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In the graph above is an example that
illustrates how the time error of a clock grows with days since
synchronization and syntonization (i.e., calibration). The clock is assumed to be in a system that
requires a 25 millisecond accuracy, the clock is assumed to have an average
frequency offset due to temperature of 2 x 10-8, an aging rate of
5 x 10-10 per day, and negligible other error sources. Upon calibration, the clock is assumed to
have zero frequency and time error.
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The clock is assumed to be resynchronized
every four days. During the initial
period, the time error is caused almost entirely by the frequency error due
to temperature, i.e., 2 x 10-8
in the example. Aging, however, adds 5
x 10-10 to the frequency error every day, so, after 40 days, the
frequency error due to aging equals that due to temperature. After 40 days, aging is the dominant cause
of the frequency error. The time error
increases more and more in each four day resynchronization interval. Eventually, after about 100 days, the time
error at the end of the the four days reaches the 25 ms limit. At that point, either the resynchronization
interval must be made shorter, or the clock must be recalibrated, i.e., its
oscillator’s frequency must be readjusted to the correct value.
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