# [time-nuts] Low-long-term-drift clock for board levelintegration?

Tom Van Baak tvb at LeapSecond.com
Mon Feb 20 09:37:10 UTC 2012

> I think a box that can't get some external source of time in three years is one that we can pretty well write off as lost.
> Thank you (several of you, actually) for the clear explanation of the math.
>
> http://www.msc-ge.com/en/news/pressroom/manu/1241-www/3567-www.html
>
> So if I'm reading those specs right, they both offer 2E-10, or 100 microseconds per 500,000,000,000, or 121 microseconds per
> week.  So, if those are affordable (and I haven't yet called to check), that's telling me that in order to be useful in the long
> term, these boxes need to be getting some reference time from somewhere at least once a week.

Hi Bill,

Not quite. The 2E-10 isn't a time or frequency *accuracy* spec; it's a *frequency drift* spec.
What this means is that the frequency may change by up to 2e-10 per day, day after day...

Let's say the oscillator is keeping perfect time now.
Then 24 hours from now it may be fast or slow in frequency by 2e-10.
If the oscillator is fast by 2e-10 it will be gaining time at the rate of 0.2 nanoseconds per second.
That doesn't sound like much but since there are 86400 seconds in a day, that's equivalent to gaining at a rate of 17 microseconds
a day. But that's just the first day.

The second day the oscillator may be fast by yet another 2e-10. By the end of the day it's now 4e-10 fast so it's now gaining at a
rate of 35 microseconds a day, in addition to all the time error from yesterday.

Think of frequency changing like an upward *ramp*. The time error accumulates like the *area* under that growing triangle.
Hence the quadratic growth of time error (1/2 * drift * t^2).
After a week the total time error is over 400 microseconds; you hit your 100 microsecond limit in about 3.5 days.

The SC-10 starts at \$250, presumably for a low-grade version, not the one you want.
The DX-170 looks interesting. Let us know when you get a price quote.
Note also the temperature spec; can you maintain the temperature of your device to +/- 1 C?

/tvb