Clock Accuracy

Timing depends on two components: a trigger that determines when we read the time; and a clock that tell us what the time is when we read it. Overall accuracy depends on how precise the trigger is (before or after the real event); how much resolution the clock shows; and how accurate the clock is compared to the true time.

If we use hand timing, then we need to make sure that the clock we use is more accurate than the precision of the button press:

  • If the button press is precise to about 0.1 seconds then we need to make sure the stopwatch (or the timer, or the computer, or iPhone) has better accuracy than that.

If we use an image or a photocell to trigger a time then we need to make sure that the clock we use is as accurate as we can afford:

  • if a photo finish image is precise to 0.001 of a second or better, then we cannot use that level of precision for timing unless the the clock is as accurate as that, which is highly demanding.

Standard clock accuracy does not meet these requirements. We should not assume that the clocks in various types of equipment are sufficiently accurate.

Time Reference

One Second is defined by the International System of Units (known as SI) as a multiple of the radiation frequency of an atom of caesium. The mathematical relationship with caesium is such that the Second is also a fraction of the solar day: SI Second.

Caesium clocks have an accuracy measured in billionths of a second, or nanoseconds, per year against the theoretical perfect time. The accuracy of a clock is measured against a time source with a known variation from a caesium clock. For example, time in the US is provided by a Caesium Fountain Atomic Clock operated by the National Institute of Standards and Technology (NIST) at Boulder, Colorado: US Time. Various laboratories provide equipment with a traceable relationship with the NIST clock, or the equivalent in other countries, that can be used to measure and certify timing equipment.

The fundamentals of time and frequency are covered in this document by NIST.

Digital clocks

Time and frequency are two sides of the same coin. Anything that counts a frequency is a clock. Scientific clocks use rubidium, hydrogen or caesium to generate a frequency (e.g. Symmetricom frequency references). The most common source of a frequency for consumer clocks is a crystal oscillator.

A typical digital clock contains a crystal oscillator, a microchip to count the oscillations and the associated circuitry.

Oscillators

A crystal oscillator uses a crystal of a material which has the property of vibrating when a current is applied to it. Quartz is commonly used for the crystal because it has a very narrow frequency of vibration compared to other substances, but other substances can be used.

The quartz crystal is physically cut to a size and pattern intended to make it oscillate at a given frequency, and mounted inside a container.

The accuracy of the crystal oscillator under test conditions depends on the quality of the crystal and the electronics around it. The accuracy is also affected by environmental conditions, in particular changes in temperature. Crystal oscillators have: a nominal frequency; a given range of accuracy around the nominal at a given temperature; and then a significant loss of accuracy as the temperature changes. The way the crystal responds to changes in temperature depends on the cut of the crystal.

Accuracy is measured by comparing the stated frequency with the actual frequency when measured against a caesium clock or some other frequency standard with a traceable relationship with a caesium clock. Any given oscillator with either have a certified accuracy, if it has been measured, or an estimated accuracy based on testing a sample.

Because of the significant effect of temperature, there are three main types of crystal oscillator:

  1. A standard crystal oscillator (XO)
  2. A temperature-compensated crystal oscillator (TCXO)
  3. An oven-controlled crystal oscillator (OCXO)

Obviously the more accurate oscillators are more expensive. It is difficult to put a figure on it because the oscillators themselves are sold in volume as components for other devices.

XO

A standard crystal oscillator (XO) has an accuracy range at a given voltage and temperature, based on manufacturing tolerances. The typical level of accuracy at room temperature for a high quality quartz XO (e.g. Seiko Instruments) will be:

  • ±20 ppm (or 20 x 10-6)
  • ±1.73 seconds per day
  • ±0.005%

Other, non-quartz, XO's typically have a wider frequency tolerance of ±30, 50 or 100 ppm.

The temperature effect depends on the cut of the crystal. The temperature curve is quite different for different cuts. For the most common cut, AT, it is a sine shaped curve. For a DT cut it is a downward parabola. We cannot assume what the temperature curve is for a particular XO.

