
> steps.

Not quite what I guessed, but similar enough.

> So there is no long-term drift, it seems, beyond that of the crystal.  I've
> pulled the pseudo-random tick sequence out of the source code and found the
> Allan variance, shown here:
>
> 	http://imgur.com/wF9F8pI

Not completely a surprise for a phase-modulation, as phase-modulation 
have that slope in the ADEV.

As a systematic modulation, MTIE analysis would be of more help, as you 
have a looped sequence and analyze the pattern you would see how the 
maximum time error will be a flat line beyond 32 s, making it easy to 
believe that on long-term there is no increase in time.

You could also attempt the TDEV, which will just give a straight line 
with wrinkles just as the ADEV.

Cheers,
Magnus