Temperature related frequency drift in crystal oscillators.


Abstract
Crystal oscillators, such as those used in digital watches, experience a shift in frequency as a function of temperature. This shift is pronounced enough to be measured by simple apparatus under every-day conditions.


Procedure
The crystal oscillators for this experiment were in the form of two inexpensive digital wristwatches. These watches were packaged with a card game, and found in the discount bin at Walmart. The other apparatus were a food storage freezer, and an indoor/outdoor digital thermometer.

To begin the experiment, the watches were labeled "A" and "B". The times were synchronized, and the watches left in the same room temperature environment to check their consistency. It was discovered that watch B gained 0.667 seconds per day with reference to watch A. This value was recorded, the watches resynchronized, and the experiment begun.

Watch B was placed in the freezer, at a temperature of -12.8C (9F). Watch A was placed in a 21C (70F) environment. This was defined as experiment time T=0. The watches were compared at T=107.5 hours (~4 days) and T=201.5 hours (~8 days).

Results
At T=107.5 hours, the B watch was 7 seconds behind (slower than) the A watch. At T=201.5 hours, B had lost 14 seconds.

This worked out to be 1.563 seconds per day and 1.667 seconds per day loss. However, Since the B watch normally gained 0.667 seconds per day on the A watch when at the same temperature, this figure was added to the raw loss rate. Thus, the adjusted figures are 2.230 seconds per day and 2.334 seconds per day lag due to the colder temperature.

Averaged, and divided by the temperature depression, we come to a final figure of 2.282 seconds per day / 33.8C = 0.0675 seconds per day per degree C.