Here we explain how time error can be calculated from published aging rates. Given the CSACs small size and power consumption, the calculated holdover performance is impressive.
Time error can be calculated from published aging rates, as shown in References. Taking the result of their derivation, the timing error accumulation over time is given as follows:
E(t): Time error accumulation at time t after initial synchronization
a: Clock frequency drift (or aging) rate
E0: Initial time error at t = 0
Ei(t): Fractional frequency offset due to environmental effects (such as temperature)
y0: Initial fractional frequency at t = 0
ε(t): Error due to random fractional frequency fluctuations
For simplification purposes, we have assumed zero initial phase or frequency offset and zero
environmental perturbation, which reduces the equation to the following:
The following graph and table show predicted time error over 72 hours of the CSAC, high-performance OCXOs, and Rubidium atomic oscillators. CSAC will accumulate ~1 μs in 24 hours, ~5 μs in 48 hours, and 8 μs to 12 μs in 72 hours. These calculations were made based on typical observed aging rates of 0.6 ppb /mo to 0.9 ppb/mo.
Note: Throughout this series of articles, RF output (10 MHz) performance of the CSAC will be shown. The CSAC 1PPS output is directly derived from the RF output, so it should be expected that the 1PPS would behave in a similar manner.
In the next article in this series, I’ll write about the effects on timing error: temperature.
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