For the Seiko VT-Series of quartz XO's it is specified as a downward parabola, so they always lose time whether the temperature increases or reduces, around the turning point of 25 degrees C. The colder (or hotter) it gets, the more they lose time.

The reason this is significant is that ~2 seconds per day is ~0.1 seconds per hour. This is in the same region of accuracy as the precision of hand timing, and obviously far worse than the precision of photo finish. So if the accuracy of the clock is not better than this, then it may be the limiting factor in our timing system.

Crystals can be cut with greater precision; or they can be tested and sorted according to accuracy; or they can be modified to adjust the accuracy. But, since the accuracy varies mainly according to temperature, it is more cost effective to either account for the temperature difference or control the temperature.

TCXO

A temperature-compensated crystal oscillator (TCXO) uses a temperature sensor and a lookup table to adjust the oscillation count according to the temperature. This increases the accuracy significantly. A typical TCXO might have an accuracy over a range of 0-40 degrees C of:

  • ±3 ppm (3 x 10-6)
  • ±0.26 seconds per day
  • ±0.0003%

A TCXO gives us an accuracy to within about one hundredth per hour, and stable across temperature variation. This is certainly accurate enough for hand timing. It will be a limiting factor in photo finish or photocell timing.

OCXO

As an alternative to compensating for the change in temperature you can control the temperature.

An oven-controlled crystal oscillator (OCXO) encloses the oscillator in a small temperature-controlled enclosure. The oscillator can be adjusted to operate at a set frequency at the temperature of the oven. This makes the OXCO highly accurate over a long period. A typical OCXO might have an accuracy of:

  • ±0.1 ppm (1 x 10-7)
  • ±0.09 seconds per day
  • ±0.00001%

An OCXO gives us an accuracy to within about one millisecond or better, per hour. This is comparable to the precision of photo finish or photocell timing. It can only be bettered (as an independent clock source) by expensive laboratory-style frequency generators.

Time interval

Accuracy is expressed as a variation from nominal over time. If we want to measure all competitors in a Head race to, say, the nearest tenth of a second, then it makes a difference over what period we time them, and over what range of fluctuation in temperature. It is quite difficult to assess the impact. It is made more complicated by using separate clocks at Start and Finish.

If one clock is used (for example by radioing a start through to a clock at the finish) then the elapsed times of individual competitors will not be affected as the clock gains or loses time through the day, since the time interval will only be the time taken by an individual competitor (say, 20 minutes or less).

If two clocks are used then there will be a difference in sample accuracy between the clocks. If the type of clock has an accuracy of ±20 ppm, then two clocks will together have a variation of up to 40 ppm. This variation will extend over the duration of the event. The longer the event, the more the time between the two clocks will diverge and the greater the error.

If both clocks lose the same amount of time with temperature changes, then it will not make a difference. But if one loses more time than the other because of a difference in temperature, then later competitors will have different times than earlier competitors. This might not matter if the Elites go first and the Novices later, because no-one will be comparing times to that level of accuracy. But if, for example, the Elites go later in the day their times will be fractionally different from true time. For all competitors, as the day warms up in the morning the times might get faster. As it gets colder in the afternoon the times may get slower. These are by very small amounts, but significant if we give times to the nearest tenth of a second.

If we change clocks at any point, for example by using a backup watch or a video to obtain a missing time, then we can introduce errors that are much larger than one tenth.

Impact

It would be simple if all the clocks we might use were sufficiently accurate, but that is not the case. A clock with a high quality quartz crystal oscillator may be sufficiently accurate if two samples are calibrated and the temperature remains roughly the same. A clock with a standard crystal oscillator of unknown performance will not. Therefore we should assume that the clock in a standard watch or stopwatch, a computer, an iPhone, or a video camera will not be sufficiently accurate even for hand timing. The solution is always to use a clock that is more accurate than the timing accuracy we want to achieve, over the duration of the whole event.

If we want to time competitors to one tenth of a second or better over the course of the whole event, we need to use a clock that has a TCXO or better frequency standard. Ideally the clock should either have a manufacturer's specification within the accuracy we require, or be specifically tested by a certification laboratory.

References

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