3.3. Clock Quality

When discussing clocks, the following quality factors are quite helpful:

3.3.1. Frequency Error

As explained before, it's not sufficient to correct the clock once. To illustrate the problem, have a look at Figure 1. The offset of a precision reference pulse has been measured with the free-running system clock. The figure shows that the system clock gains about 50 milliseconds per hour (red line). Even if the frequency error is taken into account, the error spans a few milliseconds within a few hours (blue line).

Figure 1. Offset for a free-running Clock

Even if the offset seems to drift away in a linear way, a closer examination reveals that the drift is not linear.

Example 3. Quartz Oscillators in IBM compatible PCs

In my experiments with PCs running Linux I found out that the frequency of the oscillator's correction value increases by about 11 PPM after powering up the system. This is quite likely due to the increase of temperature. A typical quartz is expected to drift about 1 PPM per C.

Even for a system that has been running for several days in a non-air-conditioned office, the correction value changed by more than 1 PPM within a week (See Figure 2 for a snapshot from that machine). It is possible that a change in supply voltage also changes the drift value of the quartz.

As a consequence, without continuous adjustments the clock must be expected to drift away at roughly one second per day in the worst case. Even worse, the values quoted above may increase significantly for other circuits, or even more for extreme environmental conditions.

Figure 2. Frequency Correction within a Week

Some spikes may be due to the fact that the DCF77 signal failed several times during the observation, causing the receiver to resynchronize with an unknown phase.

3.3.1.1. How bad is a Frequency Error of 500 PPM?
3.3.1.2. What is the Frequency Error of a good Clock?

3.3.1.1. How bad is a Frequency Error of 500 PPM?

As most people have some trouble with that abstract PPM (parts per million, 0.0001%), I'll simply state that 12 PPM correspond to one second per day roughly. So 500 PPM mean the clock is off by about 43 seconds per day. Only poor old mechanical wristwatches are worse.

3.3.1.2. What is the Frequency Error of a good Clock?

I'm not sure, but but I think a chronometer is allowed to drift mostly by six seconds a day when the temperature doesn't change by more than 15 Celsius from room temperature. That corresponds to a frequency error of 69 PPM.

I read about a temperature compensated quartz that should guarantee a clock error of less than 15 seconds per year, but I think they were actually talking about the frequency variation instead of absolute frequency error. In any case that would be 0.47 PPM. As I actually own a wrist watch that should include that quartz, I can state that the absolute frequency error is about 2.78 PPM, or 6 seconds in 25 days.

For the Meinberg GPS 167 the frequency error of the free running oven-controlled quartz is specified as 0.5 PPM after one year, or 43 milliseconds per day (roughly 16 seconds per year).[1]

Notes

[1]

See the examples about Mills-speak in Q: 9.1..