Definition of Time Error

The definition of time error is given in G.810 as:

4.5.13 time error function: The time error of a clock, with respect to a frequency standard, is the difference between the time of that clock and the frequency standard one. Mathematically, the Time Error function x(t) between a clock generating time T(t) and a reference clock generating time T_ref(t) is defined as:

x(t) = T(t) - T_ref(t)

From a test equipment perspective, the reference time is from the test equipment; the measured time is from the device under test (DUT).

Lead / Lag and Positive / Negative Time Error

Unlike delay variation, time error results may be positive or negative. The sign of the the time error may indicate whether the DUT’s clock is ahead (leading) the reference clock or behind (lagging) the reference clock.

Consider a 1pps measurement as shown below:

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This is perhaps more clearly shown below.

DUT Lags Reference by 40ms

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DUT Leads Reference by 40ms

So, if the DUT time lags (is behind) the reference, then the time error is negative; if the DUT leads (is ahead of) the reference, then the time error is positive.

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